mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83

@@ -72,38 +72,38 @@ variable [NormedAddCommGroup E] {f g : α → E} {s t : Set α} {μ ν : Measure
 
 variable [CompleteSpace E] [NormedSpace ℝ E]
 
-#print MeasureTheory.set_integral_congr_ae₀ /-
-theorem set_integral_congr_ae₀ (hs : NullMeasurableSet s μ) (h : ∀ᵐ x ∂μ, x ∈ s → f x = g x) :
+#print MeasureTheory.setIntegral_congr_ae₀ /-
+theorem setIntegral_congr_ae₀ (hs : NullMeasurableSet s μ) (h : ∀ᵐ x ∂μ, x ∈ s → f x = g x) :
     ∫ x in s, f x ∂μ = ∫ x in s, g x ∂μ :=
   integral_congr_ae ((ae_restrict_iff'₀ hs).2 h)
-#align measure_theory.set_integral_congr_ae₀ MeasureTheory.set_integral_congr_ae₀
+#align measure_theory.set_integral_congr_ae₀ MeasureTheory.setIntegral_congr_ae₀
 -/
 
-#print MeasureTheory.set_integral_congr_ae /-
-theorem set_integral_congr_ae (hs : MeasurableSet s) (h : ∀ᵐ x ∂μ, x ∈ s → f x = g x) :
+#print MeasureTheory.setIntegral_congr_ae /-
+theorem setIntegral_congr_ae (hs : MeasurableSet s) (h : ∀ᵐ x ∂μ, x ∈ s → f x = g x) :
     ∫ x in s, f x ∂μ = ∫ x in s, g x ∂μ :=
   integral_congr_ae ((ae_restrict_iff' hs).2 h)
-#align measure_theory.set_integral_congr_ae MeasureTheory.set_integral_congr_ae
+#align measure_theory.set_integral_congr_ae MeasureTheory.setIntegral_congr_ae
 -/
 
-#print MeasureTheory.set_integral_congr₀ /-
-theorem set_integral_congr₀ (hs : NullMeasurableSet s μ) (h : EqOn f g s) :
+#print MeasureTheory.setIntegral_congr₀ /-
+theorem setIntegral_congr₀ (hs : NullMeasurableSet s μ) (h : EqOn f g s) :
     ∫ x in s, f x ∂μ = ∫ x in s, g x ∂μ :=
-  set_integral_congr_ae₀ hs <| eventually_of_forall h
-#align measure_theory.set_integral_congr₀ MeasureTheory.set_integral_congr₀
+  setIntegral_congr_ae₀ hs <| eventually_of_forall h
+#align measure_theory.set_integral_congr₀ MeasureTheory.setIntegral_congr₀
 -/
 
-#print MeasureTheory.set_integral_congr /-
-theorem set_integral_congr (hs : MeasurableSet s) (h : EqOn f g s) :
+#print MeasureTheory.setIntegral_congr /-
+theorem setIntegral_congr (hs : MeasurableSet s) (h : EqOn f g s) :
     ∫ x in s, f x ∂μ = ∫ x in s, g x ∂μ :=
-  set_integral_congr_ae hs <| eventually_of_forall h
-#align measure_theory.set_integral_congr MeasureTheory.set_integral_congr
+  setIntegral_congr_ae hs <| eventually_of_forall h
+#align measure_theory.set_integral_congr MeasureTheory.setIntegral_congr
 -/
 
-#print MeasureTheory.set_integral_congr_set_ae /-
-theorem set_integral_congr_set_ae (hst : s =ᵐ[μ] t) : ∫ x in s, f x ∂μ = ∫ x in t, f x ∂μ := by
+#print MeasureTheory.setIntegral_congr_set_ae /-
+theorem setIntegral_congr_set_ae (hst : s =ᵐ[μ] t) : ∫ x in s, f x ∂μ = ∫ x in t, f x ∂μ := by
   rw [measure.restrict_congr_set hst]
-#align measure_theory.set_integral_congr_set_ae MeasureTheory.set_integral_congr_set_ae
+#align measure_theory.set_integral_congr_set_ae MeasureTheory.setIntegral_congr_set_ae
 -/
 
 #print MeasureTheory.integral_union_ae /-
@@ -222,15 +222,15 @@ theorem integral_indicator (hs : MeasurableSet s) : ∫ x, indicator s f x ∂μ
 #align measure_theory.integral_indicator MeasureTheory.integral_indicator
 -/
 
-#print MeasureTheory.set_integral_indicator /-
-theorem set_integral_indicator (ht : MeasurableSet t) :
+#print MeasureTheory.setIntegral_indicator /-
+theorem setIntegral_indicator (ht : MeasurableSet t) :
     ∫ x in s, t.indicator f x ∂μ = ∫ x in s ∩ t, f x ∂μ := by
   rw [integral_indicator ht, measure.restrict_restrict ht, Set.inter_comm]
-#align measure_theory.set_integral_indicator MeasureTheory.set_integral_indicator
+#align measure_theory.set_integral_indicator MeasureTheory.setIntegral_indicator
 -/
 
-#print MeasureTheory.ofReal_set_integral_one_of_measure_ne_top /-
-theorem ofReal_set_integral_one_of_measure_ne_top {α : Type _} {m : MeasurableSpace α}
+#print MeasureTheory.ofReal_setIntegral_one_of_measure_ne_top /-
+theorem ofReal_setIntegral_one_of_measure_ne_top {α : Type _} {m : MeasurableSpace α}
     {μ : Measure α} {s : Set α} (hs : μ s ≠ ∞) : ENNReal.ofReal (∫ x in s, (1 : ℝ) ∂μ) = μ s :=
   calc
     ENNReal.ofReal (∫ x in s, (1 : ℝ) ∂μ) = ENNReal.ofReal (∫ x in s, ‖(1 : ℝ)‖ ∂μ) := by
@@ -240,14 +240,14 @@ theorem ofReal_set_integral_one_of_measure_ne_top {α : Type _} {m : MeasurableS
       rw [of_real_integral_norm_eq_lintegral_nnnorm (integrable_on_const.2 (Or.inr hs.lt_top))]
       simp only [nnnorm_one, ENNReal.coe_one]
     _ = μ s := set_lintegral_one _
-#align measure_theory.of_real_set_integral_one_of_measure_ne_top MeasureTheory.ofReal_set_integral_one_of_measure_ne_top
+#align measure_theory.of_real_set_integral_one_of_measure_ne_top MeasureTheory.ofReal_setIntegral_one_of_measure_ne_top
 -/
 
-#print MeasureTheory.ofReal_set_integral_one /-
-theorem ofReal_set_integral_one {α : Type _} {m : MeasurableSpace α} (μ : Measure α)
+#print MeasureTheory.ofReal_setIntegral_one /-
+theorem ofReal_setIntegral_one {α : Type _} {m : MeasurableSpace α} (μ : Measure α)
     [IsFiniteMeasure μ] (s : Set α) : ENNReal.ofReal (∫ x in s, (1 : ℝ) ∂μ) = μ s :=
-  ofReal_set_integral_one_of_measure_ne_top (measure_ne_top μ s)
-#align measure_theory.of_real_set_integral_one MeasureTheory.ofReal_set_integral_one
+  ofReal_setIntegral_one_of_measure_ne_top (measure_ne_top μ s)
+#align measure_theory.of_real_set_integral_one MeasureTheory.ofReal_setIntegral_one
 -/
 
 #print MeasureTheory.integral_piecewise /-
@@ -260,8 +260,8 @@ theorem integral_piecewise [DecidablePred (· ∈ s)] (hs : MeasurableSet s) (hf
 #align measure_theory.integral_piecewise MeasureTheory.integral_piecewise
 -/
 
-#print MeasureTheory.tendsto_set_integral_of_monotone /-
-theorem tendsto_set_integral_of_monotone {ι : Type _} [Countable ι] [SemilatticeSup ι]
+#print MeasureTheory.tendsto_setIntegral_of_monotone /-
+theorem tendsto_setIntegral_of_monotone {ι : Type _} [Countable ι] [SemilatticeSup ι]
     {s : ι → Set α} (hsm : ∀ i, MeasurableSet (s i)) (h_mono : Monotone s)
     (hfi : IntegrableOn f (⋃ n, s n) μ) :
     Tendsto (fun i => ∫ a in s i, f a ∂μ) atTop (𝓝 (∫ a in ⋃ n, s n, f a ∂μ)) :=
@@ -283,7 +283,7 @@ theorem tendsto_set_integral_of_monotone {ι : Type _} [Countable ι] [Semilatti
   rw [← with_density_apply _ (hSm.diff (hsm _)), ← hν, measure_diff hsub (hsm _)]
   exacts [tsub_le_iff_tsub_le.mp hi.1,
     (hi.2.trans_lt <| ENNReal.add_lt_top.2 ⟨hfi', ENNReal.coe_lt_top⟩).Ne]
-#align measure_theory.tendsto_set_integral_of_monotone MeasureTheory.tendsto_set_integral_of_monotone
+#align measure_theory.tendsto_set_integral_of_monotone MeasureTheory.tendsto_setIntegral_of_monotone
 -/
 
 #print MeasureTheory.hasSum_integral_iUnion_ae /-
@@ -323,8 +323,8 @@ theorem integral_iUnion_ae {ι : Type _} [Countable ι] {s : ι → Set α}
 #align measure_theory.integral_Union_ae MeasureTheory.integral_iUnion_ae
 -/
 
-#print MeasureTheory.set_integral_eq_zero_of_ae_eq_zero /-
-theorem set_integral_eq_zero_of_ae_eq_zero (ht_eq : ∀ᵐ x ∂μ, x ∈ t → f x = 0) :
+#print MeasureTheory.setIntegral_eq_zero_of_ae_eq_zero /-
+theorem setIntegral_eq_zero_of_ae_eq_zero (ht_eq : ∀ᵐ x ∂μ, x ∈ t → f x = 0) :
     ∫ x in t, f x ∂μ = 0 :=
   by
   by_cases hf : ae_strongly_measurable f (μ.restrict t); swap
@@ -341,13 +341,13 @@ theorem set_integral_eq_zero_of_ae_eq_zero (ht_eq : ∀ᵐ x ∂μ, x ∈ t →
     exact h'x h''x
   rw [← this]
   exact integral_congr_ae hf.ae_eq_mk
-#align measure_theory.set_integral_eq_zero_of_ae_eq_zero MeasureTheory.set_integral_eq_zero_of_ae_eq_zero
+#align measure_theory.set_integral_eq_zero_of_ae_eq_zero MeasureTheory.setIntegral_eq_zero_of_ae_eq_zero
 -/
 
-#print MeasureTheory.set_integral_eq_zero_of_forall_eq_zero /-
-theorem set_integral_eq_zero_of_forall_eq_zero (ht_eq : ∀ x ∈ t, f x = 0) : ∫ x in t, f x ∂μ = 0 :=
-  set_integral_eq_zero_of_ae_eq_zero (eventually_of_forall ht_eq)
-#align measure_theory.set_integral_eq_zero_of_forall_eq_zero MeasureTheory.set_integral_eq_zero_of_forall_eq_zero
+#print MeasureTheory.setIntegral_eq_zero_of_forall_eq_zero /-
+theorem setIntegral_eq_zero_of_forall_eq_zero (ht_eq : ∀ x ∈ t, f x = 0) : ∫ x in t, f x ∂μ = 0 :=
+  setIntegral_eq_zero_of_ae_eq_zero (eventually_of_forall ht_eq)
+#align measure_theory.set_integral_eq_zero_of_forall_eq_zero MeasureTheory.setIntegral_eq_zero_of_forall_eq_zero
 -/
 
 #print MeasureTheory.integral_union_eq_left_of_ae_aux /-
@@ -407,8 +407,8 @@ theorem integral_union_eq_left_of_forall {f : α → E} (ht : MeasurableSet t)
 #align measure_theory.integral_union_eq_left_of_forall MeasureTheory.integral_union_eq_left_of_forall
 -/
 
-#print MeasureTheory.set_integral_eq_of_subset_of_ae_diff_eq_zero_aux /-
-theorem set_integral_eq_of_subset_of_ae_diff_eq_zero_aux (hts : s ⊆ t)
+#print MeasureTheory.setIntegral_eq_of_subset_of_ae_diff_eq_zero_aux /-
+theorem setIntegral_eq_of_subset_of_ae_diff_eq_zero_aux (hts : s ⊆ t)
     (h't : ∀ᵐ x ∂μ, x ∈ t \ s → f x = 0) (haux : StronglyMeasurable f)
     (h'aux : IntegrableOn f t μ) : ∫ x in t, f x ∂μ = ∫ x in s, f x ∂μ :=
   by
@@ -435,13 +435,13 @@ theorem set_integral_eq_of_subset_of_ae_diff_eq_zero_aux (hts : s ⊆ t)
       have : ∀ x ∈ s ∩ k, f x = 0 := fun x hx => hx.2
       rw [set_integral_eq_zero_of_forall_eq_zero this, zero_add]
     _ = ∫ x in s, f x ∂μ := by rw [integral_inter_add_diff hk (h'aux.mono hts le_rfl)]
-#align measure_theory.set_integral_eq_of_subset_of_ae_diff_eq_zero_aux MeasureTheory.set_integral_eq_of_subset_of_ae_diff_eq_zero_aux
+#align measure_theory.set_integral_eq_of_subset_of_ae_diff_eq_zero_aux MeasureTheory.setIntegral_eq_of_subset_of_ae_diff_eq_zero_aux
 -/
 
-#print MeasureTheory.set_integral_eq_of_subset_of_ae_diff_eq_zero /-
+#print MeasureTheory.setIntegral_eq_of_subset_of_ae_diff_eq_zero /-
 /-- If a function vanishes almost everywhere on `t \ s` with `s ⊆ t`, then its integrals on `s`
 and `t` coincide if `t` is null-measurable. -/
-theorem set_integral_eq_of_subset_of_ae_diff_eq_zero (ht : NullMeasurableSet t μ) (hts : s ⊆ t)
+theorem setIntegral_eq_of_subset_of_ae_diff_eq_zero (ht : NullMeasurableSet t μ) (hts : s ⊆ t)
     (h't : ∀ᵐ x ∂μ, x ∈ t \ s → f x = 0) : ∫ x in t, f x ∂μ = ∫ x in s, f x ∂μ :=
   by
   by_cases h : integrable_on f t μ; swap
@@ -461,43 +461,43 @@ theorem set_integral_eq_of_subset_of_ae_diff_eq_zero (ht : NullMeasurableSet t 
       apply integral_congr_ae
       apply ae_restrict_of_ae_restrict_of_subset hts
       exact h.1.ae_eq_mk.symm
-#align measure_theory.set_integral_eq_of_subset_of_ae_diff_eq_zero MeasureTheory.set_integral_eq_of_subset_of_ae_diff_eq_zero
+#align measure_theory.set_integral_eq_of_subset_of_ae_diff_eq_zero MeasureTheory.setIntegral_eq_of_subset_of_ae_diff_eq_zero
 -/
 
-#print MeasureTheory.set_integral_eq_of_subset_of_forall_diff_eq_zero /-
+#print MeasureTheory.setIntegral_eq_of_subset_of_forall_diff_eq_zero /-
 /-- If a function vanishes on `t \ s` with `s ⊆ t`, then its integrals on `s`
 and `t` coincide if `t` is measurable. -/
-theorem set_integral_eq_of_subset_of_forall_diff_eq_zero (ht : MeasurableSet t) (hts : s ⊆ t)
+theorem setIntegral_eq_of_subset_of_forall_diff_eq_zero (ht : MeasurableSet t) (hts : s ⊆ t)
     (h't : ∀ x ∈ t \ s, f x = 0) : ∫ x in t, f x ∂μ = ∫ x in s, f x ∂μ :=
-  set_integral_eq_of_subset_of_ae_diff_eq_zero ht.NullMeasurableSet hts
+  setIntegral_eq_of_subset_of_ae_diff_eq_zero ht.NullMeasurableSet hts
     (eventually_of_forall fun x hx => h't x hx)
-#align measure_theory.set_integral_eq_of_subset_of_forall_diff_eq_zero MeasureTheory.set_integral_eq_of_subset_of_forall_diff_eq_zero
+#align measure_theory.set_integral_eq_of_subset_of_forall_diff_eq_zero MeasureTheory.setIntegral_eq_of_subset_of_forall_diff_eq_zero
 -/
 
-#print MeasureTheory.set_integral_eq_integral_of_ae_compl_eq_zero /-
+#print MeasureTheory.setIntegral_eq_integral_of_ae_compl_eq_zero /-
 /-- If a function vanishes almost everywhere on `sᶜ`, then its integral on `s`
 coincides with its integral on the whole space. -/
-theorem set_integral_eq_integral_of_ae_compl_eq_zero (h : ∀ᵐ x ∂μ, x ∉ s → f x = 0) :
+theorem setIntegral_eq_integral_of_ae_compl_eq_zero (h : ∀ᵐ x ∂μ, x ∉ s → f x = 0) :
     ∫ x in s, f x ∂μ = ∫ x, f x ∂μ :=
   by
   conv_rhs => rw [← integral_univ]
   symm
   apply set_integral_eq_of_subset_of_ae_diff_eq_zero null_measurable_set_univ (subset_univ _)
   filter_upwards [h] with x hx h'x using hx h'x.2
-#align measure_theory.set_integral_eq_integral_of_ae_compl_eq_zero MeasureTheory.set_integral_eq_integral_of_ae_compl_eq_zero
+#align measure_theory.set_integral_eq_integral_of_ae_compl_eq_zero MeasureTheory.setIntegral_eq_integral_of_ae_compl_eq_zero
 -/
 
-#print MeasureTheory.set_integral_eq_integral_of_forall_compl_eq_zero /-
+#print MeasureTheory.setIntegral_eq_integral_of_forall_compl_eq_zero /-
 /-- If a function vanishes on `sᶜ`, then its integral on `s` coincides with its integral on the
 whole space. -/
-theorem set_integral_eq_integral_of_forall_compl_eq_zero (h : ∀ x, x ∉ s → f x = 0) :
+theorem setIntegral_eq_integral_of_forall_compl_eq_zero (h : ∀ x, x ∉ s → f x = 0) :
     ∫ x in s, f x ∂μ = ∫ x, f x ∂μ :=
-  set_integral_eq_integral_of_ae_compl_eq_zero (eventually_of_forall h)
-#align measure_theory.set_integral_eq_integral_of_forall_compl_eq_zero MeasureTheory.set_integral_eq_integral_of_forall_compl_eq_zero
+  setIntegral_eq_integral_of_ae_compl_eq_zero (eventually_of_forall h)
+#align measure_theory.set_integral_eq_integral_of_forall_compl_eq_zero MeasureTheory.setIntegral_eq_integral_of_forall_compl_eq_zero
 -/
 
-#print MeasureTheory.set_integral_neg_eq_set_integral_nonpos /-
-theorem set_integral_neg_eq_set_integral_nonpos [LinearOrder E] {f : α → E}
+#print MeasureTheory.setIntegral_neg_eq_setIntegral_nonpos /-
+theorem setIntegral_neg_eq_setIntegral_nonpos [LinearOrder E] {f : α → E}
     (hf : AEStronglyMeasurable f μ) : ∫ x in {x | f x < 0}, f x ∂μ = ∫ x in {x | f x ≤ 0}, f x ∂μ :=
   by
   have h_union : {x | f x ≤ 0} = {x | f x < 0} ∪ {x | f x = 0} := by ext;
@@ -508,7 +508,7 @@ theorem set_integral_neg_eq_set_integral_nonpos [LinearOrder E] {f : α → E}
   symm
   refine' integral_union_eq_left_of_ae _
   filter_upwards [ae_restrict_mem₀ B] with x hx using hx
-#align measure_theory.set_integral_neg_eq_set_integral_nonpos MeasureTheory.set_integral_neg_eq_set_integral_nonpos
+#align measure_theory.set_integral_neg_eq_set_integral_nonpos MeasureTheory.setIntegral_neg_eq_setIntegral_nonpos
 -/
 
 #print MeasureTheory.integral_norm_eq_pos_sub_neg /-
@@ -540,10 +540,10 @@ theorem integral_norm_eq_pos_sub_neg {f : α → ℝ} (hfi : Integrable f μ) :
 #align measure_theory.integral_norm_eq_pos_sub_neg MeasureTheory.integral_norm_eq_pos_sub_neg
 -/
 
-#print MeasureTheory.set_integral_const /-
-theorem set_integral_const (c : E) : ∫ x in s, c ∂μ = (μ s).toReal • c := by
+#print MeasureTheory.setIntegral_const /-
+theorem setIntegral_const (c : E) : ∫ x in s, c ∂μ = (μ s).toReal • c := by
   rw [integral_const, measure.restrict_apply_univ]
-#align measure_theory.set_integral_const MeasureTheory.set_integral_const
+#align measure_theory.set_integral_const MeasureTheory.setIntegral_const
 -/
 
 #print MeasureTheory.integral_indicator_const /-
@@ -562,14 +562,14 @@ theorem integral_indicator_one ⦃s : Set α⦄ (hs : MeasurableSet s) :
 #align measure_theory.integral_indicator_one MeasureTheory.integral_indicator_one
 -/
 
-#print MeasureTheory.set_integral_indicatorConstLp /-
-theorem set_integral_indicatorConstLp {p : ℝ≥0∞} (hs : MeasurableSet s) (ht : MeasurableSet t)
+#print MeasureTheory.setIntegral_indicatorConstLp /-
+theorem setIntegral_indicatorConstLp {p : ℝ≥0∞} (hs : MeasurableSet s) (ht : MeasurableSet t)
     (hμt : μ t ≠ ∞) (x : E) : ∫ a in s, indicatorConstLp p ht hμt x a ∂μ = (μ (t ∩ s)).toReal • x :=
   calc
     ∫ a in s, indicatorConstLp p ht hμt x a ∂μ = ∫ a in s, t.indicator (fun _ => x) a ∂μ := by
       rw [set_integral_congr_ae hs (indicator_const_Lp_coe_fn.mono fun x hx hxs => hx)]
     _ = (μ (t ∩ s)).toReal • x := by rw [integral_indicator_const _ ht, measure.restrict_apply ht]
-#align measure_theory.set_integral_indicator_const_Lp MeasureTheory.set_integral_indicatorConstLp
+#align measure_theory.set_integral_indicator_const_Lp MeasureTheory.setIntegral_indicatorConstLp
 -/
 
 #print MeasureTheory.integral_indicatorConstLp /-
@@ -578,73 +578,73 @@ theorem integral_indicatorConstLp {p : ℝ≥0∞} (ht : MeasurableSet t) (hμt
   calc
     ∫ a, indicatorConstLp p ht hμt x a ∂μ = ∫ a in univ, indicatorConstLp p ht hμt x a ∂μ := by
       rw [integral_univ]
-    _ = (μ (t ∩ univ)).toReal • x := (set_integral_indicatorConstLp MeasurableSet.univ ht hμt x)
+    _ = (μ (t ∩ univ)).toReal • x := (setIntegral_indicatorConstLp MeasurableSet.univ ht hμt x)
     _ = (μ t).toReal • x := by rw [inter_univ]
 #align measure_theory.integral_indicator_const_Lp MeasureTheory.integral_indicatorConstLp
 -/
 
-#print MeasureTheory.set_integral_map /-
-theorem set_integral_map {β} [MeasurableSpace β] {g : α → β} {f : β → E} {s : Set β}
+#print MeasureTheory.setIntegral_map /-
+theorem setIntegral_map {β} [MeasurableSpace β] {g : α → β} {f : β → E} {s : Set β}
     (hs : MeasurableSet s) (hf : AEStronglyMeasurable f (Measure.map g μ)) (hg : AEMeasurable g μ) :
     ∫ y in s, f y ∂Measure.map g μ = ∫ x in g ⁻¹' s, f (g x) ∂μ :=
   by
   rw [measure.restrict_map_of_ae_measurable hg hs,
     integral_map (hg.mono_measure measure.restrict_le_self) (hf.mono_measure _)]
   exact measure.map_mono_of_ae_measurable measure.restrict_le_self hg
-#align measure_theory.set_integral_map MeasureTheory.set_integral_map
+#align measure_theory.set_integral_map MeasureTheory.setIntegral_map
 -/
 
-#print MeasurableEmbedding.set_integral_map /-
-theorem MeasurableEmbedding.set_integral_map {β} {_ : MeasurableSpace β} {f : α → β}
+#print MeasurableEmbedding.setIntegral_map /-
+theorem MeasurableEmbedding.setIntegral_map {β} {_ : MeasurableSpace β} {f : α → β}
     (hf : MeasurableEmbedding f) (g : β → E) (s : Set β) :
     ∫ y in s, g y ∂Measure.map f μ = ∫ x in f ⁻¹' s, g (f x) ∂μ := by
   rw [hf.restrict_map, hf.integral_map]
-#align measurable_embedding.set_integral_map MeasurableEmbedding.set_integral_map
+#align measurable_embedding.set_integral_map MeasurableEmbedding.setIntegral_map
 -/
 
-#print ClosedEmbedding.set_integral_map /-
-theorem ClosedEmbedding.set_integral_map [TopologicalSpace α] [BorelSpace α] {β} [MeasurableSpace β]
+#print ClosedEmbedding.setIntegral_map /-
+theorem ClosedEmbedding.setIntegral_map [TopologicalSpace α] [BorelSpace α] {β} [MeasurableSpace β]
     [TopologicalSpace β] [BorelSpace β] {g : α → β} {f : β → E} (s : Set β)
     (hg : ClosedEmbedding g) : ∫ y in s, f y ∂Measure.map g μ = ∫ x in g ⁻¹' s, f (g x) ∂μ :=
-  hg.MeasurableEmbedding.set_integral_map _ _
-#align closed_embedding.set_integral_map ClosedEmbedding.set_integral_map
+  hg.MeasurableEmbedding.setIntegral_map _ _
+#align closed_embedding.set_integral_map ClosedEmbedding.setIntegral_map
 -/
 
-#print MeasureTheory.MeasurePreserving.set_integral_preimage_emb /-
-theorem MeasurePreserving.set_integral_preimage_emb {β} {_ : MeasurableSpace β} {f : α → β} {ν}
+#print MeasureTheory.MeasurePreserving.setIntegral_preimage_emb /-
+theorem MeasurePreserving.setIntegral_preimage_emb {β} {_ : MeasurableSpace β} {f : α → β} {ν}
     (h₁ : MeasurePreserving f μ ν) (h₂ : MeasurableEmbedding f) (g : β → E) (s : Set β) :
     ∫ x in f ⁻¹' s, g (f x) ∂μ = ∫ y in s, g y ∂ν :=
   (h₁.restrict_preimage_emb h₂ s).integral_comp h₂ _
-#align measure_theory.measure_preserving.set_integral_preimage_emb MeasureTheory.MeasurePreserving.set_integral_preimage_emb
+#align measure_theory.measure_preserving.set_integral_preimage_emb MeasureTheory.MeasurePreserving.setIntegral_preimage_emb
 -/
 
-#print MeasureTheory.MeasurePreserving.set_integral_image_emb /-
-theorem MeasurePreserving.set_integral_image_emb {β} {_ : MeasurableSpace β} {f : α → β} {ν}
+#print MeasureTheory.MeasurePreserving.setIntegral_image_emb /-
+theorem MeasurePreserving.setIntegral_image_emb {β} {_ : MeasurableSpace β} {f : α → β} {ν}
     (h₁ : MeasurePreserving f μ ν) (h₂ : MeasurableEmbedding f) (g : β → E) (s : Set α) :
     ∫ y in f '' s, g y ∂ν = ∫ x in s, g (f x) ∂μ :=
   Eq.symm <| (h₁.restrict_image_emb h₂ s).integral_comp h₂ _
-#align measure_theory.measure_preserving.set_integral_image_emb MeasureTheory.MeasurePreserving.set_integral_image_emb
+#align measure_theory.measure_preserving.set_integral_image_emb MeasureTheory.MeasurePreserving.setIntegral_image_emb
 -/
 
-#print MeasureTheory.set_integral_map_equiv /-
-theorem set_integral_map_equiv {β} [MeasurableSpace β] (e : α ≃ᵐ β) (f : β → E) (s : Set β) :
+#print MeasureTheory.setIntegral_map_equiv /-
+theorem setIntegral_map_equiv {β} [MeasurableSpace β] (e : α ≃ᵐ β) (f : β → E) (s : Set β) :
     ∫ y in s, f y ∂Measure.map e μ = ∫ x in e ⁻¹' s, f (e x) ∂μ :=
-  e.MeasurableEmbedding.set_integral_map f s
-#align measure_theory.set_integral_map_equiv MeasureTheory.set_integral_map_equiv
+  e.MeasurableEmbedding.setIntegral_map f s
+#align measure_theory.set_integral_map_equiv MeasureTheory.setIntegral_map_equiv
 -/
 
-#print MeasureTheory.norm_set_integral_le_of_norm_le_const_ae /-
-theorem norm_set_integral_le_of_norm_le_const_ae {C : ℝ} (hs : μ s < ∞)
+#print MeasureTheory.norm_setIntegral_le_of_norm_le_const_ae /-
+theorem norm_setIntegral_le_of_norm_le_const_ae {C : ℝ} (hs : μ s < ∞)
     (hC : ∀ᵐ x ∂μ.restrict s, ‖f x‖ ≤ C) : ‖∫ x in s, f x ∂μ‖ ≤ C * (μ s).toReal :=
   by
   rw [← measure.restrict_apply_univ] at *
   haveI : is_finite_measure (μ.restrict s) := ⟨‹_›⟩
   exact norm_integral_le_of_norm_le_const hC
-#align measure_theory.norm_set_integral_le_of_norm_le_const_ae MeasureTheory.norm_set_integral_le_of_norm_le_const_ae
+#align measure_theory.norm_set_integral_le_of_norm_le_const_ae MeasureTheory.norm_setIntegral_le_of_norm_le_const_ae
 -/
 
-#print MeasureTheory.norm_set_integral_le_of_norm_le_const_ae' /-
-theorem norm_set_integral_le_of_norm_le_const_ae' {C : ℝ} (hs : μ s < ∞)
+#print MeasureTheory.norm_setIntegral_le_of_norm_le_const_ae' /-
+theorem norm_setIntegral_le_of_norm_le_const_ae' {C : ℝ} (hs : μ s < ∞)
     (hC : ∀ᵐ x ∂μ, x ∈ s → ‖f x‖ ≤ C) (hfm : AEStronglyMeasurable f (μ.restrict s)) :
     ‖∫ x in s, f x ∂μ‖ ≤ C * (μ s).toReal :=
   by
@@ -658,50 +658,50 @@ theorem norm_set_integral_le_of_norm_le_const_ae' {C : ℝ} (hs : μ s < ∞)
     hfm.strongly_measurable_mk.norm.measurable measurableSet_Iic
   filter_upwards [hfm.ae_eq_mk, (ae_restrict_iff B).2 A] with _ h1 _
   rwa [h1]
-#align measure_theory.norm_set_integral_le_of_norm_le_const_ae' MeasureTheory.norm_set_integral_le_of_norm_le_const_ae'
+#align measure_theory.norm_set_integral_le_of_norm_le_const_ae' MeasureTheory.norm_setIntegral_le_of_norm_le_const_ae'
 -/
 
-#print MeasureTheory.norm_set_integral_le_of_norm_le_const_ae'' /-
-theorem norm_set_integral_le_of_norm_le_const_ae'' {C : ℝ} (hs : μ s < ∞) (hsm : MeasurableSet s)
+#print MeasureTheory.norm_setIntegral_le_of_norm_le_const_ae'' /-
+theorem norm_setIntegral_le_of_norm_le_const_ae'' {C : ℝ} (hs : μ s < ∞) (hsm : MeasurableSet s)
     (hC : ∀ᵐ x ∂μ, x ∈ s → ‖f x‖ ≤ C) : ‖∫ x in s, f x ∂μ‖ ≤ C * (μ s).toReal :=
-  norm_set_integral_le_of_norm_le_const_ae hs <| by
+  norm_setIntegral_le_of_norm_le_const_ae hs <| by
     rwa [ae_restrict_eq hsm, eventually_inf_principal]
-#align measure_theory.norm_set_integral_le_of_norm_le_const_ae'' MeasureTheory.norm_set_integral_le_of_norm_le_const_ae''
+#align measure_theory.norm_set_integral_le_of_norm_le_const_ae'' MeasureTheory.norm_setIntegral_le_of_norm_le_const_ae''
 -/
 
-#print MeasureTheory.norm_set_integral_le_of_norm_le_const /-
-theorem norm_set_integral_le_of_norm_le_const {C : ℝ} (hs : μ s < ∞) (hC : ∀ x ∈ s, ‖f x‖ ≤ C)
+#print MeasureTheory.norm_setIntegral_le_of_norm_le_const /-
+theorem norm_setIntegral_le_of_norm_le_const {C : ℝ} (hs : μ s < ∞) (hC : ∀ x ∈ s, ‖f x‖ ≤ C)
     (hfm : AEStronglyMeasurable f (μ.restrict s)) : ‖∫ x in s, f x ∂μ‖ ≤ C * (μ s).toReal :=
-  norm_set_integral_le_of_norm_le_const_ae' hs (eventually_of_forall hC) hfm
-#align measure_theory.norm_set_integral_le_of_norm_le_const MeasureTheory.norm_set_integral_le_of_norm_le_const
+  norm_setIntegral_le_of_norm_le_const_ae' hs (eventually_of_forall hC) hfm
+#align measure_theory.norm_set_integral_le_of_norm_le_const MeasureTheory.norm_setIntegral_le_of_norm_le_const
 -/
 
-#print MeasureTheory.norm_set_integral_le_of_norm_le_const' /-
-theorem norm_set_integral_le_of_norm_le_const' {C : ℝ} (hs : μ s < ∞) (hsm : MeasurableSet s)
+#print MeasureTheory.norm_setIntegral_le_of_norm_le_const' /-
+theorem norm_setIntegral_le_of_norm_le_const' {C : ℝ} (hs : μ s < ∞) (hsm : MeasurableSet s)
     (hC : ∀ x ∈ s, ‖f x‖ ≤ C) : ‖∫ x in s, f x ∂μ‖ ≤ C * (μ s).toReal :=
-  norm_set_integral_le_of_norm_le_const_ae'' hs hsm <| eventually_of_forall hC
-#align measure_theory.norm_set_integral_le_of_norm_le_const' MeasureTheory.norm_set_integral_le_of_norm_le_const'
+  norm_setIntegral_le_of_norm_le_const_ae'' hs hsm <| eventually_of_forall hC
+#align measure_theory.norm_set_integral_le_of_norm_le_const' MeasureTheory.norm_setIntegral_le_of_norm_le_const'
 -/
 
-#print MeasureTheory.set_integral_eq_zero_iff_of_nonneg_ae /-
-theorem set_integral_eq_zero_iff_of_nonneg_ae {f : α → ℝ} (hf : 0 ≤ᵐ[μ.restrict s] f)
+#print MeasureTheory.setIntegral_eq_zero_iff_of_nonneg_ae /-
+theorem setIntegral_eq_zero_iff_of_nonneg_ae {f : α → ℝ} (hf : 0 ≤ᵐ[μ.restrict s] f)
     (hfi : IntegrableOn f s μ) : ∫ x in s, f x ∂μ = 0 ↔ f =ᵐ[μ.restrict s] 0 :=
   integral_eq_zero_iff_of_nonneg_ae hf hfi
-#align measure_theory.set_integral_eq_zero_iff_of_nonneg_ae MeasureTheory.set_integral_eq_zero_iff_of_nonneg_ae
+#align measure_theory.set_integral_eq_zero_iff_of_nonneg_ae MeasureTheory.setIntegral_eq_zero_iff_of_nonneg_ae
 -/
 
-#print MeasureTheory.set_integral_pos_iff_support_of_nonneg_ae /-
-theorem set_integral_pos_iff_support_of_nonneg_ae {f : α → ℝ} (hf : 0 ≤ᵐ[μ.restrict s] f)
+#print MeasureTheory.setIntegral_pos_iff_support_of_nonneg_ae /-
+theorem setIntegral_pos_iff_support_of_nonneg_ae {f : α → ℝ} (hf : 0 ≤ᵐ[μ.restrict s] f)
     (hfi : IntegrableOn f s μ) : 0 < ∫ x in s, f x ∂μ ↔ 0 < μ (support f ∩ s) :=
   by
   rw [integral_pos_iff_support_of_nonneg_ae hf hfi, measure.restrict_apply₀]
   rw [support_eq_preimage]
   exact hfi.ae_strongly_measurable.ae_measurable.null_measurable (measurable_set_singleton 0).compl
-#align measure_theory.set_integral_pos_iff_support_of_nonneg_ae MeasureTheory.set_integral_pos_iff_support_of_nonneg_ae
+#align measure_theory.set_integral_pos_iff_support_of_nonneg_ae MeasureTheory.setIntegral_pos_iff_support_of_nonneg_ae
 -/
 
-#print MeasureTheory.set_integral_gt_gt /-
-theorem set_integral_gt_gt {R : ℝ} {f : α → ℝ} (hR : 0 ≤ R) (hfm : Measurable f)
+#print MeasureTheory.setIntegral_gt_gt /-
+theorem setIntegral_gt_gt {R : ℝ} {f : α → ℝ} (hR : 0 ≤ R) (hfm : Measurable f)
     (hfint : IntegrableOn f {x | ↑R < f x} μ) (hμ : μ {x | ↑R < f x} ≠ 0) :
     (μ {x | ↑R < f x}).toReal * R < ∫ x in {x | ↑R < f x}, f x ∂μ :=
   by
@@ -725,15 +725,15 @@ theorem set_integral_gt_gt {R : ℝ} {f : α → ℝ} (hR : 0 ≤ R) (hfm : Meas
     · exact eventually_of_forall fun x hx => sub_nonneg.2 <| le_of_lt hx
     · exact measurableSet_le measurable_zero (hfm.sub measurable_const)
   · exact integrable.sub hfint this
-#align measure_theory.set_integral_gt_gt MeasureTheory.set_integral_gt_gt
+#align measure_theory.set_integral_gt_gt MeasureTheory.setIntegral_gt_gt
 -/
 
-#print MeasureTheory.set_integral_trim /-
-theorem set_integral_trim {α} {m m0 : MeasurableSpace α} {μ : Measure α} (hm : m ≤ m0) {f : α → E}
+#print MeasureTheory.setIntegral_trim /-
+theorem setIntegral_trim {α} {m m0 : MeasurableSpace α} {μ : Measure α} (hm : m ≤ m0) {f : α → E}
     (hf_meas : strongly_measurable[m] f) {s : Set α} (hs : measurable_set[m] s) :
     ∫ x in s, f x ∂μ = ∫ x in s, f x ∂μ.trim hm := by
   rwa [integral_trim hm hf_meas, restrict_trim hm μ]
-#align measure_theory.set_integral_trim MeasureTheory.set_integral_trim
+#align measure_theory.set_integral_trim MeasureTheory.setIntegral_trim
 -/
 
 /-! ### Lemmas about adding and removing interval boundaries
@@ -750,49 +750,49 @@ variable [PartialOrder α] {a b : α}
 #print MeasureTheory.integral_Icc_eq_integral_Ioc' /-
 theorem integral_Icc_eq_integral_Ioc' (ha : μ {a} = 0) :
     ∫ t in Icc a b, f t ∂μ = ∫ t in Ioc a b, f t ∂μ :=
-  set_integral_congr_set_ae (Ioc_ae_eq_Icc' ha).symm
+  setIntegral_congr_set_ae (Ioc_ae_eq_Icc' ha).symm
 #align measure_theory.integral_Icc_eq_integral_Ioc' MeasureTheory.integral_Icc_eq_integral_Ioc'
 -/
 
 #print MeasureTheory.integral_Icc_eq_integral_Ico' /-
 theorem integral_Icc_eq_integral_Ico' (hb : μ {b} = 0) :
     ∫ t in Icc a b, f t ∂μ = ∫ t in Ico a b, f t ∂μ :=
-  set_integral_congr_set_ae (Ico_ae_eq_Icc' hb).symm
+  setIntegral_congr_set_ae (Ico_ae_eq_Icc' hb).symm
 #align measure_theory.integral_Icc_eq_integral_Ico' MeasureTheory.integral_Icc_eq_integral_Ico'
 -/
 
 #print MeasureTheory.integral_Ioc_eq_integral_Ioo' /-
 theorem integral_Ioc_eq_integral_Ioo' (hb : μ {b} = 0) :
     ∫ t in Ioc a b, f t ∂μ = ∫ t in Ioo a b, f t ∂μ :=
-  set_integral_congr_set_ae (Ioo_ae_eq_Ioc' hb).symm
+  setIntegral_congr_set_ae (Ioo_ae_eq_Ioc' hb).symm
 #align measure_theory.integral_Ioc_eq_integral_Ioo' MeasureTheory.integral_Ioc_eq_integral_Ioo'
 -/
 
 #print MeasureTheory.integral_Ico_eq_integral_Ioo' /-
 theorem integral_Ico_eq_integral_Ioo' (ha : μ {a} = 0) :
     ∫ t in Ico a b, f t ∂μ = ∫ t in Ioo a b, f t ∂μ :=
-  set_integral_congr_set_ae (Ioo_ae_eq_Ico' ha).symm
+  setIntegral_congr_set_ae (Ioo_ae_eq_Ico' ha).symm
 #align measure_theory.integral_Ico_eq_integral_Ioo' MeasureTheory.integral_Ico_eq_integral_Ioo'
 -/
 
 #print MeasureTheory.integral_Icc_eq_integral_Ioo' /-
 theorem integral_Icc_eq_integral_Ioo' (ha : μ {a} = 0) (hb : μ {b} = 0) :
     ∫ t in Icc a b, f t ∂μ = ∫ t in Ioo a b, f t ∂μ :=
-  set_integral_congr_set_ae (Ioo_ae_eq_Icc' ha hb).symm
+  setIntegral_congr_set_ae (Ioo_ae_eq_Icc' ha hb).symm
 #align measure_theory.integral_Icc_eq_integral_Ioo' MeasureTheory.integral_Icc_eq_integral_Ioo'
 -/
 
 #print MeasureTheory.integral_Iic_eq_integral_Iio' /-
 theorem integral_Iic_eq_integral_Iio' (ha : μ {a} = 0) :
     ∫ t in Iic a, f t ∂μ = ∫ t in Iio a, f t ∂μ :=
-  set_integral_congr_set_ae (Iio_ae_eq_Iic' ha).symm
+  setIntegral_congr_set_ae (Iio_ae_eq_Iic' ha).symm
 #align measure_theory.integral_Iic_eq_integral_Iio' MeasureTheory.integral_Iic_eq_integral_Iio'
 -/
 
 #print MeasureTheory.integral_Ici_eq_integral_Ioi' /-
 theorem integral_Ici_eq_integral_Ioi' (ha : μ {a} = 0) :
     ∫ t in Ici a, f t ∂μ = ∫ t in Ioi a, f t ∂μ :=
-  set_integral_congr_set_ae (Ioi_ae_eq_Ici' ha).symm
+  setIntegral_congr_set_ae (Ioi_ae_eq_Ici' ha).symm
 #align measure_theory.integral_Ici_eq_integral_Ioi' MeasureTheory.integral_Ici_eq_integral_Ioi'
 -/
 
@@ -849,56 +849,56 @@ section Mono
 variable {μ : Measure α} {f g : α → ℝ} {s t : Set α} (hf : IntegrableOn f s μ)
   (hg : IntegrableOn g s μ)
 
-#print MeasureTheory.set_integral_mono_ae_restrict /-
-theorem set_integral_mono_ae_restrict (h : f ≤ᵐ[μ.restrict s] g) :
+#print MeasureTheory.setIntegral_mono_ae_restrict /-
+theorem setIntegral_mono_ae_restrict (h : f ≤ᵐ[μ.restrict s] g) :
     ∫ a in s, f a ∂μ ≤ ∫ a in s, g a ∂μ :=
   integral_mono_ae hf hg h
-#align measure_theory.set_integral_mono_ae_restrict MeasureTheory.set_integral_mono_ae_restrict
+#align measure_theory.set_integral_mono_ae_restrict MeasureTheory.setIntegral_mono_ae_restrict
 -/
 
-#print MeasureTheory.set_integral_mono_ae /-
-theorem set_integral_mono_ae (h : f ≤ᵐ[μ] g) : ∫ a in s, f a ∂μ ≤ ∫ a in s, g a ∂μ :=
-  set_integral_mono_ae_restrict hf hg (ae_restrict_of_ae h)
-#align measure_theory.set_integral_mono_ae MeasureTheory.set_integral_mono_ae
+#print MeasureTheory.setIntegral_mono_ae /-
+theorem setIntegral_mono_ae (h : f ≤ᵐ[μ] g) : ∫ a in s, f a ∂μ ≤ ∫ a in s, g a ∂μ :=
+  setIntegral_mono_ae_restrict hf hg (ae_restrict_of_ae h)
+#align measure_theory.set_integral_mono_ae MeasureTheory.setIntegral_mono_ae
 -/
 
-#print MeasureTheory.set_integral_mono_on /-
-theorem set_integral_mono_on (hs : MeasurableSet s) (h : ∀ x ∈ s, f x ≤ g x) :
+#print MeasureTheory.setIntegral_mono_on /-
+theorem setIntegral_mono_on (hs : MeasurableSet s) (h : ∀ x ∈ s, f x ≤ g x) :
     ∫ a in s, f a ∂μ ≤ ∫ a in s, g a ∂μ :=
-  set_integral_mono_ae_restrict hf hg
+  setIntegral_mono_ae_restrict hf hg
     (by simp [hs, eventually_le, eventually_inf_principal, ae_of_all _ h])
-#align measure_theory.set_integral_mono_on MeasureTheory.set_integral_mono_on
+#align measure_theory.set_integral_mono_on MeasureTheory.setIntegral_mono_on
 -/
 
-#print MeasureTheory.set_integral_mono_on_ae /-
+#print MeasureTheory.setIntegral_mono_on_ae /-
 -- why do I need this include, but we don't need it in other lemmas?
-theorem set_integral_mono_on_ae (hs : MeasurableSet s) (h : ∀ᵐ x ∂μ, x ∈ s → f x ≤ g x) :
+theorem setIntegral_mono_on_ae (hs : MeasurableSet s) (h : ∀ᵐ x ∂μ, x ∈ s → f x ≤ g x) :
     ∫ a in s, f a ∂μ ≤ ∫ a in s, g a ∂μ := by refine' set_integral_mono_ae_restrict hf hg _;
   rwa [eventually_le, ae_restrict_iff' hs]
-#align measure_theory.set_integral_mono_on_ae MeasureTheory.set_integral_mono_on_ae
+#align measure_theory.set_integral_mono_on_ae MeasureTheory.setIntegral_mono_on_ae
 -/
 
-#print MeasureTheory.set_integral_mono /-
-theorem set_integral_mono (h : f ≤ g) : ∫ a in s, f a ∂μ ≤ ∫ a in s, g a ∂μ :=
+#print MeasureTheory.setIntegral_mono /-
+theorem setIntegral_mono (h : f ≤ g) : ∫ a in s, f a ∂μ ≤ ∫ a in s, g a ∂μ :=
   integral_mono hf hg h
-#align measure_theory.set_integral_mono MeasureTheory.set_integral_mono
+#align measure_theory.set_integral_mono MeasureTheory.setIntegral_mono
 -/
 
-#print MeasureTheory.set_integral_mono_set /-
-theorem set_integral_mono_set (hfi : IntegrableOn f t μ) (hf : 0 ≤ᵐ[μ.restrict t] f)
+#print MeasureTheory.setIntegral_mono_set /-
+theorem setIntegral_mono_set (hfi : IntegrableOn f t μ) (hf : 0 ≤ᵐ[μ.restrict t] f)
     (hst : s ≤ᵐ[μ] t) : ∫ x in s, f x ∂μ ≤ ∫ x in t, f x ∂μ :=
   integral_mono_measure (Measure.restrict_mono_ae hst) hf hfi
-#align measure_theory.set_integral_mono_set MeasureTheory.set_integral_mono_set
+#align measure_theory.set_integral_mono_set MeasureTheory.setIntegral_mono_set
 -/
 
-#print MeasureTheory.set_integral_ge_of_const_le /-
-theorem set_integral_ge_of_const_le {c : ℝ} (hs : MeasurableSet s) (hμs : μ s ≠ ∞)
+#print MeasureTheory.setIntegral_ge_of_const_le /-
+theorem setIntegral_ge_of_const_le {c : ℝ} (hs : MeasurableSet s) (hμs : μ s ≠ ∞)
     (hf : ∀ x ∈ s, c ≤ f x) (hfint : IntegrableOn (fun x : α => f x) s μ) :
     c * (μ s).toReal ≤ ∫ x in s, f x ∂μ :=
   by
   rw [mul_comm, ← smul_eq_mul, ← set_integral_const c]
   exact set_integral_mono_on (integrable_on_const.2 (Or.inr hμs.lt_top)) hfint hs hf
-#align measure_theory.set_integral_ge_of_const_le MeasureTheory.set_integral_ge_of_const_le
+#align measure_theory.set_integral_ge_of_const_le MeasureTheory.setIntegral_ge_of_const_le
 -/
 
 end Mono
@@ -907,34 +907,34 @@ section Nonneg
 
 variable {μ : Measure α} {f : α → ℝ} {s : Set α}
 
-#print MeasureTheory.set_integral_nonneg_of_ae_restrict /-
-theorem set_integral_nonneg_of_ae_restrict (hf : 0 ≤ᵐ[μ.restrict s] f) : 0 ≤ ∫ a in s, f a ∂μ :=
+#print MeasureTheory.setIntegral_nonneg_of_ae_restrict /-
+theorem setIntegral_nonneg_of_ae_restrict (hf : 0 ≤ᵐ[μ.restrict s] f) : 0 ≤ ∫ a in s, f a ∂μ :=
   integral_nonneg_of_ae hf
-#align measure_theory.set_integral_nonneg_of_ae_restrict MeasureTheory.set_integral_nonneg_of_ae_restrict
+#align measure_theory.set_integral_nonneg_of_ae_restrict MeasureTheory.setIntegral_nonneg_of_ae_restrict
 -/
 
-#print MeasureTheory.set_integral_nonneg_of_ae /-
-theorem set_integral_nonneg_of_ae (hf : 0 ≤ᵐ[μ] f) : 0 ≤ ∫ a in s, f a ∂μ :=
-  set_integral_nonneg_of_ae_restrict (ae_restrict_of_ae hf)
-#align measure_theory.set_integral_nonneg_of_ae MeasureTheory.set_integral_nonneg_of_ae
+#print MeasureTheory.setIntegral_nonneg_of_ae /-
+theorem setIntegral_nonneg_of_ae (hf : 0 ≤ᵐ[μ] f) : 0 ≤ ∫ a in s, f a ∂μ :=
+  setIntegral_nonneg_of_ae_restrict (ae_restrict_of_ae hf)
+#align measure_theory.set_integral_nonneg_of_ae MeasureTheory.setIntegral_nonneg_of_ae
 -/
 
-#print MeasureTheory.set_integral_nonneg /-
-theorem set_integral_nonneg (hs : MeasurableSet s) (hf : ∀ a, a ∈ s → 0 ≤ f a) :
+#print MeasureTheory.setIntegral_nonneg /-
+theorem setIntegral_nonneg (hs : MeasurableSet s) (hf : ∀ a, a ∈ s → 0 ≤ f a) :
     0 ≤ ∫ a in s, f a ∂μ :=
-  set_integral_nonneg_of_ae_restrict ((ae_restrict_iff' hs).mpr (ae_of_all μ hf))
-#align measure_theory.set_integral_nonneg MeasureTheory.set_integral_nonneg
+  setIntegral_nonneg_of_ae_restrict ((ae_restrict_iff' hs).mpr (ae_of_all μ hf))
+#align measure_theory.set_integral_nonneg MeasureTheory.setIntegral_nonneg
 -/
 
-#print MeasureTheory.set_integral_nonneg_ae /-
-theorem set_integral_nonneg_ae (hs : MeasurableSet s) (hf : ∀ᵐ a ∂μ, a ∈ s → 0 ≤ f a) :
+#print MeasureTheory.setIntegral_nonneg_ae /-
+theorem setIntegral_nonneg_ae (hs : MeasurableSet s) (hf : ∀ᵐ a ∂μ, a ∈ s → 0 ≤ f a) :
     0 ≤ ∫ a in s, f a ∂μ :=
-  set_integral_nonneg_of_ae_restrict <| by rwa [eventually_le, ae_restrict_iff' hs]
-#align measure_theory.set_integral_nonneg_ae MeasureTheory.set_integral_nonneg_ae
+  setIntegral_nonneg_of_ae_restrict <| by rwa [eventually_le, ae_restrict_iff' hs]
+#align measure_theory.set_integral_nonneg_ae MeasureTheory.setIntegral_nonneg_ae
 -/
 
-#print MeasureTheory.set_integral_le_nonneg /-
-theorem set_integral_le_nonneg {s : Set α} (hs : MeasurableSet s) (hf : StronglyMeasurable f)
+#print MeasureTheory.setIntegral_le_nonneg /-
+theorem setIntegral_le_nonneg {s : Set α} (hs : MeasurableSet s) (hf : StronglyMeasurable f)
     (hfi : Integrable f μ) : ∫ x in s, f x ∂μ ≤ ∫ x in {y | 0 ≤ f y}, f x ∂μ :=
   by
   rw [← integral_indicator hs, ←
@@ -943,37 +943,37 @@ theorem set_integral_le_nonneg {s : Set α} (hs : MeasurableSet s) (hf : Strongl
     integral_mono (hfi.indicator hs)
       (hfi.indicator (strongly_measurable_const.measurable_set_le hf))
       (indicator_le_indicator_nonneg s f)
-#align measure_theory.set_integral_le_nonneg MeasureTheory.set_integral_le_nonneg
+#align measure_theory.set_integral_le_nonneg MeasureTheory.setIntegral_le_nonneg
 -/
 
-#print MeasureTheory.set_integral_nonpos_of_ae_restrict /-
-theorem set_integral_nonpos_of_ae_restrict (hf : f ≤ᵐ[μ.restrict s] 0) : ∫ a in s, f a ∂μ ≤ 0 :=
+#print MeasureTheory.setIntegral_nonpos_of_ae_restrict /-
+theorem setIntegral_nonpos_of_ae_restrict (hf : f ≤ᵐ[μ.restrict s] 0) : ∫ a in s, f a ∂μ ≤ 0 :=
   integral_nonpos_of_ae hf
-#align measure_theory.set_integral_nonpos_of_ae_restrict MeasureTheory.set_integral_nonpos_of_ae_restrict
+#align measure_theory.set_integral_nonpos_of_ae_restrict MeasureTheory.setIntegral_nonpos_of_ae_restrict
 -/
 
-#print MeasureTheory.set_integral_nonpos_of_ae /-
-theorem set_integral_nonpos_of_ae (hf : f ≤ᵐ[μ] 0) : ∫ a in s, f a ∂μ ≤ 0 :=
-  set_integral_nonpos_of_ae_restrict (ae_restrict_of_ae hf)
-#align measure_theory.set_integral_nonpos_of_ae MeasureTheory.set_integral_nonpos_of_ae
+#print MeasureTheory.setIntegral_nonpos_of_ae /-
+theorem setIntegral_nonpos_of_ae (hf : f ≤ᵐ[μ] 0) : ∫ a in s, f a ∂μ ≤ 0 :=
+  setIntegral_nonpos_of_ae_restrict (ae_restrict_of_ae hf)
+#align measure_theory.set_integral_nonpos_of_ae MeasureTheory.setIntegral_nonpos_of_ae
 -/
 
-#print MeasureTheory.set_integral_nonpos /-
-theorem set_integral_nonpos (hs : MeasurableSet s) (hf : ∀ a, a ∈ s → f a ≤ 0) :
+#print MeasureTheory.setIntegral_nonpos /-
+theorem setIntegral_nonpos (hs : MeasurableSet s) (hf : ∀ a, a ∈ s → f a ≤ 0) :
     ∫ a in s, f a ∂μ ≤ 0 :=
-  set_integral_nonpos_of_ae_restrict ((ae_restrict_iff' hs).mpr (ae_of_all μ hf))
-#align measure_theory.set_integral_nonpos MeasureTheory.set_integral_nonpos
+  setIntegral_nonpos_of_ae_restrict ((ae_restrict_iff' hs).mpr (ae_of_all μ hf))
+#align measure_theory.set_integral_nonpos MeasureTheory.setIntegral_nonpos
 -/
 
-#print MeasureTheory.set_integral_nonpos_ae /-
-theorem set_integral_nonpos_ae (hs : MeasurableSet s) (hf : ∀ᵐ a ∂μ, a ∈ s → f a ≤ 0) :
+#print MeasureTheory.setIntegral_nonpos_ae /-
+theorem setIntegral_nonpos_ae (hs : MeasurableSet s) (hf : ∀ᵐ a ∂μ, a ∈ s → f a ≤ 0) :
     ∫ a in s, f a ∂μ ≤ 0 :=
-  set_integral_nonpos_of_ae_restrict <| by rwa [eventually_le, ae_restrict_iff' hs]
-#align measure_theory.set_integral_nonpos_ae MeasureTheory.set_integral_nonpos_ae
+  setIntegral_nonpos_of_ae_restrict <| by rwa [eventually_le, ae_restrict_iff' hs]
+#align measure_theory.set_integral_nonpos_ae MeasureTheory.setIntegral_nonpos_ae
 -/
 
-#print MeasureTheory.set_integral_nonpos_le /-
-theorem set_integral_nonpos_le {s : Set α} (hs : MeasurableSet s) (hf : StronglyMeasurable f)
+#print MeasureTheory.setIntegral_nonpos_le /-
+theorem setIntegral_nonpos_le {s : Set α} (hs : MeasurableSet s) (hf : StronglyMeasurable f)
     (hfi : Integrable f μ) : ∫ x in {y | f y ≤ 0}, f x ∂μ ≤ ∫ x in s, f x ∂μ :=
   by
   rw [← integral_indicator hs, ←
@@ -981,7 +981,7 @@ theorem set_integral_nonpos_le {s : Set α} (hs : MeasurableSet s) (hf : Strongl
   exact
     integral_mono (hfi.indicator (hf.measurable_set_le strongly_measurable_const))
       (hfi.indicator hs) (indicator_nonpos_le_indicator s f)
-#align measure_theory.set_integral_nonpos_le MeasureTheory.set_integral_nonpos_le
+#align measure_theory.set_integral_nonpos_le MeasureTheory.setIntegral_nonpos_le
 -/
 
 end Nonneg
@@ -1048,8 +1048,8 @@ variable {μ : Measure α} [NormedAddCommGroup E] [CompleteSpace E] [NormedSpace
   {f : α → E}
 
 /- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:72:38: in filter_upwards #[[], ["with", ident a], ["using", expr le_trans (h_anti.tendsto_indicator _ _ _) (pure_le_nhds _)]]: ./././Mathport/Syntax/Translate/Basic.lean:355:22: unsupported: parse error @ arg 0: next failed, no more args -/
-#print Antitone.tendsto_set_integral /-
-theorem Antitone.tendsto_set_integral (hsm : ∀ i, MeasurableSet (s i)) (h_anti : Antitone s)
+#print Antitone.tendsto_setIntegral /-
+theorem Antitone.tendsto_setIntegral (hsm : ∀ i, MeasurableSet (s i)) (h_anti : Antitone s)
     (hfi : IntegrableOn f (s 0) μ) :
     Tendsto (fun i => ∫ a in s i, f a ∂μ) atTop (𝓝 (∫ a in ⋂ n, s n, f a ∂μ)) :=
   by
@@ -1070,7 +1070,7 @@ theorem Antitone.tendsto_set_integral (hsm : ∀ i, MeasurableSet (s i)) (h_anti
   ·
     trace
       "./././Mathport/Syntax/Translate/Tactic/Builtin.lean:72:38: in filter_upwards #[[], [\"with\", ident a], [\"using\", expr le_trans (h_anti.tendsto_indicator _ _ _) (pure_le_nhds _)]]: ./././Mathport/Syntax/Translate/Basic.lean:355:22: unsupported: parse error @ arg 0: next failed, no more args"
-#align antitone.tendsto_set_integral Antitone.tendsto_set_integral
+#align antitone.tendsto_set_integral Antitone.tendsto_setIntegral
 -/
 
 end TendstoMono
@@ -1161,9 +1161,9 @@ theorem LpToLpRestrictCLM_coeFn [hp : Fact (1 ≤ p)] (s : Set α) (f : Lp F p 
 
 variable {𝕜}
 
-#print MeasureTheory.continuous_set_integral /-
+#print MeasureTheory.continuous_setIntegral /-
 @[continuity]
-theorem continuous_set_integral [NormedSpace ℝ E] [CompleteSpace E] (s : Set α) :
+theorem continuous_setIntegral [NormedSpace ℝ E] [CompleteSpace E] (s : Set α) :
     Continuous fun f : α →₁[μ] E => ∫ x in s, f x ∂μ :=
   by
   haveI : Fact ((1 : ℝ≥0∞) ≤ 1) := ⟨le_rfl⟩
@@ -1175,7 +1175,7 @@ theorem continuous_set_integral [NormedSpace ℝ E] [CompleteSpace E] (s : Set 
     rw [Function.comp_apply, integral_congr_ae (Lp_to_Lp_restrict_clm_coe_fn ℝ s f)]
   rw [h_comp]
   exact continuous_integral.comp (Lp_to_Lp_restrict_clm α E ℝ μ 1 s).Continuous
-#align measure_theory.continuous_set_integral MeasureTheory.continuous_set_integral
+#align measure_theory.continuous_set_integral MeasureTheory.continuous_setIntegral
 -/
 
 end ContinuousSetIntegral
@@ -1309,11 +1309,11 @@ theorem integral_compLp (L : E →L[𝕜] F) (φ : Lp E p μ) : ∫ a, (L.compLp
 #align continuous_linear_map.integral_comp_Lp ContinuousLinearMap.integral_compLp
 -/
 
-#print ContinuousLinearMap.set_integral_compLp /-
-theorem set_integral_compLp (L : E →L[𝕜] F) (φ : Lp E p μ) {s : Set α} (hs : MeasurableSet s) :
+#print ContinuousLinearMap.setIntegral_compLp /-
+theorem setIntegral_compLp (L : E →L[𝕜] F) (φ : Lp E p μ) {s : Set α} (hs : MeasurableSet s) :
     ∫ a in s, (L.compLp φ) a ∂μ = ∫ a in s, L (φ a) ∂μ :=
-  set_integral_congr_ae hs ((L.coeFn_compLp φ).mono fun x hx hx2 => hx)
-#align continuous_linear_map.set_integral_comp_Lp ContinuousLinearMap.set_integral_compLp
+  setIntegral_congr_ae hs ((L.coeFn_compLp φ).mono fun x hx hx2 => hx)
+#align continuous_linear_map.set_integral_comp_Lp ContinuousLinearMap.setIntegral_compLp
 -/
 
 #print ContinuousLinearMap.continuous_integral_comp_L1 /-
@@ -1448,12 +1448,12 @@ theorem integral_re_add_im {f : α → 𝕜} (hf : Integrable f μ) :
 #align integral_re_add_im integral_re_add_im
 -/
 
-#print set_integral_re_add_im /-
-theorem set_integral_re_add_im {f : α → 𝕜} {i : Set α} (hf : IntegrableOn f i μ) :
+#print setIntegral_re_add_im /-
+theorem setIntegral_re_add_im {f : α → 𝕜} {i : Set α} (hf : IntegrableOn f i μ) :
     ((∫ x in i, RCLike.re (f x) ∂μ : ℝ) : 𝕜) + (∫ x in i, RCLike.im (f x) ∂μ : ℝ) * RCLike.i =
       ∫ x in i, f x ∂μ :=
   integral_re_add_im hf
-#align set_integral_re_add_im set_integral_re_add_im
+#align set_integral_re_add_im setIntegral_re_add_im
 -/
 
 #print fst_integral /-
@@ -1561,20 +1561,20 @@ theorem integral_withDensity_eq_integral_smul₀ {f : α → ℝ≥0} (hf : AEMe
 #align integral_with_density_eq_integral_smul₀ integral_withDensity_eq_integral_smul₀
 -/
 
-#print set_integral_withDensity_eq_set_integral_smul /-
-theorem set_integral_withDensity_eq_set_integral_smul {f : α → ℝ≥0} (f_meas : Measurable f)
+#print setIntegral_withDensity_eq_setIntegral_smul /-
+theorem setIntegral_withDensity_eq_setIntegral_smul {f : α → ℝ≥0} (f_meas : Measurable f)
     (g : α → E) {s : Set α} (hs : MeasurableSet s) :
     (∫ a in s, g a ∂μ.withDensity fun x => f x) = ∫ a in s, f a • g a ∂μ := by
   rw [restrict_with_density hs, integral_withDensity_eq_integral_smul f_meas]
-#align set_integral_with_density_eq_set_integral_smul set_integral_withDensity_eq_set_integral_smul
+#align set_integral_with_density_eq_set_integral_smul setIntegral_withDensity_eq_setIntegral_smul
 -/
 
-#print set_integral_withDensity_eq_set_integral_smul₀ /-
-theorem set_integral_withDensity_eq_set_integral_smul₀ {f : α → ℝ≥0} {s : Set α}
+#print setIntegral_withDensity_eq_setIntegral_smul₀ /-
+theorem setIntegral_withDensity_eq_setIntegral_smul₀ {f : α → ℝ≥0} {s : Set α}
     (hf : AEMeasurable f (μ.restrict s)) (g : α → E) (hs : MeasurableSet s) :
     (∫ a in s, g a ∂μ.withDensity fun x => f x) = ∫ a in s, f a • g a ∂μ := by
   rw [restrict_with_density hs, integral_withDensity_eq_integral_smul₀ hf]
-#align set_integral_with_density_eq_set_integral_smul₀ set_integral_withDensity_eq_set_integral_smul₀
+#align set_integral_with_density_eq_set_integral_smul₀ setIntegral_withDensity_eq_setIntegral_smul₀
 -/
 
 end

mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83

@@ -1047,7 +1047,7 @@ section TendstoMono
 variable {μ : Measure α} [NormedAddCommGroup E] [CompleteSpace E] [NormedSpace ℝ E] {s : ℕ → Set α}
   {f : α → E}
 
-/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:72:38: in filter_upwards #[[], ["with", ident a], ["using", expr le_trans (h_anti.tendsto_indicator _ _ _) (pure_le_nhds _)]]: ./././Mathport/Syntax/Translate/Basic.lean:354:22: unsupported: parse error @ arg 0: next failed, no more args -/
+/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:72:38: in filter_upwards #[[], ["with", ident a], ["using", expr le_trans (h_anti.tendsto_indicator _ _ _) (pure_le_nhds _)]]: ./././Mathport/Syntax/Translate/Basic.lean:355:22: unsupported: parse error @ arg 0: next failed, no more args -/
 #print Antitone.tendsto_set_integral /-
 theorem Antitone.tendsto_set_integral (hsm : ∀ i, MeasurableSet (s i)) (h_anti : Antitone s)
     (hfi : IntegrableOn f (s 0) μ) :
@@ -1069,7 +1069,7 @@ theorem Antitone.tendsto_set_integral (hsm : ∀ i, MeasurableSet (s i)) (h_anti
     exact indicator_le_indicator_of_subset (h_anti (zero_le n)) (fun a => norm_nonneg _) _
   ·
     trace
-      "./././Mathport/Syntax/Translate/Tactic/Builtin.lean:72:38: in filter_upwards #[[], [\"with\", ident a], [\"using\", expr le_trans (h_anti.tendsto_indicator _ _ _) (pure_le_nhds _)]]: ./././Mathport/Syntax/Translate/Basic.lean:354:22: unsupported: parse error @ arg 0: next failed, no more args"
+      "./././Mathport/Syntax/Translate/Tactic/Builtin.lean:72:38: in filter_upwards #[[], [\"with\", ident a], [\"using\", expr le_trans (h_anti.tendsto_indicator _ _ _) (pure_le_nhds _)]]: ./././Mathport/Syntax/Translate/Basic.lean:355:22: unsupported: parse error @ arg 0: next failed, no more args"
 #align antitone.tendsto_set_integral Antitone.tendsto_set_integral
 -/
 
@@ -1296,7 +1296,7 @@ as `continuous_linear_map.comp_Lp`. We take advantage of this construction here.
 
 open scoped ComplexConjugate
 
-variable {μ : Measure α} {𝕜 : Type _} [IsROrC 𝕜] [NormedSpace 𝕜 E] [NormedAddCommGroup F]
+variable {μ : Measure α} {𝕜 : Type _} [RCLike 𝕜] [NormedSpace 𝕜 E] [NormedAddCommGroup F]
   [NormedSpace 𝕜 F] {p : ENNReal}
 
 namespace ContinuousLinearMap
@@ -1404,53 +1404,53 @@ variable [CompleteSpace E] [NormedSpace ℝ E] [CompleteSpace F] [NormedSpace 
 #print integral_ofReal /-
 @[norm_cast]
 theorem integral_ofReal {f : α → ℝ} : ∫ a, (f a : 𝕜) ∂μ = ↑(∫ a, f a ∂μ) :=
-  (@IsROrC.ofRealLI 𝕜 _).integral_comp_comm f
+  (@RCLike.ofRealLI 𝕜 _).integral_comp_comm f
 #align integral_of_real integral_ofReal
 -/
 
 #print integral_re /-
 theorem integral_re {f : α → 𝕜} (hf : Integrable f μ) :
-    ∫ a, IsROrC.re (f a) ∂μ = IsROrC.re (∫ a, f a ∂μ) :=
-  (@IsROrC.reCLM 𝕜 _).integral_comp_comm hf
+    ∫ a, RCLike.re (f a) ∂μ = RCLike.re (∫ a, f a ∂μ) :=
+  (@RCLike.reCLM 𝕜 _).integral_comp_comm hf
 #align integral_re integral_re
 -/
 
 #print integral_im /-
 theorem integral_im {f : α → 𝕜} (hf : Integrable f μ) :
-    ∫ a, IsROrC.im (f a) ∂μ = IsROrC.im (∫ a, f a ∂μ) :=
-  (@IsROrC.imCLM 𝕜 _).integral_comp_comm hf
+    ∫ a, RCLike.im (f a) ∂μ = RCLike.im (∫ a, f a ∂μ) :=
+  (@RCLike.imCLM 𝕜 _).integral_comp_comm hf
 #align integral_im integral_im
 -/
 
 #print integral_conj /-
 theorem integral_conj {f : α → 𝕜} : ∫ a, conj (f a) ∂μ = conj (∫ a, f a ∂μ) :=
-  (@IsROrC.conjLIE 𝕜 _).toLinearIsometry.integral_comp_comm f
+  (@RCLike.conjLIE 𝕜 _).toLinearIsometry.integral_comp_comm f
 #align integral_conj integral_conj
 -/
 
 #print integral_coe_re_add_coe_im /-
 theorem integral_coe_re_add_coe_im {f : α → 𝕜} (hf : Integrable f μ) :
-    ∫ x, (IsROrC.re (f x) : 𝕜) ∂μ + (∫ x, IsROrC.im (f x) ∂μ) * IsROrC.i = ∫ x, f x ∂μ :=
+    ∫ x, (RCLike.re (f x) : 𝕜) ∂μ + (∫ x, RCLike.im (f x) ∂μ) * RCLike.i = ∫ x, f x ∂μ :=
   by
   rw [mul_comm, ← smul_eq_mul, ← integral_smul, ← integral_add]
   · congr
     ext1 x
-    rw [smul_eq_mul, mul_comm, IsROrC.re_add_im]
+    rw [smul_eq_mul, mul_comm, RCLike.re_add_im]
   · exact hf.re.of_real
-  · exact hf.im.of_real.smul IsROrC.i
+  · exact hf.im.of_real.smul RCLike.i
 #align integral_coe_re_add_coe_im integral_coe_re_add_coe_im
 -/
 
 #print integral_re_add_im /-
 theorem integral_re_add_im {f : α → 𝕜} (hf : Integrable f μ) :
-    ((∫ x, IsROrC.re (f x) ∂μ : ℝ) : 𝕜) + (∫ x, IsROrC.im (f x) ∂μ : ℝ) * IsROrC.i = ∫ x, f x ∂μ :=
+    ((∫ x, RCLike.re (f x) ∂μ : ℝ) : 𝕜) + (∫ x, RCLike.im (f x) ∂μ : ℝ) * RCLike.i = ∫ x, f x ∂μ :=
   by rw [← integral_ofReal, ← integral_ofReal, integral_coe_re_add_coe_im hf]
 #align integral_re_add_im integral_re_add_im
 -/
 
 #print set_integral_re_add_im /-
 theorem set_integral_re_add_im {f : α → 𝕜} {i : Set α} (hf : IntegrableOn f i μ) :
-    ((∫ x in i, IsROrC.re (f x) ∂μ : ℝ) : 𝕜) + (∫ x in i, IsROrC.im (f x) ∂μ : ℝ) * IsROrC.i =
+    ((∫ x in i, RCLike.re (f x) ∂μ : ℝ) : 𝕜) + (∫ x in i, RCLike.im (f x) ∂μ : ℝ) * RCLike.i =
       ∫ x in i, f x ∂μ :=
   integral_re_add_im hf
 #align set_integral_re_add_im set_integral_re_add_im
@@ -1477,7 +1477,7 @@ theorem integral_pair {f : α → E} {g : α → F} (hf : Integrable f μ) (hg :
 -/
 
 #print integral_smul_const /-
-theorem integral_smul_const {𝕜 : Type _} [IsROrC 𝕜] [NormedSpace 𝕜 E] (f : α → 𝕜) (c : E) :
+theorem integral_smul_const {𝕜 : Type _} [RCLike 𝕜] [NormedSpace 𝕜 E] (f : α → 𝕜) (c : E) :
     ∫ x, f x • c ∂μ = (∫ x, f x ∂μ) • c :=
   by
   by_cases hf : integrable f μ

mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83

@@ -270,7 +270,7 @@ theorem tendsto_set_integral_of_monotone {ι : Type _} [Countable ι] [Semilatti
   set S := ⋃ i, s i
   have hSm : MeasurableSet S := MeasurableSet.iUnion hsm
   have hsub : ∀ {i}, s i ⊆ S := subset_Union s
-  rw [← with_density_apply _ hSm] at hfi' 
+  rw [← with_density_apply _ hSm] at hfi'
   set ν := μ.with_density fun x => ‖f x‖₊ with hν
   refine' metric.nhds_basis_closed_ball.tendsto_right_iff.2 fun ε ε0 => _
   lift ε to ℝ≥0 using ε0.le
@@ -533,7 +533,7 @@ theorem integral_norm_eq_pos_sub_neg {f : α → ℝ} (hfi : Integrable f μ) :
       refine' set_integral_congr₀ h_meas.compl fun x hx => _
       dsimp only
       rw [Real.norm_eq_abs, abs_eq_neg_self.mpr _]
-      rw [Set.mem_compl_iff, Set.nmem_setOf_iff] at hx 
+      rw [Set.mem_compl_iff, Set.nmem_setOf_iff] at hx
       linarith
     _ = ∫ x in {x | 0 ≤ f x}, f x ∂μ - ∫ x in {x | f x ≤ 0}, f x ∂μ := by
       rw [← set_integral_neg_eq_set_integral_nonpos hfi.1]; congr; ext1 x; simp
@@ -717,7 +717,7 @@ theorem set_integral_gt_gt {R : ℝ} {f : α → ℝ} (hR : 0 ≤ R) (hfm : Meas
       exact le_of_lt hx
   rw [← sub_pos, ← smul_eq_mul, ← set_integral_const, ← integral_sub hfint this,
     set_integral_pos_iff_support_of_nonneg_ae]
-  · rw [← zero_lt_iff] at hμ 
+  · rw [← zero_lt_iff] at hμ
     rwa [Set.inter_eq_self_of_subset_right]
     exact fun x hx => Ne.symm (ne_of_lt <| sub_pos.2 hx)
   · change ∀ᵐ x ∂μ.restrict _, _
@@ -1004,7 +1004,7 @@ theorem integrableOn_iUnion_of_summable_integral_norm {f : α → E} {s : β →
         NNReal) :=
     by rw [← NNReal.summable_coe]; exact h
   have S'' := ENNReal.tsum_coe_eq S'.has_sum
-  simp_rw [ENNReal.coe_nnreal_eq, NNReal.coe_mk, coe_nnnorm] at S'' 
+  simp_rw [ENNReal.coe_nnreal_eq, NNReal.coe_mk, coe_nnnorm] at S''
   convert ENNReal.ofReal_lt_top
 #align measure_theory.integrable_on_Union_of_summable_integral_norm MeasureTheory.integrableOn_iUnion_of_summable_integral_norm
 -/
@@ -1505,7 +1505,7 @@ theorem integral_withDensity_eq_integral_smul {f : α → ℝ≥0} (f_meas : Mea
     · rfl
     · exact integral_nonneg fun x => NNReal.coe_nonneg _
     · refine' ⟨f_meas.coe_nnreal_real.AEMeasurable.AEStronglyMeasurable, _⟩
-      rw [with_density_apply _ s_meas] at hs 
+      rw [with_density_apply _ s_meas] at hs
       rw [has_finite_integral]
       convert hs
       ext1 x

mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83

@@ -1404,27 +1404,27 @@ variable [CompleteSpace E] [NormedSpace ℝ E] [CompleteSpace F] [NormedSpace 
 #print integral_ofReal /-
 @[norm_cast]
 theorem integral_ofReal {f : α → ℝ} : ∫ a, (f a : 𝕜) ∂μ = ↑(∫ a, f a ∂μ) :=
-  (@IsROrC.ofRealLi 𝕜 _).integral_comp_comm f
+  (@IsROrC.ofRealLI 𝕜 _).integral_comp_comm f
 #align integral_of_real integral_ofReal
 -/
 
 #print integral_re /-
 theorem integral_re {f : α → 𝕜} (hf : Integrable f μ) :
     ∫ a, IsROrC.re (f a) ∂μ = IsROrC.re (∫ a, f a ∂μ) :=
-  (@IsROrC.reClm 𝕜 _).integral_comp_comm hf
+  (@IsROrC.reCLM 𝕜 _).integral_comp_comm hf
 #align integral_re integral_re
 -/
 
 #print integral_im /-
 theorem integral_im {f : α → 𝕜} (hf : Integrable f μ) :
     ∫ a, IsROrC.im (f a) ∂μ = IsROrC.im (∫ a, f a ∂μ) :=
-  (@IsROrC.imClm 𝕜 _).integral_comp_comm hf
+  (@IsROrC.imCLM 𝕜 _).integral_comp_comm hf
 #align integral_im integral_im
 -/
 
 #print integral_conj /-
 theorem integral_conj {f : α → 𝕜} : ∫ a, conj (f a) ∂μ = conj (∫ a, f a ∂μ) :=
-  (@IsROrC.conjLie 𝕜 _).toLinearIsometry.integral_comp_comm f
+  (@IsROrC.conjLIE 𝕜 _).toLinearIsometry.integral_comp_comm f
 #align integral_conj integral_conj
 -/
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83

@@ -1021,7 +1021,7 @@ theorem integrableOn_iUnion_of_summable_norm_restrict {f : C(α, E)} {s : β →
   refine'
     integrable_on_Union_of_summable_integral_norm (fun i => (s i).IsCompact.IsClosed.MeasurableSet)
       (fun i => (map_continuous f).ContinuousOn.integrableOn_compact (s i).IsCompact)
-      (summable_of_nonneg_of_le (fun ι => integral_nonneg fun x => norm_nonneg _) (fun i => _) hf)
+      (Summable.of_nonneg_of_le (fun ι => integral_nonneg fun x => norm_nonneg _) (fun i => _) hf)
   rw [← (Real.norm_of_nonneg (integral_nonneg fun a => norm_nonneg _) : ‖_‖ = ∫ x in s i, ‖f x‖ ∂μ)]
   exact
     norm_set_integral_le_of_norm_le_const' (s i).IsCompact.measure_lt_top

mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451

@@ -3,12 +3,12 @@ Copyright (c) 2020 Zhouhang Zhou. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Zhouhang Zhou, Yury Kudryashov
 -/
-import Mathbin.MeasureTheory.Integral.IntegrableOn
-import Mathbin.MeasureTheory.Integral.Bochner
-import Mathbin.MeasureTheory.Function.LocallyIntegrable
-import Mathbin.Order.Filter.IndicatorFunction
-import Mathbin.Topology.MetricSpace.ThickenedIndicator
-import Mathbin.Topology.ContinuousFunction.Compact
+import MeasureTheory.Integral.IntegrableOn
+import MeasureTheory.Integral.Bochner
+import MeasureTheory.Function.LocallyIntegrable
+import Order.Filter.IndicatorFunction
+import Topology.MetricSpace.ThickenedIndicator
+import Topology.ContinuousFunction.Compact
 
 #align_import measure_theory.integral.set_integral from "leanprover-community/mathlib"@"c20927220ef87bb4962ba08bf6da2ce3cf50a6dd"
 
@@ -1047,7 +1047,7 @@ section TendstoMono
 variable {μ : Measure α} [NormedAddCommGroup E] [CompleteSpace E] [NormedSpace ℝ E] {s : ℕ → Set α}
   {f : α → E}
 
-/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:72:38: in filter_upwards #[[], ["with", ident a], ["using", expr le_trans (h_anti.tendsto_indicator _ _ _) (pure_le_nhds _)]]: ./././Mathport/Syntax/Translate/Basic.lean:349:22: unsupported: parse error @ arg 0: next failed, no more args -/
+/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:72:38: in filter_upwards #[[], ["with", ident a], ["using", expr le_trans (h_anti.tendsto_indicator _ _ _) (pure_le_nhds _)]]: ./././Mathport/Syntax/Translate/Basic.lean:354:22: unsupported: parse error @ arg 0: next failed, no more args -/
 #print Antitone.tendsto_set_integral /-
 theorem Antitone.tendsto_set_integral (hsm : ∀ i, MeasurableSet (s i)) (h_anti : Antitone s)
     (hfi : IntegrableOn f (s 0) μ) :
@@ -1069,7 +1069,7 @@ theorem Antitone.tendsto_set_integral (hsm : ∀ i, MeasurableSet (s i)) (h_anti
     exact indicator_le_indicator_of_subset (h_anti (zero_le n)) (fun a => norm_nonneg _) _
   ·
     trace
-      "./././Mathport/Syntax/Translate/Tactic/Builtin.lean:72:38: in filter_upwards #[[], [\"with\", ident a], [\"using\", expr le_trans (h_anti.tendsto_indicator _ _ _) (pure_le_nhds _)]]: ./././Mathport/Syntax/Translate/Basic.lean:349:22: unsupported: parse error @ arg 0: next failed, no more args"
+      "./././Mathport/Syntax/Translate/Tactic/Builtin.lean:72:38: in filter_upwards #[[], [\"with\", ident a], [\"using\", expr le_trans (h_anti.tendsto_indicator _ _ _) (pure_le_nhds _)]]: ./././Mathport/Syntax/Translate/Basic.lean:354:22: unsupported: parse error @ arg 0: next failed, no more args"
 #align antitone.tendsto_set_integral Antitone.tendsto_set_integral
 -/
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345

@@ -2,11 +2,6 @@
 Copyright (c) 2020 Zhouhang Zhou. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Zhouhang Zhou, Yury Kudryashov
-
-! This file was ported from Lean 3 source module measure_theory.integral.set_integral
-! leanprover-community/mathlib commit c20927220ef87bb4962ba08bf6da2ce3cf50a6dd
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.MeasureTheory.Integral.IntegrableOn
 import Mathbin.MeasureTheory.Integral.Bochner
@@ -15,6 +10,8 @@ import Mathbin.Order.Filter.IndicatorFunction
 import Mathbin.Topology.MetricSpace.ThickenedIndicator
 import Mathbin.Topology.ContinuousFunction.Compact
 
+#align_import measure_theory.integral.set_integral from "leanprover-community/mathlib"@"c20927220ef87bb4962ba08bf6da2ce3cf50a6dd"
+
 /-!
 # Set integral
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/9fb8964792b4237dac6200193a0d533f1b3f7423

@@ -75,48 +75,65 @@ variable [NormedAddCommGroup E] {f g : α → E} {s t : Set α} {μ ν : Measure
 
 variable [CompleteSpace E] [NormedSpace ℝ E]
 
+#print MeasureTheory.set_integral_congr_ae₀ /-
 theorem set_integral_congr_ae₀ (hs : NullMeasurableSet s μ) (h : ∀ᵐ x ∂μ, x ∈ s → f x = g x) :
     ∫ x in s, f x ∂μ = ∫ x in s, g x ∂μ :=
   integral_congr_ae ((ae_restrict_iff'₀ hs).2 h)
 #align measure_theory.set_integral_congr_ae₀ MeasureTheory.set_integral_congr_ae₀
+-/
 
+#print MeasureTheory.set_integral_congr_ae /-
 theorem set_integral_congr_ae (hs : MeasurableSet s) (h : ∀ᵐ x ∂μ, x ∈ s → f x = g x) :
     ∫ x in s, f x ∂μ = ∫ x in s, g x ∂μ :=
   integral_congr_ae ((ae_restrict_iff' hs).2 h)
 #align measure_theory.set_integral_congr_ae MeasureTheory.set_integral_congr_ae
+-/
 
+#print MeasureTheory.set_integral_congr₀ /-
 theorem set_integral_congr₀ (hs : NullMeasurableSet s μ) (h : EqOn f g s) :
     ∫ x in s, f x ∂μ = ∫ x in s, g x ∂μ :=
   set_integral_congr_ae₀ hs <| eventually_of_forall h
 #align measure_theory.set_integral_congr₀ MeasureTheory.set_integral_congr₀
+-/
 
+#print MeasureTheory.set_integral_congr /-
 theorem set_integral_congr (hs : MeasurableSet s) (h : EqOn f g s) :
     ∫ x in s, f x ∂μ = ∫ x in s, g x ∂μ :=
   set_integral_congr_ae hs <| eventually_of_forall h
 #align measure_theory.set_integral_congr MeasureTheory.set_integral_congr
+-/
 
+#print MeasureTheory.set_integral_congr_set_ae /-
 theorem set_integral_congr_set_ae (hst : s =ᵐ[μ] t) : ∫ x in s, f x ∂μ = ∫ x in t, f x ∂μ := by
   rw [measure.restrict_congr_set hst]
 #align measure_theory.set_integral_congr_set_ae MeasureTheory.set_integral_congr_set_ae
+-/
 
+#print MeasureTheory.integral_union_ae /-
 theorem integral_union_ae (hst : AEDisjoint μ s t) (ht : NullMeasurableSet t μ)
     (hfs : IntegrableOn f s μ) (hft : IntegrableOn f t μ) :
     ∫ x in s ∪ t, f x ∂μ = ∫ x in s, f x ∂μ + ∫ x in t, f x ∂μ := by
   simp only [integrable_on, measure.restrict_union₀ hst ht, integral_add_measure hfs hft]
 #align measure_theory.integral_union_ae MeasureTheory.integral_union_ae
+-/
 
+#print MeasureTheory.integral_union /-
 theorem integral_union (hst : Disjoint s t) (ht : MeasurableSet t) (hfs : IntegrableOn f s μ)
     (hft : IntegrableOn f t μ) : ∫ x in s ∪ t, f x ∂μ = ∫ x in s, f x ∂μ + ∫ x in t, f x ∂μ :=
   integral_union_ae hst.AEDisjoint ht.NullMeasurableSet hfs hft
 #align measure_theory.integral_union MeasureTheory.integral_union
+-/
 
+#print MeasureTheory.integral_diff /-
 theorem integral_diff (ht : MeasurableSet t) (hfs : IntegrableOn f s μ) (hts : t ⊆ s) :
     ∫ x in s \ t, f x ∂μ = ∫ x in s, f x ∂μ - ∫ x in t, f x ∂μ :=
   by
   rw [eq_sub_iff_add_eq, ← integral_union, diff_union_of_subset hts]
   exacts [disjoint_sdiff_self_left, ht, hfs.mono_set (diff_subset _ _), hfs.mono_set hts]
 #align measure_theory.integral_diff MeasureTheory.integral_diff
+-/
 
+#print MeasureTheory.integral_inter_add_diff₀ /-
 theorem integral_inter_add_diff₀ (ht : NullMeasurableSet t μ) (hfs : IntegrableOn f s μ) :
     ∫ x in s ∩ t, f x ∂μ + ∫ x in s \ t, f x ∂μ = ∫ x in s, f x ∂μ :=
   by
@@ -124,12 +141,16 @@ theorem integral_inter_add_diff₀ (ht : NullMeasurableSet t μ) (hfs : Integrab
   · exact integrable.mono_measure hfs (measure.restrict_mono (inter_subset_left _ _) le_rfl)
   · exact integrable.mono_measure hfs (measure.restrict_mono (diff_subset _ _) le_rfl)
 #align measure_theory.integral_inter_add_diff₀ MeasureTheory.integral_inter_add_diff₀
+-/
 
+#print MeasureTheory.integral_inter_add_diff /-
 theorem integral_inter_add_diff (ht : MeasurableSet t) (hfs : IntegrableOn f s μ) :
     ∫ x in s ∩ t, f x ∂μ + ∫ x in s \ t, f x ∂μ = ∫ x in s, f x ∂μ :=
   integral_inter_add_diff₀ ht.NullMeasurableSet hfs
 #align measure_theory.integral_inter_add_diff MeasureTheory.integral_inter_add_diff
+-/
 
+#print MeasureTheory.integral_finset_biUnion /-
 theorem integral_finset_biUnion {ι : Type _} (t : Finset ι) {s : ι → Set α}
     (hs : ∀ i ∈ t, MeasurableSet (s i)) (h's : Set.Pairwise (↑t) (Disjoint on s))
     (hf : ∀ i ∈ t, IntegrableOn f (s i) μ) :
@@ -145,7 +166,9 @@ theorem integral_finset_biUnion {ι : Type _} (t : Finset ι) {s : ι → Set α
       exact fun i hi => (h's.2 i hi (ne_of_mem_of_not_mem hi hat).symm).1
     · exact Finset.measurableSet_biUnion _ hs.2
 #align measure_theory.integral_finset_bUnion MeasureTheory.integral_finset_biUnion
+-/
 
+#print MeasureTheory.integral_fintype_iUnion /-
 theorem integral_fintype_iUnion {ι : Type _} [Fintype ι] {s : ι → Set α}
     (hs : ∀ i, MeasurableSet (s i)) (h's : Pairwise (Disjoint on s))
     (hf : ∀ i, IntegrableOn f (s i) μ) : ∫ x in ⋃ i, s i, f x ∂μ = ∑ i, ∫ x in s i, f x ∂μ :=
@@ -154,16 +177,20 @@ theorem integral_fintype_iUnion {ι : Type _} [Fintype ι] {s : ι → Set α}
   · simp
   · simp [pairwise_univ, h's]
 #align measure_theory.integral_fintype_Union MeasureTheory.integral_fintype_iUnion
+-/
 
+#print MeasureTheory.integral_empty /-
 theorem integral_empty : ∫ x in ∅, f x ∂μ = 0 := by
   rw [measure.restrict_empty, integral_zero_measure]
 #align measure_theory.integral_empty MeasureTheory.integral_empty
+-/
 
 #print MeasureTheory.integral_univ /-
 theorem integral_univ : ∫ x in univ, f x ∂μ = ∫ x, f x ∂μ := by rw [measure.restrict_univ]
 #align measure_theory.integral_univ MeasureTheory.integral_univ
 -/
 
+#print MeasureTheory.integral_add_compl₀ /-
 theorem integral_add_compl₀ (hs : NullMeasurableSet s μ) (hfi : Integrable f μ) :
     ∫ x in s, f x ∂μ + ∫ x in sᶜ, f x ∂μ = ∫ x, f x ∂μ := by
   rw [←
@@ -171,12 +198,16 @@ theorem integral_add_compl₀ (hs : NullMeasurableSet s μ) (hfi : Integrable f
       hfi.integrable_on,
     union_compl_self, integral_univ]
 #align measure_theory.integral_add_compl₀ MeasureTheory.integral_add_compl₀
+-/
 
+#print MeasureTheory.integral_add_compl /-
 theorem integral_add_compl (hs : MeasurableSet s) (hfi : Integrable f μ) :
     ∫ x in s, f x ∂μ + ∫ x in sᶜ, f x ∂μ = ∫ x, f x ∂μ :=
   integral_add_compl₀ hs.NullMeasurableSet hfi
 #align measure_theory.integral_add_compl MeasureTheory.integral_add_compl
+-/
 
+#print MeasureTheory.integral_indicator /-
 /-- For a function `f` and a measurable set `s`, the integral of `indicator s f`
 over the whole space is equal to `∫ x in s, f x ∂μ` defined as `∫ x, f x ∂(μ.restrict s)`. -/
 theorem integral_indicator (hs : MeasurableSet s) : ∫ x, indicator s f x ∂μ = ∫ x in s, f x ∂μ :=
@@ -192,12 +223,16 @@ theorem integral_indicator (hs : MeasurableSet s) : ∫ x, indicator s f x ∂μ
         (integral_congr_ae (indicator_ae_eq_restrict_compl hs)))
     _ = ∫ x in s, f x ∂μ := by simp
 #align measure_theory.integral_indicator MeasureTheory.integral_indicator
+-/
 
+#print MeasureTheory.set_integral_indicator /-
 theorem set_integral_indicator (ht : MeasurableSet t) :
     ∫ x in s, t.indicator f x ∂μ = ∫ x in s ∩ t, f x ∂μ := by
   rw [integral_indicator ht, measure.restrict_restrict ht, Set.inter_comm]
 #align measure_theory.set_integral_indicator MeasureTheory.set_integral_indicator
+-/
 
+#print MeasureTheory.ofReal_set_integral_one_of_measure_ne_top /-
 theorem ofReal_set_integral_one_of_measure_ne_top {α : Type _} {m : MeasurableSpace α}
     {μ : Measure α} {s : Set α} (hs : μ s ≠ ∞) : ENNReal.ofReal (∫ x in s, (1 : ℝ) ∂μ) = μ s :=
   calc
@@ -209,12 +244,16 @@ theorem ofReal_set_integral_one_of_measure_ne_top {α : Type _} {m : MeasurableS
       simp only [nnnorm_one, ENNReal.coe_one]
     _ = μ s := set_lintegral_one _
 #align measure_theory.of_real_set_integral_one_of_measure_ne_top MeasureTheory.ofReal_set_integral_one_of_measure_ne_top
+-/
 
+#print MeasureTheory.ofReal_set_integral_one /-
 theorem ofReal_set_integral_one {α : Type _} {m : MeasurableSpace α} (μ : Measure α)
     [IsFiniteMeasure μ] (s : Set α) : ENNReal.ofReal (∫ x in s, (1 : ℝ) ∂μ) = μ s :=
   ofReal_set_integral_one_of_measure_ne_top (measure_ne_top μ s)
 #align measure_theory.of_real_set_integral_one MeasureTheory.ofReal_set_integral_one
+-/
 
+#print MeasureTheory.integral_piecewise /-
 theorem integral_piecewise [DecidablePred (· ∈ s)] (hs : MeasurableSet s) (hf : IntegrableOn f s μ)
     (hg : IntegrableOn g (sᶜ) μ) :
     ∫ x, s.piecewise f g x ∂μ = ∫ x in s, f x ∂μ + ∫ x in sᶜ, g x ∂μ := by
@@ -222,7 +261,9 @@ theorem integral_piecewise [DecidablePred (· ∈ s)] (hs : MeasurableSet s) (hf
     integral_add' (hf.integrable_indicator hs) (hg.integrable_indicator hs.compl),
     integral_indicator hs, integral_indicator hs.compl]
 #align measure_theory.integral_piecewise MeasureTheory.integral_piecewise
+-/
 
+#print MeasureTheory.tendsto_set_integral_of_monotone /-
 theorem tendsto_set_integral_of_monotone {ι : Type _} [Countable ι] [SemilatticeSup ι]
     {s : ι → Set α} (hsm : ∀ i, MeasurableSet (s i)) (h_mono : Monotone s)
     (hfi : IntegrableOn f (⋃ n, s n) μ) :
@@ -246,7 +287,9 @@ theorem tendsto_set_integral_of_monotone {ι : Type _} [Countable ι] [Semilatti
   exacts [tsub_le_iff_tsub_le.mp hi.1,
     (hi.2.trans_lt <| ENNReal.add_lt_top.2 ⟨hfi', ENNReal.coe_lt_top⟩).Ne]
 #align measure_theory.tendsto_set_integral_of_monotone MeasureTheory.tendsto_set_integral_of_monotone
+-/
 
+#print MeasureTheory.hasSum_integral_iUnion_ae /-
 theorem hasSum_integral_iUnion_ae {ι : Type _} [Countable ι] {s : ι → Set α}
     (hm : ∀ i, NullMeasurableSet (s i) μ) (hd : Pairwise (AEDisjoint μ on s))
     (hfi : IntegrableOn f (⋃ i, s i) μ) :
@@ -255,7 +298,9 @@ theorem hasSum_integral_iUnion_ae {ι : Type _} [Countable ι] {s : ι → Set 
   simp only [integrable_on, measure.restrict_Union_ae hd hm] at hfi ⊢
   exact has_sum_integral_measure hfi
 #align measure_theory.has_sum_integral_Union_ae MeasureTheory.hasSum_integral_iUnion_ae
+-/
 
+#print MeasureTheory.hasSum_integral_iUnion /-
 theorem hasSum_integral_iUnion {ι : Type _} [Countable ι] {s : ι → Set α}
     (hm : ∀ i, MeasurableSet (s i)) (hd : Pairwise (Disjoint on s))
     (hfi : IntegrableOn f (⋃ i, s i) μ) :
@@ -263,19 +308,25 @@ theorem hasSum_integral_iUnion {ι : Type _} [Countable ι] {s : ι → Set α}
   hasSum_integral_iUnion_ae (fun i => (hm i).NullMeasurableSet) (hd.mono fun i j h => h.AEDisjoint)
     hfi
 #align measure_theory.has_sum_integral_Union MeasureTheory.hasSum_integral_iUnion
+-/
 
+#print MeasureTheory.integral_iUnion /-
 theorem integral_iUnion {ι : Type _} [Countable ι] {s : ι → Set α} (hm : ∀ i, MeasurableSet (s i))
     (hd : Pairwise (Disjoint on s)) (hfi : IntegrableOn f (⋃ i, s i) μ) :
     ∫ a in ⋃ n, s n, f a ∂μ = ∑' n, ∫ a in s n, f a ∂μ :=
   (HasSum.tsum_eq (hasSum_integral_iUnion hm hd hfi)).symm
 #align measure_theory.integral_Union MeasureTheory.integral_iUnion
+-/
 
+#print MeasureTheory.integral_iUnion_ae /-
 theorem integral_iUnion_ae {ι : Type _} [Countable ι] {s : ι → Set α}
     (hm : ∀ i, NullMeasurableSet (s i) μ) (hd : Pairwise (AEDisjoint μ on s))
     (hfi : IntegrableOn f (⋃ i, s i) μ) : ∫ a in ⋃ n, s n, f a ∂μ = ∑' n, ∫ a in s n, f a ∂μ :=
   (HasSum.tsum_eq (hasSum_integral_iUnion_ae hm hd hfi)).symm
 #align measure_theory.integral_Union_ae MeasureTheory.integral_iUnion_ae
+-/
 
+#print MeasureTheory.set_integral_eq_zero_of_ae_eq_zero /-
 theorem set_integral_eq_zero_of_ae_eq_zero (ht_eq : ∀ᵐ x ∂μ, x ∈ t → f x = 0) :
     ∫ x in t, f x ∂μ = 0 :=
   by
@@ -294,11 +345,15 @@ theorem set_integral_eq_zero_of_ae_eq_zero (ht_eq : ∀ᵐ x ∂μ, x ∈ t →
   rw [← this]
   exact integral_congr_ae hf.ae_eq_mk
 #align measure_theory.set_integral_eq_zero_of_ae_eq_zero MeasureTheory.set_integral_eq_zero_of_ae_eq_zero
+-/
 
+#print MeasureTheory.set_integral_eq_zero_of_forall_eq_zero /-
 theorem set_integral_eq_zero_of_forall_eq_zero (ht_eq : ∀ x ∈ t, f x = 0) : ∫ x in t, f x ∂μ = 0 :=
   set_integral_eq_zero_of_ae_eq_zero (eventually_of_forall ht_eq)
 #align measure_theory.set_integral_eq_zero_of_forall_eq_zero MeasureTheory.set_integral_eq_zero_of_forall_eq_zero
+-/
 
+#print MeasureTheory.integral_union_eq_left_of_ae_aux /-
 theorem integral_union_eq_left_of_ae_aux (ht_eq : ∀ᵐ x ∂μ.restrict t, f x = 0)
     (haux : StronglyMeasurable f) (H : IntegrableOn f (s ∪ t) μ) :
     ∫ x in s ∪ t, f x ∂μ = ∫ x in s, f x ∂μ :=
@@ -316,7 +371,9 @@ theorem integral_union_eq_left_of_ae_aux (ht_eq : ∀ᵐ x ∂μ.restrict t, f x
   rw [measure_zero_iff_ae_nmem]
   filter_upwards [ae_imp_of_ae_restrict ht_eq] with x hx h'x using h'x.2 (hx h'x.1)
 #align measure_theory.integral_union_eq_left_of_ae_aux MeasureTheory.integral_union_eq_left_of_ae_aux
+-/
 
+#print MeasureTheory.integral_union_eq_left_of_ae /-
 theorem integral_union_eq_left_of_ae (ht_eq : ∀ᵐ x ∂μ.restrict t, f x = 0) :
     ∫ x in s ∪ t, f x ∂μ = ∫ x in s, f x ∂μ :=
   by
@@ -337,17 +394,23 @@ theorem integral_union_eq_left_of_ae (ht_eq : ∀ᵐ x ∂μ.restrict t, f x = 0
       integral_congr_ae
         (ae_mono (measure.restrict_mono (subset_union_left s t) le_rfl) H.1.ae_eq_mk.symm)
 #align measure_theory.integral_union_eq_left_of_ae MeasureTheory.integral_union_eq_left_of_ae
+-/
 
+#print MeasureTheory.integral_union_eq_left_of_forall₀ /-
 theorem integral_union_eq_left_of_forall₀ {f : α → E} (ht : NullMeasurableSet t μ)
     (ht_eq : ∀ x ∈ t, f x = 0) : ∫ x in s ∪ t, f x ∂μ = ∫ x in s, f x ∂μ :=
   integral_union_eq_left_of_ae ((ae_restrict_iff'₀ ht).2 (eventually_of_forall ht_eq))
 #align measure_theory.integral_union_eq_left_of_forall₀ MeasureTheory.integral_union_eq_left_of_forall₀
+-/
 
+#print MeasureTheory.integral_union_eq_left_of_forall /-
 theorem integral_union_eq_left_of_forall {f : α → E} (ht : MeasurableSet t)
     (ht_eq : ∀ x ∈ t, f x = 0) : ∫ x in s ∪ t, f x ∂μ = ∫ x in s, f x ∂μ :=
   integral_union_eq_left_of_forall₀ ht.NullMeasurableSet ht_eq
 #align measure_theory.integral_union_eq_left_of_forall MeasureTheory.integral_union_eq_left_of_forall
+-/
 
+#print MeasureTheory.set_integral_eq_of_subset_of_ae_diff_eq_zero_aux /-
 theorem set_integral_eq_of_subset_of_ae_diff_eq_zero_aux (hts : s ⊆ t)
     (h't : ∀ᵐ x ∂μ, x ∈ t \ s → f x = 0) (haux : StronglyMeasurable f)
     (h'aux : IntegrableOn f t μ) : ∫ x in t, f x ∂μ = ∫ x in s, f x ∂μ :=
@@ -376,7 +439,9 @@ theorem set_integral_eq_of_subset_of_ae_diff_eq_zero_aux (hts : s ⊆ t)
       rw [set_integral_eq_zero_of_forall_eq_zero this, zero_add]
     _ = ∫ x in s, f x ∂μ := by rw [integral_inter_add_diff hk (h'aux.mono hts le_rfl)]
 #align measure_theory.set_integral_eq_of_subset_of_ae_diff_eq_zero_aux MeasureTheory.set_integral_eq_of_subset_of_ae_diff_eq_zero_aux
+-/
 
+#print MeasureTheory.set_integral_eq_of_subset_of_ae_diff_eq_zero /-
 /-- If a function vanishes almost everywhere on `t \ s` with `s ⊆ t`, then its integrals on `s`
 and `t` coincide if `t` is null-measurable. -/
 theorem set_integral_eq_of_subset_of_ae_diff_eq_zero (ht : NullMeasurableSet t μ) (hts : s ⊆ t)
@@ -400,7 +465,9 @@ theorem set_integral_eq_of_subset_of_ae_diff_eq_zero (ht : NullMeasurableSet t 
       apply ae_restrict_of_ae_restrict_of_subset hts
       exact h.1.ae_eq_mk.symm
 #align measure_theory.set_integral_eq_of_subset_of_ae_diff_eq_zero MeasureTheory.set_integral_eq_of_subset_of_ae_diff_eq_zero
+-/
 
+#print MeasureTheory.set_integral_eq_of_subset_of_forall_diff_eq_zero /-
 /-- If a function vanishes on `t \ s` with `s ⊆ t`, then its integrals on `s`
 and `t` coincide if `t` is measurable. -/
 theorem set_integral_eq_of_subset_of_forall_diff_eq_zero (ht : MeasurableSet t) (hts : s ⊆ t)
@@ -408,7 +475,9 @@ theorem set_integral_eq_of_subset_of_forall_diff_eq_zero (ht : MeasurableSet t)
   set_integral_eq_of_subset_of_ae_diff_eq_zero ht.NullMeasurableSet hts
     (eventually_of_forall fun x hx => h't x hx)
 #align measure_theory.set_integral_eq_of_subset_of_forall_diff_eq_zero MeasureTheory.set_integral_eq_of_subset_of_forall_diff_eq_zero
+-/
 
+#print MeasureTheory.set_integral_eq_integral_of_ae_compl_eq_zero /-
 /-- If a function vanishes almost everywhere on `sᶜ`, then its integral on `s`
 coincides with its integral on the whole space. -/
 theorem set_integral_eq_integral_of_ae_compl_eq_zero (h : ∀ᵐ x ∂μ, x ∉ s → f x = 0) :
@@ -419,13 +488,16 @@ theorem set_integral_eq_integral_of_ae_compl_eq_zero (h : ∀ᵐ x ∂μ, x ∉
   apply set_integral_eq_of_subset_of_ae_diff_eq_zero null_measurable_set_univ (subset_univ _)
   filter_upwards [h] with x hx h'x using hx h'x.2
 #align measure_theory.set_integral_eq_integral_of_ae_compl_eq_zero MeasureTheory.set_integral_eq_integral_of_ae_compl_eq_zero
+-/
 
+#print MeasureTheory.set_integral_eq_integral_of_forall_compl_eq_zero /-
 /-- If a function vanishes on `sᶜ`, then its integral on `s` coincides with its integral on the
 whole space. -/
 theorem set_integral_eq_integral_of_forall_compl_eq_zero (h : ∀ x, x ∉ s → f x = 0) :
     ∫ x in s, f x ∂μ = ∫ x, f x ∂μ :=
   set_integral_eq_integral_of_ae_compl_eq_zero (eventually_of_forall h)
 #align measure_theory.set_integral_eq_integral_of_forall_compl_eq_zero MeasureTheory.set_integral_eq_integral_of_forall_compl_eq_zero
+-/
 
 #print MeasureTheory.set_integral_neg_eq_set_integral_nonpos /-
 theorem set_integral_neg_eq_set_integral_nonpos [LinearOrder E] {f : α → E}
@@ -442,6 +514,7 @@ theorem set_integral_neg_eq_set_integral_nonpos [LinearOrder E] {f : α → E}
 #align measure_theory.set_integral_neg_eq_set_integral_nonpos MeasureTheory.set_integral_neg_eq_set_integral_nonpos
 -/
 
+#print MeasureTheory.integral_norm_eq_pos_sub_neg /-
 theorem integral_norm_eq_pos_sub_neg {f : α → ℝ} (hfi : Integrable f μ) :
     ∫ x, ‖f x‖ ∂μ = ∫ x in {x | 0 ≤ f x}, f x ∂μ - ∫ x in {x | f x ≤ 0}, f x ∂μ :=
   have h_meas : NullMeasurableSet {x | 0 ≤ f x} μ :=
@@ -468,6 +541,7 @@ theorem integral_norm_eq_pos_sub_neg {f : α → ℝ} (hfi : Integrable f μ) :
     _ = ∫ x in {x | 0 ≤ f x}, f x ∂μ - ∫ x in {x | f x ≤ 0}, f x ∂μ := by
       rw [← set_integral_neg_eq_set_integral_nonpos hfi.1]; congr; ext1 x; simp
 #align measure_theory.integral_norm_eq_pos_sub_neg MeasureTheory.integral_norm_eq_pos_sub_neg
+-/
 
 #print MeasureTheory.set_integral_const /-
 theorem set_integral_const (c : E) : ∫ x in s, c ∂μ = (μ s).toReal • c := by
@@ -475,18 +549,23 @@ theorem set_integral_const (c : E) : ∫ x in s, c ∂μ = (μ s).toReal • c :
 #align measure_theory.set_integral_const MeasureTheory.set_integral_const
 -/
 
+#print MeasureTheory.integral_indicator_const /-
 @[simp]
 theorem integral_indicator_const (e : E) ⦃s : Set α⦄ (s_meas : MeasurableSet s) :
     ∫ a : α, s.indicator (fun x : α => e) a ∂μ = (μ s).toReal • e := by
   rw [integral_indicator s_meas, ← set_integral_const]
 #align measure_theory.integral_indicator_const MeasureTheory.integral_indicator_const
+-/
 
+#print MeasureTheory.integral_indicator_one /-
 @[simp]
 theorem integral_indicator_one ⦃s : Set α⦄ (hs : MeasurableSet s) :
     ∫ a, s.indicator 1 a ∂μ = (μ s).toReal :=
   (integral_indicator_const 1 hs).trans ((smul_eq_mul _).trans (mul_one _))
 #align measure_theory.integral_indicator_one MeasureTheory.integral_indicator_one
+-/
 
+#print MeasureTheory.set_integral_indicatorConstLp /-
 theorem set_integral_indicatorConstLp {p : ℝ≥0∞} (hs : MeasurableSet s) (ht : MeasurableSet t)
     (hμt : μ t ≠ ∞) (x : E) : ∫ a in s, indicatorConstLp p ht hμt x a ∂μ = (μ (t ∩ s)).toReal • x :=
   calc
@@ -494,7 +573,9 @@ theorem set_integral_indicatorConstLp {p : ℝ≥0∞} (hs : MeasurableSet s) (h
       rw [set_integral_congr_ae hs (indicator_const_Lp_coe_fn.mono fun x hx hxs => hx)]
     _ = (μ (t ∩ s)).toReal • x := by rw [integral_indicator_const _ ht, measure.restrict_apply ht]
 #align measure_theory.set_integral_indicator_const_Lp MeasureTheory.set_integral_indicatorConstLp
+-/
 
+#print MeasureTheory.integral_indicatorConstLp /-
 theorem integral_indicatorConstLp {p : ℝ≥0∞} (ht : MeasurableSet t) (hμt : μ t ≠ ∞) (x : E) :
     ∫ a, indicatorConstLp p ht hμt x a ∂μ = (μ t).toReal • x :=
   calc
@@ -503,6 +584,7 @@ theorem integral_indicatorConstLp {p : ℝ≥0∞} (ht : MeasurableSet t) (hμt
     _ = (μ (t ∩ univ)).toReal • x := (set_integral_indicatorConstLp MeasurableSet.univ ht hμt x)
     _ = (μ t).toReal • x := by rw [inter_univ]
 #align measure_theory.integral_indicator_const_Lp MeasureTheory.integral_indicatorConstLp
+-/
 
 #print MeasureTheory.set_integral_map /-
 theorem set_integral_map {β} [MeasurableSpace β] {g : α → β} {f : β → E} {s : Set β}
@@ -515,35 +597,46 @@ theorem set_integral_map {β} [MeasurableSpace β] {g : α → β} {f : β → E
 #align measure_theory.set_integral_map MeasureTheory.set_integral_map
 -/
 
+#print MeasurableEmbedding.set_integral_map /-
 theorem MeasurableEmbedding.set_integral_map {β} {_ : MeasurableSpace β} {f : α → β}
     (hf : MeasurableEmbedding f) (g : β → E) (s : Set β) :
     ∫ y in s, g y ∂Measure.map f μ = ∫ x in f ⁻¹' s, g (f x) ∂μ := by
   rw [hf.restrict_map, hf.integral_map]
 #align measurable_embedding.set_integral_map MeasurableEmbedding.set_integral_map
+-/
 
+#print ClosedEmbedding.set_integral_map /-
 theorem ClosedEmbedding.set_integral_map [TopologicalSpace α] [BorelSpace α] {β} [MeasurableSpace β]
     [TopologicalSpace β] [BorelSpace β] {g : α → β} {f : β → E} (s : Set β)
     (hg : ClosedEmbedding g) : ∫ y in s, f y ∂Measure.map g μ = ∫ x in g ⁻¹' s, f (g x) ∂μ :=
   hg.MeasurableEmbedding.set_integral_map _ _
 #align closed_embedding.set_integral_map ClosedEmbedding.set_integral_map
+-/
 
+#print MeasureTheory.MeasurePreserving.set_integral_preimage_emb /-
 theorem MeasurePreserving.set_integral_preimage_emb {β} {_ : MeasurableSpace β} {f : α → β} {ν}
     (h₁ : MeasurePreserving f μ ν) (h₂ : MeasurableEmbedding f) (g : β → E) (s : Set β) :
     ∫ x in f ⁻¹' s, g (f x) ∂μ = ∫ y in s, g y ∂ν :=
   (h₁.restrict_preimage_emb h₂ s).integral_comp h₂ _
 #align measure_theory.measure_preserving.set_integral_preimage_emb MeasureTheory.MeasurePreserving.set_integral_preimage_emb
+-/
 
+#print MeasureTheory.MeasurePreserving.set_integral_image_emb /-
 theorem MeasurePreserving.set_integral_image_emb {β} {_ : MeasurableSpace β} {f : α → β} {ν}
     (h₁ : MeasurePreserving f μ ν) (h₂ : MeasurableEmbedding f) (g : β → E) (s : Set α) :
     ∫ y in f '' s, g y ∂ν = ∫ x in s, g (f x) ∂μ :=
   Eq.symm <| (h₁.restrict_image_emb h₂ s).integral_comp h₂ _
 #align measure_theory.measure_preserving.set_integral_image_emb MeasureTheory.MeasurePreserving.set_integral_image_emb
+-/
 
+#print MeasureTheory.set_integral_map_equiv /-
 theorem set_integral_map_equiv {β} [MeasurableSpace β] (e : α ≃ᵐ β) (f : β → E) (s : Set β) :
     ∫ y in s, f y ∂Measure.map e μ = ∫ x in e ⁻¹' s, f (e x) ∂μ :=
   e.MeasurableEmbedding.set_integral_map f s
 #align measure_theory.set_integral_map_equiv MeasureTheory.set_integral_map_equiv
+-/
 
+#print MeasureTheory.norm_set_integral_le_of_norm_le_const_ae /-
 theorem norm_set_integral_le_of_norm_le_const_ae {C : ℝ} (hs : μ s < ∞)
     (hC : ∀ᵐ x ∂μ.restrict s, ‖f x‖ ≤ C) : ‖∫ x in s, f x ∂μ‖ ≤ C * (μ s).toReal :=
   by
@@ -551,7 +644,9 @@ theorem norm_set_integral_le_of_norm_le_const_ae {C : ℝ} (hs : μ s < ∞)
   haveI : is_finite_measure (μ.restrict s) := ⟨‹_›⟩
   exact norm_integral_le_of_norm_le_const hC
 #align measure_theory.norm_set_integral_le_of_norm_le_const_ae MeasureTheory.norm_set_integral_le_of_norm_le_const_ae
+-/
 
+#print MeasureTheory.norm_set_integral_le_of_norm_le_const_ae' /-
 theorem norm_set_integral_le_of_norm_le_const_ae' {C : ℝ} (hs : μ s < ∞)
     (hC : ∀ᵐ x ∂μ, x ∈ s → ‖f x‖ ≤ C) (hfm : AEStronglyMeasurable f (μ.restrict s)) :
     ‖∫ x in s, f x ∂μ‖ ≤ C * (μ s).toReal :=
@@ -567,22 +662,29 @@ theorem norm_set_integral_le_of_norm_le_const_ae' {C : ℝ} (hs : μ s < ∞)
   filter_upwards [hfm.ae_eq_mk, (ae_restrict_iff B).2 A] with _ h1 _
   rwa [h1]
 #align measure_theory.norm_set_integral_le_of_norm_le_const_ae' MeasureTheory.norm_set_integral_le_of_norm_le_const_ae'
+-/
 
+#print MeasureTheory.norm_set_integral_le_of_norm_le_const_ae'' /-
 theorem norm_set_integral_le_of_norm_le_const_ae'' {C : ℝ} (hs : μ s < ∞) (hsm : MeasurableSet s)
     (hC : ∀ᵐ x ∂μ, x ∈ s → ‖f x‖ ≤ C) : ‖∫ x in s, f x ∂μ‖ ≤ C * (μ s).toReal :=
   norm_set_integral_le_of_norm_le_const_ae hs <| by
     rwa [ae_restrict_eq hsm, eventually_inf_principal]
 #align measure_theory.norm_set_integral_le_of_norm_le_const_ae'' MeasureTheory.norm_set_integral_le_of_norm_le_const_ae''
+-/
 
+#print MeasureTheory.norm_set_integral_le_of_norm_le_const /-
 theorem norm_set_integral_le_of_norm_le_const {C : ℝ} (hs : μ s < ∞) (hC : ∀ x ∈ s, ‖f x‖ ≤ C)
     (hfm : AEStronglyMeasurable f (μ.restrict s)) : ‖∫ x in s, f x ∂μ‖ ≤ C * (μ s).toReal :=
   norm_set_integral_le_of_norm_le_const_ae' hs (eventually_of_forall hC) hfm
 #align measure_theory.norm_set_integral_le_of_norm_le_const MeasureTheory.norm_set_integral_le_of_norm_le_const
+-/
 
+#print MeasureTheory.norm_set_integral_le_of_norm_le_const' /-
 theorem norm_set_integral_le_of_norm_le_const' {C : ℝ} (hs : μ s < ∞) (hsm : MeasurableSet s)
     (hC : ∀ x ∈ s, ‖f x‖ ≤ C) : ‖∫ x in s, f x ∂μ‖ ≤ C * (μ s).toReal :=
   norm_set_integral_le_of_norm_le_const_ae'' hs hsm <| eventually_of_forall hC
 #align measure_theory.norm_set_integral_le_of_norm_le_const' MeasureTheory.norm_set_integral_le_of_norm_le_const'
+-/
 
 #print MeasureTheory.set_integral_eq_zero_iff_of_nonneg_ae /-
 theorem set_integral_eq_zero_iff_of_nonneg_ae {f : α → ℝ} (hf : 0 ≤ᵐ[μ.restrict s] f)
@@ -601,6 +703,7 @@ theorem set_integral_pos_iff_support_of_nonneg_ae {f : α → ℝ} (hf : 0 ≤
 #align measure_theory.set_integral_pos_iff_support_of_nonneg_ae MeasureTheory.set_integral_pos_iff_support_of_nonneg_ae
 -/
 
+#print MeasureTheory.set_integral_gt_gt /-
 theorem set_integral_gt_gt {R : ℝ} {f : α → ℝ} (hR : 0 ≤ R) (hfm : Measurable f)
     (hfint : IntegrableOn f {x | ↑R < f x} μ) (hμ : μ {x | ↑R < f x} ≠ 0) :
     (μ {x | ↑R < f x}).toReal * R < ∫ x in {x | ↑R < f x}, f x ∂μ :=
@@ -626,6 +729,7 @@ theorem set_integral_gt_gt {R : ℝ} {f : α → ℝ} (hR : 0 ≤ R) (hfm : Meas
     · exact measurableSet_le measurable_zero (hfm.sub measurable_const)
   · exact integrable.sub hfint this
 #align measure_theory.set_integral_gt_gt MeasureTheory.set_integral_gt_gt
+-/
 
 #print MeasureTheory.set_integral_trim /-
 theorem set_integral_trim {α} {m m0 : MeasurableSpace α} {μ : Measure α} (hm : m ≤ m0) {f : α → E}
@@ -646,40 +750,54 @@ section PartialOrder
 
 variable [PartialOrder α] {a b : α}
 
+#print MeasureTheory.integral_Icc_eq_integral_Ioc' /-
 theorem integral_Icc_eq_integral_Ioc' (ha : μ {a} = 0) :
     ∫ t in Icc a b, f t ∂μ = ∫ t in Ioc a b, f t ∂μ :=
   set_integral_congr_set_ae (Ioc_ae_eq_Icc' ha).symm
 #align measure_theory.integral_Icc_eq_integral_Ioc' MeasureTheory.integral_Icc_eq_integral_Ioc'
+-/
 
+#print MeasureTheory.integral_Icc_eq_integral_Ico' /-
 theorem integral_Icc_eq_integral_Ico' (hb : μ {b} = 0) :
     ∫ t in Icc a b, f t ∂μ = ∫ t in Ico a b, f t ∂μ :=
   set_integral_congr_set_ae (Ico_ae_eq_Icc' hb).symm
 #align measure_theory.integral_Icc_eq_integral_Ico' MeasureTheory.integral_Icc_eq_integral_Ico'
+-/
 
+#print MeasureTheory.integral_Ioc_eq_integral_Ioo' /-
 theorem integral_Ioc_eq_integral_Ioo' (hb : μ {b} = 0) :
     ∫ t in Ioc a b, f t ∂μ = ∫ t in Ioo a b, f t ∂μ :=
   set_integral_congr_set_ae (Ioo_ae_eq_Ioc' hb).symm
 #align measure_theory.integral_Ioc_eq_integral_Ioo' MeasureTheory.integral_Ioc_eq_integral_Ioo'
+-/
 
+#print MeasureTheory.integral_Ico_eq_integral_Ioo' /-
 theorem integral_Ico_eq_integral_Ioo' (ha : μ {a} = 0) :
     ∫ t in Ico a b, f t ∂μ = ∫ t in Ioo a b, f t ∂μ :=
   set_integral_congr_set_ae (Ioo_ae_eq_Ico' ha).symm
 #align measure_theory.integral_Ico_eq_integral_Ioo' MeasureTheory.integral_Ico_eq_integral_Ioo'
+-/
 
+#print MeasureTheory.integral_Icc_eq_integral_Ioo' /-
 theorem integral_Icc_eq_integral_Ioo' (ha : μ {a} = 0) (hb : μ {b} = 0) :
     ∫ t in Icc a b, f t ∂μ = ∫ t in Ioo a b, f t ∂μ :=
   set_integral_congr_set_ae (Ioo_ae_eq_Icc' ha hb).symm
 #align measure_theory.integral_Icc_eq_integral_Ioo' MeasureTheory.integral_Icc_eq_integral_Ioo'
+-/
 
+#print MeasureTheory.integral_Iic_eq_integral_Iio' /-
 theorem integral_Iic_eq_integral_Iio' (ha : μ {a} = 0) :
     ∫ t in Iic a, f t ∂μ = ∫ t in Iio a, f t ∂μ :=
   set_integral_congr_set_ae (Iio_ae_eq_Iic' ha).symm
 #align measure_theory.integral_Iic_eq_integral_Iio' MeasureTheory.integral_Iic_eq_integral_Iio'
+-/
 
+#print MeasureTheory.integral_Ici_eq_integral_Ioi' /-
 theorem integral_Ici_eq_integral_Ioi' (ha : μ {a} = 0) :
     ∫ t in Ici a, f t ∂μ = ∫ t in Ioi a, f t ∂μ :=
   set_integral_congr_set_ae (Ioi_ae_eq_Ici' ha).symm
 #align measure_theory.integral_Ici_eq_integral_Ioi' MeasureTheory.integral_Ici_eq_integral_Ioi'
+-/
 
 variable [NoAtoms μ]
 
@@ -741,29 +859,33 @@ theorem set_integral_mono_ae_restrict (h : f ≤ᵐ[μ.restrict s] g) :
 #align measure_theory.set_integral_mono_ae_restrict MeasureTheory.set_integral_mono_ae_restrict
 -/
 
+#print MeasureTheory.set_integral_mono_ae /-
 theorem set_integral_mono_ae (h : f ≤ᵐ[μ] g) : ∫ a in s, f a ∂μ ≤ ∫ a in s, g a ∂μ :=
   set_integral_mono_ae_restrict hf hg (ae_restrict_of_ae h)
 #align measure_theory.set_integral_mono_ae MeasureTheory.set_integral_mono_ae
+-/
 
+#print MeasureTheory.set_integral_mono_on /-
 theorem set_integral_mono_on (hs : MeasurableSet s) (h : ∀ x ∈ s, f x ≤ g x) :
     ∫ a in s, f a ∂μ ≤ ∫ a in s, g a ∂μ :=
   set_integral_mono_ae_restrict hf hg
     (by simp [hs, eventually_le, eventually_inf_principal, ae_of_all _ h])
 #align measure_theory.set_integral_mono_on MeasureTheory.set_integral_mono_on
+-/
 
-include hf hg
-
+#print MeasureTheory.set_integral_mono_on_ae /-
 -- why do I need this include, but we don't need it in other lemmas?
 theorem set_integral_mono_on_ae (hs : MeasurableSet s) (h : ∀ᵐ x ∂μ, x ∈ s → f x ≤ g x) :
     ∫ a in s, f a ∂μ ≤ ∫ a in s, g a ∂μ := by refine' set_integral_mono_ae_restrict hf hg _;
   rwa [eventually_le, ae_restrict_iff' hs]
 #align measure_theory.set_integral_mono_on_ae MeasureTheory.set_integral_mono_on_ae
+-/
 
-omit hf hg
-
+#print MeasureTheory.set_integral_mono /-
 theorem set_integral_mono (h : f ≤ g) : ∫ a in s, f a ∂μ ≤ ∫ a in s, g a ∂μ :=
   integral_mono hf hg h
 #align measure_theory.set_integral_mono MeasureTheory.set_integral_mono
+-/
 
 #print MeasureTheory.set_integral_mono_set /-
 theorem set_integral_mono_set (hfi : IntegrableOn f t μ) (hf : 0 ≤ᵐ[μ.restrict t] f)
@@ -772,6 +894,7 @@ theorem set_integral_mono_set (hfi : IntegrableOn f t μ) (hf : 0 ≤ᵐ[μ.rest
 #align measure_theory.set_integral_mono_set MeasureTheory.set_integral_mono_set
 -/
 
+#print MeasureTheory.set_integral_ge_of_const_le /-
 theorem set_integral_ge_of_const_le {c : ℝ} (hs : MeasurableSet s) (hμs : μ s ≠ ∞)
     (hf : ∀ x ∈ s, c ≤ f x) (hfint : IntegrableOn (fun x : α => f x) s μ) :
     c * (μ s).toReal ≤ ∫ x in s, f x ∂μ :=
@@ -779,6 +902,7 @@ theorem set_integral_ge_of_const_le {c : ℝ} (hs : MeasurableSet s) (hμs : μ
   rw [mul_comm, ← smul_eq_mul, ← set_integral_const c]
   exact set_integral_mono_on (integrable_on_const.2 (Or.inr hμs.lt_top)) hfint hs hf
 #align measure_theory.set_integral_ge_of_const_le MeasureTheory.set_integral_ge_of_const_le
+-/
 
 end Mono
 
@@ -792,20 +916,27 @@ theorem set_integral_nonneg_of_ae_restrict (hf : 0 ≤ᵐ[μ.restrict s] f) : 0
 #align measure_theory.set_integral_nonneg_of_ae_restrict MeasureTheory.set_integral_nonneg_of_ae_restrict
 -/
 
+#print MeasureTheory.set_integral_nonneg_of_ae /-
 theorem set_integral_nonneg_of_ae (hf : 0 ≤ᵐ[μ] f) : 0 ≤ ∫ a in s, f a ∂μ :=
   set_integral_nonneg_of_ae_restrict (ae_restrict_of_ae hf)
 #align measure_theory.set_integral_nonneg_of_ae MeasureTheory.set_integral_nonneg_of_ae
+-/
 
+#print MeasureTheory.set_integral_nonneg /-
 theorem set_integral_nonneg (hs : MeasurableSet s) (hf : ∀ a, a ∈ s → 0 ≤ f a) :
     0 ≤ ∫ a in s, f a ∂μ :=
   set_integral_nonneg_of_ae_restrict ((ae_restrict_iff' hs).mpr (ae_of_all μ hf))
 #align measure_theory.set_integral_nonneg MeasureTheory.set_integral_nonneg
+-/
 
+#print MeasureTheory.set_integral_nonneg_ae /-
 theorem set_integral_nonneg_ae (hs : MeasurableSet s) (hf : ∀ᵐ a ∂μ, a ∈ s → 0 ≤ f a) :
     0 ≤ ∫ a in s, f a ∂μ :=
   set_integral_nonneg_of_ae_restrict <| by rwa [eventually_le, ae_restrict_iff' hs]
 #align measure_theory.set_integral_nonneg_ae MeasureTheory.set_integral_nonneg_ae
+-/
 
+#print MeasureTheory.set_integral_le_nonneg /-
 theorem set_integral_le_nonneg {s : Set α} (hs : MeasurableSet s) (hf : StronglyMeasurable f)
     (hfi : Integrable f μ) : ∫ x in s, f x ∂μ ≤ ∫ x in {y | 0 ≤ f y}, f x ∂μ :=
   by
@@ -816,6 +947,7 @@ theorem set_integral_le_nonneg {s : Set α} (hs : MeasurableSet s) (hf : Strongl
       (hfi.indicator (strongly_measurable_const.measurable_set_le hf))
       (indicator_le_indicator_nonneg s f)
 #align measure_theory.set_integral_le_nonneg MeasureTheory.set_integral_le_nonneg
+-/
 
 #print MeasureTheory.set_integral_nonpos_of_ae_restrict /-
 theorem set_integral_nonpos_of_ae_restrict (hf : f ≤ᵐ[μ.restrict s] 0) : ∫ a in s, f a ∂μ ≤ 0 :=
@@ -823,20 +955,27 @@ theorem set_integral_nonpos_of_ae_restrict (hf : f ≤ᵐ[μ.restrict s] 0) : 
 #align measure_theory.set_integral_nonpos_of_ae_restrict MeasureTheory.set_integral_nonpos_of_ae_restrict
 -/
 
+#print MeasureTheory.set_integral_nonpos_of_ae /-
 theorem set_integral_nonpos_of_ae (hf : f ≤ᵐ[μ] 0) : ∫ a in s, f a ∂μ ≤ 0 :=
   set_integral_nonpos_of_ae_restrict (ae_restrict_of_ae hf)
 #align measure_theory.set_integral_nonpos_of_ae MeasureTheory.set_integral_nonpos_of_ae
+-/
 
+#print MeasureTheory.set_integral_nonpos /-
 theorem set_integral_nonpos (hs : MeasurableSet s) (hf : ∀ a, a ∈ s → f a ≤ 0) :
     ∫ a in s, f a ∂μ ≤ 0 :=
   set_integral_nonpos_of_ae_restrict ((ae_restrict_iff' hs).mpr (ae_of_all μ hf))
 #align measure_theory.set_integral_nonpos MeasureTheory.set_integral_nonpos
+-/
 
+#print MeasureTheory.set_integral_nonpos_ae /-
 theorem set_integral_nonpos_ae (hs : MeasurableSet s) (hf : ∀ᵐ a ∂μ, a ∈ s → f a ≤ 0) :
     ∫ a in s, f a ∂μ ≤ 0 :=
   set_integral_nonpos_of_ae_restrict <| by rwa [eventually_le, ae_restrict_iff' hs]
 #align measure_theory.set_integral_nonpos_ae MeasureTheory.set_integral_nonpos_ae
+-/
 
+#print MeasureTheory.set_integral_nonpos_le /-
 theorem set_integral_nonpos_le {s : Set α} (hs : MeasurableSet s) (hf : StronglyMeasurable f)
     (hfi : Integrable f μ) : ∫ x in {y | f y ≤ 0}, f x ∂μ ≤ ∫ x in s, f x ∂μ :=
   by
@@ -846,6 +985,7 @@ theorem set_integral_nonpos_le {s : Set α} (hs : MeasurableSet s) (hf : Strongl
     integral_mono (hfi.indicator (hf.measurable_set_le strongly_measurable_const))
       (hfi.indicator hs) (indicator_nonpos_le_indicator s f)
 #align measure_theory.set_integral_nonpos_le MeasureTheory.set_integral_nonpos_le
+-/
 
 end Nonneg
 
@@ -853,6 +993,7 @@ section IntegrableUnion
 
 variable {μ : Measure α} [NormedAddCommGroup E] [Countable β]
 
+#print MeasureTheory.integrableOn_iUnion_of_summable_integral_norm /-
 theorem integrableOn_iUnion_of_summable_integral_norm {f : α → E} {s : β → Set α}
     (hs : ∀ b : β, MeasurableSet (s b)) (hi : ∀ b : β, IntegrableOn f (s b) μ)
     (h : Summable fun b : β => ∫ a : α in s b, ‖f a‖ ∂μ) : IntegrableOn f (iUnion s) μ :=
@@ -869,9 +1010,11 @@ theorem integrableOn_iUnion_of_summable_integral_norm {f : α → E} {s : β →
   simp_rw [ENNReal.coe_nnreal_eq, NNReal.coe_mk, coe_nnnorm] at S'' 
   convert ENNReal.ofReal_lt_top
 #align measure_theory.integrable_on_Union_of_summable_integral_norm MeasureTheory.integrableOn_iUnion_of_summable_integral_norm
+-/
 
 variable [TopologicalSpace α] [BorelSpace α] [MetrizableSpace α] [IsLocallyFiniteMeasure μ]
 
+#print MeasureTheory.integrableOn_iUnion_of_summable_norm_restrict /-
 /-- If `s` is a countable family of compact sets, `f` is a continuous function, and the sequence
 `‖f.restrict (s i)‖ * μ (s i)` is summable, then `f` is integrable on the union of the `s i`. -/
 theorem integrableOn_iUnion_of_summable_norm_restrict {f : C(α, E)} {s : β → Compacts α}
@@ -888,7 +1031,9 @@ theorem integrableOn_iUnion_of_summable_norm_restrict {f : C(α, E)} {s : β →
       (s i).IsCompact.IsClosed.MeasurableSet fun x hx =>
       (norm_norm (f x)).symm ▸ (f.restrict ↑(s i)).norm_coe_le_norm ⟨x, hx⟩
 #align measure_theory.integrable_on_Union_of_summable_norm_restrict MeasureTheory.integrableOn_iUnion_of_summable_norm_restrict
+-/
 
+#print MeasureTheory.integrable_of_summable_norm_restrict /-
 /-- If `s` is a countable family of compact sets covering `α`, `f` is a continuous function, and
 the sequence `‖f.restrict (s i)‖ * μ (s i)` is summable, then `f` is integrable. -/
 theorem integrable_of_summable_norm_restrict {f : C(α, E)} {s : β → Compacts α}
@@ -896,6 +1041,7 @@ theorem integrable_of_summable_norm_restrict {f : C(α, E)} {s : β → Compacts
     (hs : (⋃ i : β, ↑(s i)) = (univ : Set α)) : Integrable f μ := by
   simpa only [hs, integrable_on_univ] using integrable_on_Union_of_summable_norm_restrict hf
 #align measure_theory.integrable_of_summable_norm_restrict MeasureTheory.integrable_of_summable_norm_restrict
+-/
 
 end IntegrableUnion
 
@@ -905,6 +1051,7 @@ variable {μ : Measure α} [NormedAddCommGroup E] [CompleteSpace E] [NormedSpace
   {f : α → E}
 
 /- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:72:38: in filter_upwards #[[], ["with", ident a], ["using", expr le_trans (h_anti.tendsto_indicator _ _ _) (pure_le_nhds _)]]: ./././Mathport/Syntax/Translate/Basic.lean:349:22: unsupported: parse error @ arg 0: next failed, no more args -/
+#print Antitone.tendsto_set_integral /-
 theorem Antitone.tendsto_set_integral (hsm : ∀ i, MeasurableSet (s i)) (h_anti : Antitone s)
     (hfi : IntegrableOn f (s 0) μ) :
     Tendsto (fun i => ∫ a in s i, f a ∂μ) atTop (𝓝 (∫ a in ⋂ n, s n, f a ∂μ)) :=
@@ -927,6 +1074,7 @@ theorem Antitone.tendsto_set_integral (hsm : ∀ i, MeasurableSet (s i)) (h_anti
     trace
       "./././Mathport/Syntax/Translate/Tactic/Builtin.lean:72:38: in filter_upwards #[[], [\"with\", ident a], [\"using\", expr le_trans (h_anti.tendsto_indicator _ _ _) (pure_le_nhds _)]]: ./././Mathport/Syntax/Translate/Basic.lean:349:22: unsupported: parse error @ arg 0: next failed, no more args"
 #align antitone.tendsto_set_integral Antitone.tendsto_set_integral
+-/
 
 end TendstoMono
 
@@ -940,6 +1088,7 @@ section ContinuousSetIntegral
 variable [NormedAddCommGroup E] {𝕜 : Type _} [NormedField 𝕜] [NormedAddCommGroup F]
   [NormedSpace 𝕜 F] {p : ℝ≥0∞} {μ : Measure α}
 
+#print MeasureTheory.Lp_toLp_restrict_add /-
 /-- For `f : Lp E p μ`, we can define an element of `Lp E p (μ.restrict s)` by
 `(Lp.mem_ℒp f).restrict s).to_Lp f`. This map is additive. -/
 theorem Lp_toLp_restrict_add (f g : Lp E p μ) (s : Set α) :
@@ -957,7 +1106,9 @@ theorem Lp_toLp_restrict_add (f g : Lp E p μ) (s : Set α) :
   refine' (mem_ℒp.coe_fn_to_Lp ((Lp.mem_ℒp (f + g)).restrict s)).mono fun x hx1 hx2 hx3 hx4 hx5 => _
   rw [hx4, hx1, Pi.add_apply, hx2, hx3, hx5, Pi.add_apply]
 #align measure_theory.Lp_to_Lp_restrict_add MeasureTheory.Lp_toLp_restrict_add
+-/
 
+#print MeasureTheory.Lp_toLp_restrict_smul /-
 /-- For `f : Lp E p μ`, we can define an element of `Lp E p (μ.restrict s)` by
 `(Lp.mem_ℒp f).restrict s).to_Lp f`. This map commutes with scalar multiplication. -/
 theorem Lp_toLp_restrict_smul (c : 𝕜) (f : Lp F p μ) (s : Set α) :
@@ -971,7 +1122,9 @@ theorem Lp_toLp_restrict_smul (c : 𝕜) (f : Lp F p μ) (s : Set α) :
     (Lp.coe_fn_smul c (mem_ℒp.to_Lp f ((Lp.mem_ℒp f).restrict s))).mono fun x hx1 hx2 hx3 hx4 => _
   rw [hx2, hx1, Pi.smul_apply, hx3, hx4, Pi.smul_apply]
 #align measure_theory.Lp_to_Lp_restrict_smul MeasureTheory.Lp_toLp_restrict_smul
+-/
 
+#print MeasureTheory.norm_Lp_toLp_restrict_le /-
 /-- For `f : Lp E p μ`, we can define an element of `Lp E p (μ.restrict s)` by
 `(Lp.mem_ℒp f).restrict s).to_Lp f`. This map is non-expansive. -/
 theorem norm_Lp_toLp_restrict_le (s : Set α) (f : Lp E p μ) :
@@ -982,9 +1135,11 @@ theorem norm_Lp_toLp_restrict_le (s : Set α) (f : Lp E p μ) :
   · exact s
   exact snorm_congr_ae (mem_ℒp.coe_fn_to_Lp _)
 #align measure_theory.norm_Lp_to_Lp_restrict_le MeasureTheory.norm_Lp_toLp_restrict_le
+-/
 
 variable (α F 𝕜)
 
+#print MeasureTheory.LpToLpRestrictCLM /-
 /-- Continuous linear map sending a function of `Lp F p μ` to the same function in
 `Lp F p (μ.restrict s)`. -/
 def LpToLpRestrictCLM (μ : Measure α) (p : ℝ≥0∞) [hp : Fact (1 ≤ p)] (s : Set α) :
@@ -994,18 +1149,22 @@ def LpToLpRestrictCLM (μ : Measure α) (p : ℝ≥0∞) [hp : Fact (1 ≤ p)] (
       fun c f => Lp_toLp_restrict_smul c f s⟩
     1 (by intro f; rw [one_mul]; exact norm_Lp_to_Lp_restrict_le s f)
 #align measure_theory.Lp_to_Lp_restrict_clm MeasureTheory.LpToLpRestrictCLM
+-/
 
 variable {α F 𝕜}
 
 variable (𝕜)
 
+#print MeasureTheory.LpToLpRestrictCLM_coeFn /-
 theorem LpToLpRestrictCLM_coeFn [hp : Fact (1 ≤ p)] (s : Set α) (f : Lp F p μ) :
     LpToLpRestrictCLM α F 𝕜 μ p s f =ᵐ[μ.restrict s] f :=
   Memℒp.coeFn_toLp ((Lp.memℒp f).restrict s)
 #align measure_theory.Lp_to_Lp_restrict_clm_coe_fn MeasureTheory.LpToLpRestrictCLM_coeFn
+-/
 
 variable {𝕜}
 
+#print MeasureTheory.continuous_set_integral /-
 @[continuity]
 theorem continuous_set_integral [NormedSpace ℝ E] [CompleteSpace E] (s : Set α) :
     Continuous fun f : α →₁[μ] E => ∫ x in s, f x ∂μ :=
@@ -1020,6 +1179,7 @@ theorem continuous_set_integral [NormedSpace ℝ E] [CompleteSpace E] (s : Set 
   rw [h_comp]
   exact continuous_integral.comp (Lp_to_Lp_restrict_clm α E ℝ μ 1 s).Continuous
 #align measure_theory.continuous_set_integral MeasureTheory.continuous_set_integral
+-/
 
 end ContinuousSetIntegral
 
@@ -1029,6 +1189,7 @@ open MeasureTheory Asymptotics Metric
 
 variable {ι : Type _} [NormedAddCommGroup E]
 
+#print Filter.Tendsto.integral_sub_linear_isLittleO_ae /-
 /-- Fundamental theorem of calculus for set integrals: if `μ` is a measure that is finite at a
 filter `l` and `f` is a measurable function that has a finite limit `b` at `l ⊓ μ.ae`, then `∫ x in
 s i, f x ∂μ = μ (s i) • b + o(μ (s i))` at a filter `li` provided that `s i` tends to `l.small_sets`
@@ -1058,7 +1219,9 @@ theorem Filter.Tendsto.integral_sub_linear_isLittleO_ae [NormedSpace ℝ E] [Com
     Real.norm_eq_abs, abs_of_nonneg ENNReal.toReal_nonneg]
   exact norm_set_integral_le_of_norm_le_const_ae' hμs h_norm (hfm.sub ae_strongly_measurable_const)
 #align filter.tendsto.integral_sub_linear_is_o_ae Filter.Tendsto.integral_sub_linear_isLittleO_ae
+-/
 
+#print ContinuousWithinAt.integral_sub_linear_isLittleO_ae /-
 /-- Fundamental theorem of calculus for set integrals, `nhds_within` version: if `μ` is a locally
 finite measure and `f` is an almost everywhere measurable function that is continuous at a point `a`
 within a measurable set `t`, then `∫ x in s i, f x ∂μ = μ (s i) • f a + o(μ (s i))` at a filter `li`
@@ -1079,7 +1242,9 @@ theorem ContinuousWithinAt.integral_sub_linear_isLittleO_ae [TopologicalSpace α
   (ha.mono_left inf_le_left).integral_sub_linear_isLittleO_ae hfm (μ.finite_at_nhds_within a t) hs m
     hsμ
 #align continuous_within_at.integral_sub_linear_is_o_ae ContinuousWithinAt.integral_sub_linear_isLittleO_ae
+-/
 
+#print ContinuousAt.integral_sub_linear_isLittleO_ae /-
 /-- Fundamental theorem of calculus for set integrals, `nhds` version: if `μ` is a locally finite
 measure and `f` is an almost everywhere measurable function that is continuous at a point `a`, then
 `∫ x in s i, f x ∂μ = μ (s i) • f a + o(μ (s i))` at `li` provided that `s` tends to
@@ -1097,7 +1262,9 @@ theorem ContinuousAt.integral_sub_linear_isLittleO_ae [TopologicalSpace α] [Ope
     (fun i => ∫ x in s i, f x ∂μ - m i • f a) =o[li] m :=
   (ha.mono_left inf_le_left).integral_sub_linear_isLittleO_ae hfm (μ.finiteAtNhds a) hs m hsμ
 #align continuous_at.integral_sub_linear_is_o_ae ContinuousAt.integral_sub_linear_isLittleO_ae
+-/
 
+#print ContinuousOn.integral_sub_linear_isLittleO_ae /-
 /-- Fundamental theorem of calculus for set integrals, `nhds_within` version: if `μ` is a locally
 finite measure, `f` is continuous on a measurable set `t`, and `a ∈ t`, then `∫ x in (s i), f x ∂μ =
 μ (s i) • f a + o(μ (s i))` at `li` provided that `s i` tends to `(𝓝[t] a).small_sets` along `li`.
@@ -1116,6 +1283,7 @@ theorem ContinuousOn.integral_sub_linear_isLittleO_ae [TopologicalSpace α] [Ope
   (hft a ha).integral_sub_linear_isLittleO_ae ht
     ⟨t, self_mem_nhdsWithin, hft.AEStronglyMeasurable ht⟩ hs m hsμ
 #align continuous_on.integral_sub_linear_is_o_ae ContinuousOn.integral_sub_linear_isLittleO_ae
+-/
 
 section
 
@@ -1138,22 +1306,29 @@ namespace ContinuousLinearMap
 
 variable [CompleteSpace F] [NormedSpace ℝ F]
 
+#print ContinuousLinearMap.integral_compLp /-
 theorem integral_compLp (L : E →L[𝕜] F) (φ : Lp E p μ) : ∫ a, (L.compLp φ) a ∂μ = ∫ a, L (φ a) ∂μ :=
   integral_congr_ae <| coeFn_compLp _ _
 #align continuous_linear_map.integral_comp_Lp ContinuousLinearMap.integral_compLp
+-/
 
+#print ContinuousLinearMap.set_integral_compLp /-
 theorem set_integral_compLp (L : E →L[𝕜] F) (φ : Lp E p μ) {s : Set α} (hs : MeasurableSet s) :
     ∫ a in s, (L.compLp φ) a ∂μ = ∫ a in s, L (φ a) ∂μ :=
   set_integral_congr_ae hs ((L.coeFn_compLp φ).mono fun x hx hx2 => hx)
 #align continuous_linear_map.set_integral_comp_Lp ContinuousLinearMap.set_integral_compLp
+-/
 
+#print ContinuousLinearMap.continuous_integral_comp_L1 /-
 theorem continuous_integral_comp_L1 (L : E →L[𝕜] F) :
     Continuous fun φ : α →₁[μ] E => ∫ a : α, L (φ a) ∂μ := by rw [← funext L.integral_comp_Lp];
   exact continuous_integral.comp (L.comp_LpL 1 μ).Continuous
 #align continuous_linear_map.continuous_integral_comp_L1 ContinuousLinearMap.continuous_integral_comp_L1
+-/
 
 variable [CompleteSpace E] [NormedSpace ℝ E]
 
+#print ContinuousLinearMap.integral_comp_comm /-
 theorem integral_comp_comm (L : E →L[𝕜] F) {φ : α → E} (φ_int : Integrable φ μ) :
     ∫ a, L (φ a) ∂μ = L (∫ a, φ a ∂μ) :=
   by
@@ -1174,12 +1349,16 @@ theorem integral_comp_comm (L : E →L[𝕜] F) {φ : α → E} (φ_int : Integr
     · rw [integral_congr_ae hfg.symm]
   all_goals assumption
 #align continuous_linear_map.integral_comp_comm ContinuousLinearMap.integral_comp_comm
+-/
 
+#print ContinuousLinearMap.integral_apply /-
 theorem integral_apply {H : Type _} [NormedAddCommGroup H] [NormedSpace 𝕜 H] {φ : α → H →L[𝕜] E}
     (φ_int : Integrable φ μ) (v : H) : (∫ a, φ a ∂μ) v = ∫ a, φ a v ∂μ :=
   ((ContinuousLinearMap.apply 𝕜 E v).integral_comp_comm φ_int).symm
 #align continuous_linear_map.integral_apply ContinuousLinearMap.integral_apply
+-/
 
+#print ContinuousLinearMap.integral_comp_comm' /-
 theorem integral_comp_comm' (L : E →L[𝕜] F) {K} (hL : AntilipschitzWith K L) (φ : α → E) :
     ∫ a, L (φ a) ∂μ = L (∫ a, φ a ∂μ) :=
   by
@@ -1189,10 +1368,13 @@ theorem integral_comp_comm' (L : E →L[𝕜] F) {K} (hL : AntilipschitzWith K L
     rwa [lipschitz_with.integrable_comp_iff_of_antilipschitz L.lipschitz hL L.map_zero]
   simp [integral_undef, h, this]
 #align continuous_linear_map.integral_comp_comm' ContinuousLinearMap.integral_comp_comm'
+-/
 
+#print ContinuousLinearMap.integral_comp_L1_comm /-
 theorem integral_comp_L1_comm (L : E →L[𝕜] F) (φ : α →₁[μ] E) : ∫ a, L (φ a) ∂μ = L (∫ a, φ a ∂μ) :=
   L.integral_comp_comm (L1.integrable_coeFn φ)
 #align continuous_linear_map.integral_comp_L1_comm ContinuousLinearMap.integral_comp_L1_comm
+-/
 
 end ContinuousLinearMap
 
@@ -1200,9 +1382,11 @@ namespace LinearIsometry
 
 variable [CompleteSpace F] [NormedSpace ℝ F] [CompleteSpace E] [NormedSpace ℝ E]
 
+#print LinearIsometry.integral_comp_comm /-
 theorem integral_comp_comm (L : E →ₗᵢ[𝕜] F) (φ : α → E) : ∫ a, L (φ a) ∂μ = L (∫ a, φ a ∂μ) :=
   L.toContinuousLinearMap.integral_comp_comm' L.antilipschitz _
 #align linear_isometry.integral_comp_comm LinearIsometry.integral_comp_comm
+-/
 
 end LinearIsometry
 
@@ -1210,9 +1394,11 @@ namespace ContinuousLinearEquiv
 
 variable [CompleteSpace F] [NormedSpace ℝ F] [CompleteSpace E] [NormedSpace ℝ E]
 
+#print ContinuousLinearEquiv.integral_comp_comm /-
 theorem integral_comp_comm (L : E ≃L[𝕜] F) (φ : α → E) : ∫ a, L (φ a) ∂μ = L (∫ a, φ a ∂μ) :=
   L.toContinuousLinearMap.integral_comp_comm' L.antilipschitz _
 #align continuous_linear_equiv.integral_comp_comm ContinuousLinearEquiv.integral_comp_comm
+-/
 
 end ContinuousLinearEquiv
 
@@ -1225,20 +1411,27 @@ theorem integral_ofReal {f : α → ℝ} : ∫ a, (f a : 𝕜) ∂μ = ↑(∫ a
 #align integral_of_real integral_ofReal
 -/
 
+#print integral_re /-
 theorem integral_re {f : α → 𝕜} (hf : Integrable f μ) :
     ∫ a, IsROrC.re (f a) ∂μ = IsROrC.re (∫ a, f a ∂μ) :=
   (@IsROrC.reClm 𝕜 _).integral_comp_comm hf
 #align integral_re integral_re
+-/
 
+#print integral_im /-
 theorem integral_im {f : α → 𝕜} (hf : Integrable f μ) :
     ∫ a, IsROrC.im (f a) ∂μ = IsROrC.im (∫ a, f a ∂μ) :=
   (@IsROrC.imClm 𝕜 _).integral_comp_comm hf
 #align integral_im integral_im
+-/
 
+#print integral_conj /-
 theorem integral_conj {f : α → 𝕜} : ∫ a, conj (f a) ∂μ = conj (∫ a, f a ∂μ) :=
   (@IsROrC.conjLie 𝕜 _).toLinearIsometry.integral_comp_comm f
 #align integral_conj integral_conj
+-/
 
+#print integral_coe_re_add_coe_im /-
 theorem integral_coe_re_add_coe_im {f : α → 𝕜} (hf : Integrable f μ) :
     ∫ x, (IsROrC.re (f x) : 𝕜) ∂μ + (∫ x, IsROrC.im (f x) ∂μ) * IsROrC.i = ∫ x, f x ∂μ :=
   by
@@ -1249,31 +1442,42 @@ theorem integral_coe_re_add_coe_im {f : α → 𝕜} (hf : Integrable f μ) :
   · exact hf.re.of_real
   · exact hf.im.of_real.smul IsROrC.i
 #align integral_coe_re_add_coe_im integral_coe_re_add_coe_im
+-/
 
+#print integral_re_add_im /-
 theorem integral_re_add_im {f : α → 𝕜} (hf : Integrable f μ) :
     ((∫ x, IsROrC.re (f x) ∂μ : ℝ) : 𝕜) + (∫ x, IsROrC.im (f x) ∂μ : ℝ) * IsROrC.i = ∫ x, f x ∂μ :=
   by rw [← integral_ofReal, ← integral_ofReal, integral_coe_re_add_coe_im hf]
 #align integral_re_add_im integral_re_add_im
+-/
 
+#print set_integral_re_add_im /-
 theorem set_integral_re_add_im {f : α → 𝕜} {i : Set α} (hf : IntegrableOn f i μ) :
     ((∫ x in i, IsROrC.re (f x) ∂μ : ℝ) : 𝕜) + (∫ x in i, IsROrC.im (f x) ∂μ : ℝ) * IsROrC.i =
       ∫ x in i, f x ∂μ :=
   integral_re_add_im hf
 #align set_integral_re_add_im set_integral_re_add_im
+-/
 
+#print fst_integral /-
 theorem fst_integral {f : α → E × F} (hf : Integrable f μ) : (∫ x, f x ∂μ).1 = ∫ x, (f x).1 ∂μ :=
   ((ContinuousLinearMap.fst ℝ E F).integral_comp_comm hf).symm
 #align fst_integral fst_integral
+-/
 
+#print snd_integral /-
 theorem snd_integral {f : α → E × F} (hf : Integrable f μ) : (∫ x, f x ∂μ).2 = ∫ x, (f x).2 ∂μ :=
   ((ContinuousLinearMap.snd ℝ E F).integral_comp_comm hf).symm
 #align snd_integral snd_integral
+-/
 
+#print integral_pair /-
 theorem integral_pair {f : α → E} {g : α → F} (hf : Integrable f μ) (hg : Integrable g μ) :
     ∫ x, (f x, g x) ∂μ = (∫ x, f x ∂μ, ∫ x, g x ∂μ) :=
   have := hf.prod_mk hg
   Prod.ext (fst_integral this) (snd_integral this)
 #align integral_pair integral_pair
+-/
 
 #print integral_smul_const /-
 theorem integral_smul_const {𝕜 : Type _} [IsROrC 𝕜] [NormedSpace 𝕜 E] (f : α → 𝕜) (c : E) :
@@ -1288,6 +1492,7 @@ theorem integral_smul_const {𝕜 : Type _} [IsROrC 𝕜] [NormedSpace 𝕜 E] (
 #align integral_smul_const integral_smul_const
 -/
 
+#print integral_withDensity_eq_integral_smul /-
 theorem integral_withDensity_eq_integral_smul {f : α → ℝ≥0} (f_meas : Measurable f) (g : α → E) :
     (∫ a, g a ∂μ.withDensity fun x => f x) = ∫ a, f a • g a ∂μ :=
   by
@@ -1337,7 +1542,9 @@ theorem integral_withDensity_eq_integral_smul {f : α → ℝ≥0} (f_meas : Mea
     · rw [hx _]
       simpa only [Ne.def, ENNReal.coe_eq_zero] using h'x
 #align integral_with_density_eq_integral_smul integral_withDensity_eq_integral_smul
+-/
 
+#print integral_withDensity_eq_integral_smul₀ /-
 theorem integral_withDensity_eq_integral_smul₀ {f : α → ℝ≥0} (hf : AEMeasurable f μ) (g : α → E) :
     (∫ a, g a ∂μ.withDensity fun x => f x) = ∫ a, f a • g a ∂μ :=
   by
@@ -1355,18 +1562,23 @@ theorem integral_withDensity_eq_integral_smul₀ {f : α → ℝ≥0} (hf : AEMe
       filter_upwards [hf.ae_eq_mk] with x hx
       rw [hx]
 #align integral_with_density_eq_integral_smul₀ integral_withDensity_eq_integral_smul₀
+-/
 
+#print set_integral_withDensity_eq_set_integral_smul /-
 theorem set_integral_withDensity_eq_set_integral_smul {f : α → ℝ≥0} (f_meas : Measurable f)
     (g : α → E) {s : Set α} (hs : MeasurableSet s) :
     (∫ a in s, g a ∂μ.withDensity fun x => f x) = ∫ a in s, f a • g a ∂μ := by
   rw [restrict_with_density hs, integral_withDensity_eq_integral_smul f_meas]
 #align set_integral_with_density_eq_set_integral_smul set_integral_withDensity_eq_set_integral_smul
+-/
 
+#print set_integral_withDensity_eq_set_integral_smul₀ /-
 theorem set_integral_withDensity_eq_set_integral_smul₀ {f : α → ℝ≥0} {s : Set α}
     (hf : AEMeasurable f (μ.restrict s)) (g : α → E) (hs : MeasurableSet s) :
     (∫ a in s, g a ∂μ.withDensity fun x => f x) = ∫ a in s, f a • g a ∂μ := by
   rw [restrict_with_density hs, integral_withDensity_eq_integral_smul₀ hf]
 #align set_integral_with_density_eq_set_integral_smul₀ set_integral_withDensity_eq_set_integral_smul₀
+-/
 
 end
 
@@ -1374,6 +1586,7 @@ section thickenedIndicator
 
 variable [PseudoEMetricSpace α]
 
+#print measure_le_lintegral_thickenedIndicatorAux /-
 theorem measure_le_lintegral_thickenedIndicatorAux (μ : Measure α) {E : Set α}
     (E_mble : MeasurableSet E) (δ : ℝ) : μ E ≤ ∫⁻ a, (thickenedIndicatorAux δ E a : ℝ≥0∞) ∂μ :=
   by
@@ -1383,7 +1596,9 @@ theorem measure_le_lintegral_thickenedIndicatorAux (μ : Measure α) {E : Set α
   · apply lintegral_mono
     apply indicator_le_thickenedIndicatorAux
 #align measure_le_lintegral_thickened_indicator_aux measure_le_lintegral_thickenedIndicatorAux
+-/
 
+#print measure_le_lintegral_thickenedIndicator /-
 theorem measure_le_lintegral_thickenedIndicator (μ : Measure α) {E : Set α}
     (E_mble : MeasurableSet E) {δ : ℝ} (δ_pos : 0 < δ) :
     μ E ≤ ∫⁻ a, (thickenedIndicator δ_pos E a : ℝ≥0∞) ∂μ :=
@@ -1392,6 +1607,7 @@ theorem measure_le_lintegral_thickenedIndicator (μ : Measure α) {E : Set α}
   dsimp
   simp only [thickened_indicator_aux_lt_top.ne, ENNReal.coe_toNNReal, Ne.def, not_false_iff]
 #align measure_le_lintegral_thickened_indicator measure_le_lintegral_thickenedIndicator
+-/
 
 end thickenedIndicator
 
@@ -1401,6 +1617,7 @@ namespace MeasureTheory
 
 variable {f : β → ℝ} {m m0 : MeasurableSpace β} {μ : Measure β}
 
+#print MeasureTheory.Integrable.simpleFunc_mul /-
 theorem Integrable.simpleFunc_mul (g : SimpleFunc β ℝ) (hf : Integrable f μ) :
     Integrable (g * f) μ :=
   by
@@ -1420,11 +1637,14 @@ theorem Integrable.simpleFunc_mul (g : SimpleFunc β ℝ) (hf : Integrable f μ)
   rw [this, integrable_indicator_iff hs]
   exact (hf.smul c).IntegrableOn
 #align measure_theory.integrable.simple_func_mul MeasureTheory.Integrable.simpleFunc_mul
+-/
 
+#print MeasureTheory.Integrable.simpleFunc_mul' /-
 theorem Integrable.simpleFunc_mul' (hm : m ≤ m0) (g : @SimpleFunc β m ℝ) (hf : Integrable f μ) :
     Integrable (g * f) μ := by rw [← simple_func.coe_to_larger_space_eq hm g];
   exact hf.simple_func_mul (g.to_larger_space hm)
 #align measure_theory.integrable.simple_func_mul' MeasureTheory.Integrable.simpleFunc_mul'
+-/
 
 end MeasureTheory
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/a3e83f0fa4391c8740f7d773a7a9b74e311ae2a3

@@ -76,49 +76,49 @@ variable [NormedAddCommGroup E] {f g : α → E} {s t : Set α} {μ ν : Measure
 variable [CompleteSpace E] [NormedSpace ℝ E]
 
 theorem set_integral_congr_ae₀ (hs : NullMeasurableSet s μ) (h : ∀ᵐ x ∂μ, x ∈ s → f x = g x) :
-    (∫ x in s, f x ∂μ) = ∫ x in s, g x ∂μ :=
+    ∫ x in s, f x ∂μ = ∫ x in s, g x ∂μ :=
   integral_congr_ae ((ae_restrict_iff'₀ hs).2 h)
 #align measure_theory.set_integral_congr_ae₀ MeasureTheory.set_integral_congr_ae₀
 
 theorem set_integral_congr_ae (hs : MeasurableSet s) (h : ∀ᵐ x ∂μ, x ∈ s → f x = g x) :
-    (∫ x in s, f x ∂μ) = ∫ x in s, g x ∂μ :=
+    ∫ x in s, f x ∂μ = ∫ x in s, g x ∂μ :=
   integral_congr_ae ((ae_restrict_iff' hs).2 h)
 #align measure_theory.set_integral_congr_ae MeasureTheory.set_integral_congr_ae
 
 theorem set_integral_congr₀ (hs : NullMeasurableSet s μ) (h : EqOn f g s) :
-    (∫ x in s, f x ∂μ) = ∫ x in s, g x ∂μ :=
+    ∫ x in s, f x ∂μ = ∫ x in s, g x ∂μ :=
   set_integral_congr_ae₀ hs <| eventually_of_forall h
 #align measure_theory.set_integral_congr₀ MeasureTheory.set_integral_congr₀
 
 theorem set_integral_congr (hs : MeasurableSet s) (h : EqOn f g s) :
-    (∫ x in s, f x ∂μ) = ∫ x in s, g x ∂μ :=
+    ∫ x in s, f x ∂μ = ∫ x in s, g x ∂μ :=
   set_integral_congr_ae hs <| eventually_of_forall h
 #align measure_theory.set_integral_congr MeasureTheory.set_integral_congr
 
-theorem set_integral_congr_set_ae (hst : s =ᵐ[μ] t) : (∫ x in s, f x ∂μ) = ∫ x in t, f x ∂μ := by
+theorem set_integral_congr_set_ae (hst : s =ᵐ[μ] t) : ∫ x in s, f x ∂μ = ∫ x in t, f x ∂μ := by
   rw [measure.restrict_congr_set hst]
 #align measure_theory.set_integral_congr_set_ae MeasureTheory.set_integral_congr_set_ae
 
 theorem integral_union_ae (hst : AEDisjoint μ s t) (ht : NullMeasurableSet t μ)
     (hfs : IntegrableOn f s μ) (hft : IntegrableOn f t μ) :
-    (∫ x in s ∪ t, f x ∂μ) = (∫ x in s, f x ∂μ) + ∫ x in t, f x ∂μ := by
+    ∫ x in s ∪ t, f x ∂μ = ∫ x in s, f x ∂μ + ∫ x in t, f x ∂μ := by
   simp only [integrable_on, measure.restrict_union₀ hst ht, integral_add_measure hfs hft]
 #align measure_theory.integral_union_ae MeasureTheory.integral_union_ae
 
 theorem integral_union (hst : Disjoint s t) (ht : MeasurableSet t) (hfs : IntegrableOn f s μ)
-    (hft : IntegrableOn f t μ) : (∫ x in s ∪ t, f x ∂μ) = (∫ x in s, f x ∂μ) + ∫ x in t, f x ∂μ :=
+    (hft : IntegrableOn f t μ) : ∫ x in s ∪ t, f x ∂μ = ∫ x in s, f x ∂μ + ∫ x in t, f x ∂μ :=
   integral_union_ae hst.AEDisjoint ht.NullMeasurableSet hfs hft
 #align measure_theory.integral_union MeasureTheory.integral_union
 
 theorem integral_diff (ht : MeasurableSet t) (hfs : IntegrableOn f s μ) (hts : t ⊆ s) :
-    (∫ x in s \ t, f x ∂μ) = (∫ x in s, f x ∂μ) - ∫ x in t, f x ∂μ :=
+    ∫ x in s \ t, f x ∂μ = ∫ x in s, f x ∂μ - ∫ x in t, f x ∂μ :=
   by
   rw [eq_sub_iff_add_eq, ← integral_union, diff_union_of_subset hts]
   exacts [disjoint_sdiff_self_left, ht, hfs.mono_set (diff_subset _ _), hfs.mono_set hts]
 #align measure_theory.integral_diff MeasureTheory.integral_diff
 
 theorem integral_inter_add_diff₀ (ht : NullMeasurableSet t μ) (hfs : IntegrableOn f s μ) :
-    ((∫ x in s ∩ t, f x ∂μ) + ∫ x in s \ t, f x ∂μ) = ∫ x in s, f x ∂μ :=
+    ∫ x in s ∩ t, f x ∂μ + ∫ x in s \ t, f x ∂μ = ∫ x in s, f x ∂μ :=
   by
   rw [← measure.restrict_inter_add_diff₀ s ht, integral_add_measure]
   · exact integrable.mono_measure hfs (measure.restrict_mono (inter_subset_left _ _) le_rfl)
@@ -126,14 +126,14 @@ theorem integral_inter_add_diff₀ (ht : NullMeasurableSet t μ) (hfs : Integrab
 #align measure_theory.integral_inter_add_diff₀ MeasureTheory.integral_inter_add_diff₀
 
 theorem integral_inter_add_diff (ht : MeasurableSet t) (hfs : IntegrableOn f s μ) :
-    ((∫ x in s ∩ t, f x ∂μ) + ∫ x in s \ t, f x ∂μ) = ∫ x in s, f x ∂μ :=
+    ∫ x in s ∩ t, f x ∂μ + ∫ x in s \ t, f x ∂μ = ∫ x in s, f x ∂μ :=
   integral_inter_add_diff₀ ht.NullMeasurableSet hfs
 #align measure_theory.integral_inter_add_diff MeasureTheory.integral_inter_add_diff
 
 theorem integral_finset_biUnion {ι : Type _} (t : Finset ι) {s : ι → Set α}
     (hs : ∀ i ∈ t, MeasurableSet (s i)) (h's : Set.Pairwise (↑t) (Disjoint on s))
     (hf : ∀ i ∈ t, IntegrableOn f (s i) μ) :
-    (∫ x in ⋃ i ∈ t, s i, f x ∂μ) = ∑ i in t, ∫ x in s i, f x ∂μ :=
+    ∫ x in ⋃ i ∈ t, s i, f x ∂μ = ∑ i in t, ∫ x in s i, f x ∂μ :=
   by
   induction' t using Finset.induction_on with a t hat IH hs h's
   · simp
@@ -148,24 +148,24 @@ theorem integral_finset_biUnion {ι : Type _} (t : Finset ι) {s : ι → Set α
 
 theorem integral_fintype_iUnion {ι : Type _} [Fintype ι] {s : ι → Set α}
     (hs : ∀ i, MeasurableSet (s i)) (h's : Pairwise (Disjoint on s))
-    (hf : ∀ i, IntegrableOn f (s i) μ) : (∫ x in ⋃ i, s i, f x ∂μ) = ∑ i, ∫ x in s i, f x ∂μ :=
+    (hf : ∀ i, IntegrableOn f (s i) μ) : ∫ x in ⋃ i, s i, f x ∂μ = ∑ i, ∫ x in s i, f x ∂μ :=
   by
   convert integral_finset_bUnion Finset.univ (fun i hi => hs i) _ fun i _ => hf i
   · simp
   · simp [pairwise_univ, h's]
 #align measure_theory.integral_fintype_Union MeasureTheory.integral_fintype_iUnion
 
-theorem integral_empty : (∫ x in ∅, f x ∂μ) = 0 := by
+theorem integral_empty : ∫ x in ∅, f x ∂μ = 0 := by
   rw [measure.restrict_empty, integral_zero_measure]
 #align measure_theory.integral_empty MeasureTheory.integral_empty
 
 #print MeasureTheory.integral_univ /-
-theorem integral_univ : (∫ x in univ, f x ∂μ) = ∫ x, f x ∂μ := by rw [measure.restrict_univ]
+theorem integral_univ : ∫ x in univ, f x ∂μ = ∫ x, f x ∂μ := by rw [measure.restrict_univ]
 #align measure_theory.integral_univ MeasureTheory.integral_univ
 -/
 
 theorem integral_add_compl₀ (hs : NullMeasurableSet s μ) (hfi : Integrable f μ) :
-    ((∫ x in s, f x ∂μ) + ∫ x in sᶜ, f x ∂μ) = ∫ x, f x ∂μ := by
+    ∫ x in s, f x ∂μ + ∫ x in sᶜ, f x ∂μ = ∫ x, f x ∂μ := by
   rw [←
     integral_union_ae (@disjoint_compl_right (Set α) _ _).AEDisjoint hs.compl hfi.integrable_on
       hfi.integrable_on,
@@ -173,28 +173,28 @@ theorem integral_add_compl₀ (hs : NullMeasurableSet s μ) (hfi : Integrable f
 #align measure_theory.integral_add_compl₀ MeasureTheory.integral_add_compl₀
 
 theorem integral_add_compl (hs : MeasurableSet s) (hfi : Integrable f μ) :
-    ((∫ x in s, f x ∂μ) + ∫ x in sᶜ, f x ∂μ) = ∫ x, f x ∂μ :=
+    ∫ x in s, f x ∂μ + ∫ x in sᶜ, f x ∂μ = ∫ x, f x ∂μ :=
   integral_add_compl₀ hs.NullMeasurableSet hfi
 #align measure_theory.integral_add_compl MeasureTheory.integral_add_compl
 
 /-- For a function `f` and a measurable set `s`, the integral of `indicator s f`
 over the whole space is equal to `∫ x in s, f x ∂μ` defined as `∫ x, f x ∂(μ.restrict s)`. -/
-theorem integral_indicator (hs : MeasurableSet s) : (∫ x, indicator s f x ∂μ) = ∫ x in s, f x ∂μ :=
+theorem integral_indicator (hs : MeasurableSet s) : ∫ x, indicator s f x ∂μ = ∫ x in s, f x ∂μ :=
   by
   by_cases hfi : integrable_on f s μ; swap
   · rwa [integral_undef, integral_undef]
     rwa [integrable_indicator_iff hs]
   calc
-    (∫ x, indicator s f x ∂μ) = (∫ x in s, indicator s f x ∂μ) + ∫ x in sᶜ, indicator s f x ∂μ :=
+    ∫ x, indicator s f x ∂μ = ∫ x in s, indicator s f x ∂μ + ∫ x in sᶜ, indicator s f x ∂μ :=
       (integral_add_compl hs (hfi.integrable_indicator hs)).symm
-    _ = (∫ x in s, f x ∂μ) + ∫ x in sᶜ, 0 ∂μ :=
+    _ = ∫ x in s, f x ∂μ + ∫ x in sᶜ, 0 ∂μ :=
       (congr_arg₂ (· + ·) (integral_congr_ae (indicator_ae_eq_restrict hs))
         (integral_congr_ae (indicator_ae_eq_restrict_compl hs)))
     _ = ∫ x in s, f x ∂μ := by simp
 #align measure_theory.integral_indicator MeasureTheory.integral_indicator
 
 theorem set_integral_indicator (ht : MeasurableSet t) :
-    (∫ x in s, t.indicator f x ∂μ) = ∫ x in s ∩ t, f x ∂μ := by
+    ∫ x in s, t.indicator f x ∂μ = ∫ x in s ∩ t, f x ∂μ := by
   rw [integral_indicator ht, measure.restrict_restrict ht, Set.inter_comm]
 #align measure_theory.set_integral_indicator MeasureTheory.set_integral_indicator
 
@@ -217,7 +217,7 @@ theorem ofReal_set_integral_one {α : Type _} {m : MeasurableSpace α} (μ : Mea
 
 theorem integral_piecewise [DecidablePred (· ∈ s)] (hs : MeasurableSet s) (hf : IntegrableOn f s μ)
     (hg : IntegrableOn g (sᶜ) μ) :
-    (∫ x, s.piecewise f g x ∂μ) = (∫ x in s, f x ∂μ) + ∫ x in sᶜ, g x ∂μ := by
+    ∫ x, s.piecewise f g x ∂μ = ∫ x in s, f x ∂μ + ∫ x in sᶜ, g x ∂μ := by
   rw [← Set.indicator_add_compl_eq_piecewise,
     integral_add' (hf.integrable_indicator hs) (hg.integrable_indicator hs.compl),
     integral_indicator hs, integral_indicator hs.compl]
@@ -228,7 +228,7 @@ theorem tendsto_set_integral_of_monotone {ι : Type _} [Countable ι] [Semilatti
     (hfi : IntegrableOn f (⋃ n, s n) μ) :
     Tendsto (fun i => ∫ a in s i, f a ∂μ) atTop (𝓝 (∫ a in ⋃ n, s n, f a ∂μ)) :=
   by
-  have hfi' : (∫⁻ x in ⋃ n, s n, ‖f x‖₊ ∂μ) < ∞ := hfi.2
+  have hfi' : ∫⁻ x in ⋃ n, s n, ‖f x‖₊ ∂μ < ∞ := hfi.2
   set S := ⋃ i, s i
   have hSm : MeasurableSet S := MeasurableSet.iUnion hsm
   have hsub : ∀ {i}, s i ⊆ S := subset_Union s
@@ -266,24 +266,24 @@ theorem hasSum_integral_iUnion {ι : Type _} [Countable ι] {s : ι → Set α}
 
 theorem integral_iUnion {ι : Type _} [Countable ι] {s : ι → Set α} (hm : ∀ i, MeasurableSet (s i))
     (hd : Pairwise (Disjoint on s)) (hfi : IntegrableOn f (⋃ i, s i) μ) :
-    (∫ a in ⋃ n, s n, f a ∂μ) = ∑' n, ∫ a in s n, f a ∂μ :=
+    ∫ a in ⋃ n, s n, f a ∂μ = ∑' n, ∫ a in s n, f a ∂μ :=
   (HasSum.tsum_eq (hasSum_integral_iUnion hm hd hfi)).symm
 #align measure_theory.integral_Union MeasureTheory.integral_iUnion
 
 theorem integral_iUnion_ae {ι : Type _} [Countable ι] {s : ι → Set α}
     (hm : ∀ i, NullMeasurableSet (s i) μ) (hd : Pairwise (AEDisjoint μ on s))
-    (hfi : IntegrableOn f (⋃ i, s i) μ) : (∫ a in ⋃ n, s n, f a ∂μ) = ∑' n, ∫ a in s n, f a ∂μ :=
+    (hfi : IntegrableOn f (⋃ i, s i) μ) : ∫ a in ⋃ n, s n, f a ∂μ = ∑' n, ∫ a in s n, f a ∂μ :=
   (HasSum.tsum_eq (hasSum_integral_iUnion_ae hm hd hfi)).symm
 #align measure_theory.integral_Union_ae MeasureTheory.integral_iUnion_ae
 
 theorem set_integral_eq_zero_of_ae_eq_zero (ht_eq : ∀ᵐ x ∂μ, x ∈ t → f x = 0) :
-    (∫ x in t, f x ∂μ) = 0 :=
+    ∫ x in t, f x ∂μ = 0 :=
   by
   by_cases hf : ae_strongly_measurable f (μ.restrict t); swap
   · rw [integral_undef]
     contrapose! hf
     exact hf.1
-  have : (∫ x in t, hf.mk f x ∂μ) = 0 :=
+  have : ∫ x in t, hf.mk f x ∂μ = 0 :=
     by
     refine' integral_eq_zero_of_ae _
     rw [eventually_eq,
@@ -295,19 +295,18 @@ theorem set_integral_eq_zero_of_ae_eq_zero (ht_eq : ∀ᵐ x ∂μ, x ∈ t →
   exact integral_congr_ae hf.ae_eq_mk
 #align measure_theory.set_integral_eq_zero_of_ae_eq_zero MeasureTheory.set_integral_eq_zero_of_ae_eq_zero
 
-theorem set_integral_eq_zero_of_forall_eq_zero (ht_eq : ∀ x ∈ t, f x = 0) :
-    (∫ x in t, f x ∂μ) = 0 :=
+theorem set_integral_eq_zero_of_forall_eq_zero (ht_eq : ∀ x ∈ t, f x = 0) : ∫ x in t, f x ∂μ = 0 :=
   set_integral_eq_zero_of_ae_eq_zero (eventually_of_forall ht_eq)
 #align measure_theory.set_integral_eq_zero_of_forall_eq_zero MeasureTheory.set_integral_eq_zero_of_forall_eq_zero
 
 theorem integral_union_eq_left_of_ae_aux (ht_eq : ∀ᵐ x ∂μ.restrict t, f x = 0)
     (haux : StronglyMeasurable f) (H : IntegrableOn f (s ∪ t) μ) :
-    (∫ x in s ∪ t, f x ∂μ) = ∫ x in s, f x ∂μ :=
+    ∫ x in s ∪ t, f x ∂μ = ∫ x in s, f x ∂μ :=
   by
   let k := f ⁻¹' {0}
   have hk : MeasurableSet k := by borelize E; exact haux.measurable (measurable_set_singleton _)
   have h's : integrable_on f s μ := H.mono (subset_union_left _ _) le_rfl
-  have A : ∀ u : Set α, (∫ x in u ∩ k, f x ∂μ) = 0 := fun u =>
+  have A : ∀ u : Set α, ∫ x in u ∩ k, f x ∂μ = 0 := fun u =>
     set_integral_eq_zero_of_forall_eq_zero fun x hx => hx.2
   rw [← integral_inter_add_diff hk h's, ← integral_inter_add_diff hk H, A, A, zero_add, zero_add,
     union_diff_distrib, union_comm]
@@ -319,14 +318,14 @@ theorem integral_union_eq_left_of_ae_aux (ht_eq : ∀ᵐ x ∂μ.restrict t, f x
 #align measure_theory.integral_union_eq_left_of_ae_aux MeasureTheory.integral_union_eq_left_of_ae_aux
 
 theorem integral_union_eq_left_of_ae (ht_eq : ∀ᵐ x ∂μ.restrict t, f x = 0) :
-    (∫ x in s ∪ t, f x ∂μ) = ∫ x in s, f x ∂μ :=
+    ∫ x in s ∪ t, f x ∂μ = ∫ x in s, f x ∂μ :=
   by
   have ht : integrable_on f t μ := by apply integrable_on_zero.congr_fun_ae; symm; exact ht_eq
   by_cases H : integrable_on f (s ∪ t) μ; swap
   · rw [integral_undef H, integral_undef]; simpa [integrable_on_union, ht] using H
   let f' := H.1.mk f
   calc
-    (∫ x : α in s ∪ t, f x ∂μ) = ∫ x : α in s ∪ t, f' x ∂μ := integral_congr_ae H.1.ae_eq_mk
+    ∫ x : α in s ∪ t, f x ∂μ = ∫ x : α in s ∪ t, f' x ∂μ := integral_congr_ae H.1.ae_eq_mk
     _ = ∫ x in s, f' x ∂μ :=
       by
       apply
@@ -340,23 +339,23 @@ theorem integral_union_eq_left_of_ae (ht_eq : ∀ᵐ x ∂μ.restrict t, f x = 0
 #align measure_theory.integral_union_eq_left_of_ae MeasureTheory.integral_union_eq_left_of_ae
 
 theorem integral_union_eq_left_of_forall₀ {f : α → E} (ht : NullMeasurableSet t μ)
-    (ht_eq : ∀ x ∈ t, f x = 0) : (∫ x in s ∪ t, f x ∂μ) = ∫ x in s, f x ∂μ :=
+    (ht_eq : ∀ x ∈ t, f x = 0) : ∫ x in s ∪ t, f x ∂μ = ∫ x in s, f x ∂μ :=
   integral_union_eq_left_of_ae ((ae_restrict_iff'₀ ht).2 (eventually_of_forall ht_eq))
 #align measure_theory.integral_union_eq_left_of_forall₀ MeasureTheory.integral_union_eq_left_of_forall₀
 
 theorem integral_union_eq_left_of_forall {f : α → E} (ht : MeasurableSet t)
-    (ht_eq : ∀ x ∈ t, f x = 0) : (∫ x in s ∪ t, f x ∂μ) = ∫ x in s, f x ∂μ :=
+    (ht_eq : ∀ x ∈ t, f x = 0) : ∫ x in s ∪ t, f x ∂μ = ∫ x in s, f x ∂μ :=
   integral_union_eq_left_of_forall₀ ht.NullMeasurableSet ht_eq
 #align measure_theory.integral_union_eq_left_of_forall MeasureTheory.integral_union_eq_left_of_forall
 
 theorem set_integral_eq_of_subset_of_ae_diff_eq_zero_aux (hts : s ⊆ t)
     (h't : ∀ᵐ x ∂μ, x ∈ t \ s → f x = 0) (haux : StronglyMeasurable f)
-    (h'aux : IntegrableOn f t μ) : (∫ x in t, f x ∂μ) = ∫ x in s, f x ∂μ :=
+    (h'aux : IntegrableOn f t μ) : ∫ x in t, f x ∂μ = ∫ x in s, f x ∂μ :=
   by
   let k := f ⁻¹' {0}
   have hk : MeasurableSet k := by borelize E; exact haux.measurable (measurable_set_singleton _)
   calc
-    (∫ x in t, f x ∂μ) = (∫ x in t ∩ k, f x ∂μ) + ∫ x in t \ k, f x ∂μ := by
+    ∫ x in t, f x ∂μ = ∫ x in t ∩ k, f x ∂μ + ∫ x in t \ k, f x ∂μ := by
       rw [integral_inter_add_diff hk h'aux]
     _ = ∫ x in t \ k, f x ∂μ := by
       rw [set_integral_eq_zero_of_forall_eq_zero fun x hx => _, zero_add]; exact hx.2
@@ -371,7 +370,7 @@ theorem set_integral_eq_of_subset_of_ae_diff_eq_zero_aux (hts : s ⊆ t)
       · simp only [xs, iff_false_iff]
         intro xt
         exact h'x (hx ⟨xt, xs⟩)
-    _ = (∫ x in s ∩ k, f x ∂μ) + ∫ x in s \ k, f x ∂μ :=
+    _ = ∫ x in s ∩ k, f x ∂μ + ∫ x in s \ k, f x ∂μ :=
       by
       have : ∀ x ∈ s ∩ k, f x = 0 := fun x hx => hx.2
       rw [set_integral_eq_zero_of_forall_eq_zero this, zero_add]
@@ -381,14 +380,14 @@ theorem set_integral_eq_of_subset_of_ae_diff_eq_zero_aux (hts : s ⊆ t)
 /-- If a function vanishes almost everywhere on `t \ s` with `s ⊆ t`, then its integrals on `s`
 and `t` coincide if `t` is null-measurable. -/
 theorem set_integral_eq_of_subset_of_ae_diff_eq_zero (ht : NullMeasurableSet t μ) (hts : s ⊆ t)
-    (h't : ∀ᵐ x ∂μ, x ∈ t \ s → f x = 0) : (∫ x in t, f x ∂μ) = ∫ x in s, f x ∂μ :=
+    (h't : ∀ᵐ x ∂μ, x ∈ t \ s → f x = 0) : ∫ x in t, f x ∂μ = ∫ x in s, f x ∂μ :=
   by
   by_cases h : integrable_on f t μ; swap
   · have : ¬integrable_on f s μ := fun H => h (H.of_ae_diff_eq_zero ht h't)
     rw [integral_undef h, integral_undef this]
   let f' := h.1.mk f
   calc
-    (∫ x in t, f x ∂μ) = ∫ x in t, f' x ∂μ := integral_congr_ae h.1.ae_eq_mk
+    ∫ x in t, f x ∂μ = ∫ x in t, f' x ∂μ := integral_congr_ae h.1.ae_eq_mk
     _ = ∫ x in s, f' x ∂μ :=
       by
       apply
@@ -405,7 +404,7 @@ theorem set_integral_eq_of_subset_of_ae_diff_eq_zero (ht : NullMeasurableSet t 
 /-- If a function vanishes on `t \ s` with `s ⊆ t`, then its integrals on `s`
 and `t` coincide if `t` is measurable. -/
 theorem set_integral_eq_of_subset_of_forall_diff_eq_zero (ht : MeasurableSet t) (hts : s ⊆ t)
-    (h't : ∀ x ∈ t \ s, f x = 0) : (∫ x in t, f x ∂μ) = ∫ x in s, f x ∂μ :=
+    (h't : ∀ x ∈ t \ s, f x = 0) : ∫ x in t, f x ∂μ = ∫ x in s, f x ∂μ :=
   set_integral_eq_of_subset_of_ae_diff_eq_zero ht.NullMeasurableSet hts
     (eventually_of_forall fun x hx => h't x hx)
 #align measure_theory.set_integral_eq_of_subset_of_forall_diff_eq_zero MeasureTheory.set_integral_eq_of_subset_of_forall_diff_eq_zero
@@ -413,7 +412,7 @@ theorem set_integral_eq_of_subset_of_forall_diff_eq_zero (ht : MeasurableSet t)
 /-- If a function vanishes almost everywhere on `sᶜ`, then its integral on `s`
 coincides with its integral on the whole space. -/
 theorem set_integral_eq_integral_of_ae_compl_eq_zero (h : ∀ᵐ x ∂μ, x ∉ s → f x = 0) :
-    (∫ x in s, f x ∂μ) = ∫ x, f x ∂μ :=
+    ∫ x in s, f x ∂μ = ∫ x, f x ∂μ :=
   by
   conv_rhs => rw [← integral_univ]
   symm
@@ -424,14 +423,13 @@ theorem set_integral_eq_integral_of_ae_compl_eq_zero (h : ∀ᵐ x ∂μ, x ∉
 /-- If a function vanishes on `sᶜ`, then its integral on `s` coincides with its integral on the
 whole space. -/
 theorem set_integral_eq_integral_of_forall_compl_eq_zero (h : ∀ x, x ∉ s → f x = 0) :
-    (∫ x in s, f x ∂μ) = ∫ x, f x ∂μ :=
+    ∫ x in s, f x ∂μ = ∫ x, f x ∂μ :=
   set_integral_eq_integral_of_ae_compl_eq_zero (eventually_of_forall h)
 #align measure_theory.set_integral_eq_integral_of_forall_compl_eq_zero MeasureTheory.set_integral_eq_integral_of_forall_compl_eq_zero
 
 #print MeasureTheory.set_integral_neg_eq_set_integral_nonpos /-
 theorem set_integral_neg_eq_set_integral_nonpos [LinearOrder E] {f : α → E}
-    (hf : AEStronglyMeasurable f μ) :
-    (∫ x in {x | f x < 0}, f x ∂μ) = ∫ x in {x | f x ≤ 0}, f x ∂μ :=
+    (hf : AEStronglyMeasurable f μ) : ∫ x in {x | f x < 0}, f x ∂μ = ∫ x in {x | f x ≤ 0}, f x ∂μ :=
   by
   have h_union : {x | f x ≤ 0} = {x | f x < 0} ∪ {x | f x = 0} := by ext;
     simp_rw [Set.mem_union, Set.mem_setOf_eq]; exact le_iff_lt_or_eq
@@ -445,20 +443,20 @@ theorem set_integral_neg_eq_set_integral_nonpos [LinearOrder E] {f : α → E}
 -/
 
 theorem integral_norm_eq_pos_sub_neg {f : α → ℝ} (hfi : Integrable f μ) :
-    (∫ x, ‖f x‖ ∂μ) = (∫ x in {x | 0 ≤ f x}, f x ∂μ) - ∫ x in {x | f x ≤ 0}, f x ∂μ :=
+    ∫ x, ‖f x‖ ∂μ = ∫ x in {x | 0 ≤ f x}, f x ∂μ - ∫ x in {x | f x ≤ 0}, f x ∂μ :=
   have h_meas : NullMeasurableSet {x | 0 ≤ f x} μ :=
     aestronglyMeasurable_const.nullMeasurableSet_le hfi.1
   calc
-    (∫ x, ‖f x‖ ∂μ) = (∫ x in {x | 0 ≤ f x}, ‖f x‖ ∂μ) + ∫ x in {x | 0 ≤ f x}ᶜ, ‖f x‖ ∂μ := by
+    ∫ x, ‖f x‖ ∂μ = ∫ x in {x | 0 ≤ f x}, ‖f x‖ ∂μ + ∫ x in {x | 0 ≤ f x}ᶜ, ‖f x‖ ∂μ := by
       rw [← integral_add_compl₀ h_meas hfi.norm]
-    _ = (∫ x in {x | 0 ≤ f x}, f x ∂μ) + ∫ x in {x | 0 ≤ f x}ᶜ, ‖f x‖ ∂μ :=
+    _ = ∫ x in {x | 0 ≤ f x}, f x ∂μ + ∫ x in {x | 0 ≤ f x}ᶜ, ‖f x‖ ∂μ :=
       by
       congr 1
       refine' set_integral_congr₀ h_meas fun x hx => _
       dsimp only
       rw [Real.norm_eq_abs, abs_eq_self.mpr _]
       exact hx
-    _ = (∫ x in {x | 0 ≤ f x}, f x ∂μ) - ∫ x in {x | 0 ≤ f x}ᶜ, f x ∂μ :=
+    _ = ∫ x in {x | 0 ≤ f x}, f x ∂μ - ∫ x in {x | 0 ≤ f x}ᶜ, f x ∂μ :=
       by
       congr 1
       rw [← integral_neg]
@@ -467,41 +465,40 @@ theorem integral_norm_eq_pos_sub_neg {f : α → ℝ} (hfi : Integrable f μ) :
       rw [Real.norm_eq_abs, abs_eq_neg_self.mpr _]
       rw [Set.mem_compl_iff, Set.nmem_setOf_iff] at hx 
       linarith
-    _ = (∫ x in {x | 0 ≤ f x}, f x ∂μ) - ∫ x in {x | f x ≤ 0}, f x ∂μ := by
+    _ = ∫ x in {x | 0 ≤ f x}, f x ∂μ - ∫ x in {x | f x ≤ 0}, f x ∂μ := by
       rw [← set_integral_neg_eq_set_integral_nonpos hfi.1]; congr; ext1 x; simp
 #align measure_theory.integral_norm_eq_pos_sub_neg MeasureTheory.integral_norm_eq_pos_sub_neg
 
 #print MeasureTheory.set_integral_const /-
-theorem set_integral_const (c : E) : (∫ x in s, c ∂μ) = (μ s).toReal • c := by
+theorem set_integral_const (c : E) : ∫ x in s, c ∂μ = (μ s).toReal • c := by
   rw [integral_const, measure.restrict_apply_univ]
 #align measure_theory.set_integral_const MeasureTheory.set_integral_const
 -/
 
 @[simp]
 theorem integral_indicator_const (e : E) ⦃s : Set α⦄ (s_meas : MeasurableSet s) :
-    (∫ a : α, s.indicator (fun x : α => e) a ∂μ) = (μ s).toReal • e := by
+    ∫ a : α, s.indicator (fun x : α => e) a ∂μ = (μ s).toReal • e := by
   rw [integral_indicator s_meas, ← set_integral_const]
 #align measure_theory.integral_indicator_const MeasureTheory.integral_indicator_const
 
 @[simp]
 theorem integral_indicator_one ⦃s : Set α⦄ (hs : MeasurableSet s) :
-    (∫ a, s.indicator 1 a ∂μ) = (μ s).toReal :=
+    ∫ a, s.indicator 1 a ∂μ = (μ s).toReal :=
   (integral_indicator_const 1 hs).trans ((smul_eq_mul _).trans (mul_one _))
 #align measure_theory.integral_indicator_one MeasureTheory.integral_indicator_one
 
 theorem set_integral_indicatorConstLp {p : ℝ≥0∞} (hs : MeasurableSet s) (ht : MeasurableSet t)
-    (hμt : μ t ≠ ∞) (x : E) :
-    (∫ a in s, indicatorConstLp p ht hμt x a ∂μ) = (μ (t ∩ s)).toReal • x :=
+    (hμt : μ t ≠ ∞) (x : E) : ∫ a in s, indicatorConstLp p ht hμt x a ∂μ = (μ (t ∩ s)).toReal • x :=
   calc
-    (∫ a in s, indicatorConstLp p ht hμt x a ∂μ) = ∫ a in s, t.indicator (fun _ => x) a ∂μ := by
+    ∫ a in s, indicatorConstLp p ht hμt x a ∂μ = ∫ a in s, t.indicator (fun _ => x) a ∂μ := by
       rw [set_integral_congr_ae hs (indicator_const_Lp_coe_fn.mono fun x hx hxs => hx)]
     _ = (μ (t ∩ s)).toReal • x := by rw [integral_indicator_const _ ht, measure.restrict_apply ht]
 #align measure_theory.set_integral_indicator_const_Lp MeasureTheory.set_integral_indicatorConstLp
 
 theorem integral_indicatorConstLp {p : ℝ≥0∞} (ht : MeasurableSet t) (hμt : μ t ≠ ∞) (x : E) :
-    (∫ a, indicatorConstLp p ht hμt x a ∂μ) = (μ t).toReal • x :=
+    ∫ a, indicatorConstLp p ht hμt x a ∂μ = (μ t).toReal • x :=
   calc
-    (∫ a, indicatorConstLp p ht hμt x a ∂μ) = ∫ a in univ, indicatorConstLp p ht hμt x a ∂μ := by
+    ∫ a, indicatorConstLp p ht hμt x a ∂μ = ∫ a in univ, indicatorConstLp p ht hμt x a ∂μ := by
       rw [integral_univ]
     _ = (μ (t ∩ univ)).toReal • x := (set_integral_indicatorConstLp MeasurableSet.univ ht hμt x)
     _ = (μ t).toReal • x := by rw [inter_univ]
@@ -510,7 +507,7 @@ theorem integral_indicatorConstLp {p : ℝ≥0∞} (ht : MeasurableSet t) (hμt
 #print MeasureTheory.set_integral_map /-
 theorem set_integral_map {β} [MeasurableSpace β] {g : α → β} {f : β → E} {s : Set β}
     (hs : MeasurableSet s) (hf : AEStronglyMeasurable f (Measure.map g μ)) (hg : AEMeasurable g μ) :
-    (∫ y in s, f y ∂Measure.map g μ) = ∫ x in g ⁻¹' s, f (g x) ∂μ :=
+    ∫ y in s, f y ∂Measure.map g μ = ∫ x in g ⁻¹' s, f (g x) ∂μ :=
   by
   rw [measure.restrict_map_of_ae_measurable hg hs,
     integral_map (hg.mono_measure measure.restrict_le_self) (hf.mono_measure _)]
@@ -520,30 +517,30 @@ theorem set_integral_map {β} [MeasurableSpace β] {g : α → β} {f : β → E
 
 theorem MeasurableEmbedding.set_integral_map {β} {_ : MeasurableSpace β} {f : α → β}
     (hf : MeasurableEmbedding f) (g : β → E) (s : Set β) :
-    (∫ y in s, g y ∂Measure.map f μ) = ∫ x in f ⁻¹' s, g (f x) ∂μ := by
+    ∫ y in s, g y ∂Measure.map f μ = ∫ x in f ⁻¹' s, g (f x) ∂μ := by
   rw [hf.restrict_map, hf.integral_map]
 #align measurable_embedding.set_integral_map MeasurableEmbedding.set_integral_map
 
 theorem ClosedEmbedding.set_integral_map [TopologicalSpace α] [BorelSpace α] {β} [MeasurableSpace β]
     [TopologicalSpace β] [BorelSpace β] {g : α → β} {f : β → E} (s : Set β)
-    (hg : ClosedEmbedding g) : (∫ y in s, f y ∂Measure.map g μ) = ∫ x in g ⁻¹' s, f (g x) ∂μ :=
+    (hg : ClosedEmbedding g) : ∫ y in s, f y ∂Measure.map g μ = ∫ x in g ⁻¹' s, f (g x) ∂μ :=
   hg.MeasurableEmbedding.set_integral_map _ _
 #align closed_embedding.set_integral_map ClosedEmbedding.set_integral_map
 
 theorem MeasurePreserving.set_integral_preimage_emb {β} {_ : MeasurableSpace β} {f : α → β} {ν}
     (h₁ : MeasurePreserving f μ ν) (h₂ : MeasurableEmbedding f) (g : β → E) (s : Set β) :
-    (∫ x in f ⁻¹' s, g (f x) ∂μ) = ∫ y in s, g y ∂ν :=
+    ∫ x in f ⁻¹' s, g (f x) ∂μ = ∫ y in s, g y ∂ν :=
   (h₁.restrict_preimage_emb h₂ s).integral_comp h₂ _
 #align measure_theory.measure_preserving.set_integral_preimage_emb MeasureTheory.MeasurePreserving.set_integral_preimage_emb
 
 theorem MeasurePreserving.set_integral_image_emb {β} {_ : MeasurableSpace β} {f : α → β} {ν}
     (h₁ : MeasurePreserving f μ ν) (h₂ : MeasurableEmbedding f) (g : β → E) (s : Set α) :
-    (∫ y in f '' s, g y ∂ν) = ∫ x in s, g (f x) ∂μ :=
+    ∫ y in f '' s, g y ∂ν = ∫ x in s, g (f x) ∂μ :=
   Eq.symm <| (h₁.restrict_image_emb h₂ s).integral_comp h₂ _
 #align measure_theory.measure_preserving.set_integral_image_emb MeasureTheory.MeasurePreserving.set_integral_image_emb
 
 theorem set_integral_map_equiv {β} [MeasurableSpace β] (e : α ≃ᵐ β) (f : β → E) (s : Set β) :
-    (∫ y in s, f y ∂Measure.map e μ) = ∫ x in e ⁻¹' s, f (e x) ∂μ :=
+    ∫ y in s, f y ∂Measure.map e μ = ∫ x in e ⁻¹' s, f (e x) ∂μ :=
   e.MeasurableEmbedding.set_integral_map f s
 #align measure_theory.set_integral_map_equiv MeasureTheory.set_integral_map_equiv
 
@@ -589,14 +586,14 @@ theorem norm_set_integral_le_of_norm_le_const' {C : ℝ} (hs : μ s < ∞) (hsm
 
 #print MeasureTheory.set_integral_eq_zero_iff_of_nonneg_ae /-
 theorem set_integral_eq_zero_iff_of_nonneg_ae {f : α → ℝ} (hf : 0 ≤ᵐ[μ.restrict s] f)
-    (hfi : IntegrableOn f s μ) : (∫ x in s, f x ∂μ) = 0 ↔ f =ᵐ[μ.restrict s] 0 :=
+    (hfi : IntegrableOn f s μ) : ∫ x in s, f x ∂μ = 0 ↔ f =ᵐ[μ.restrict s] 0 :=
   integral_eq_zero_iff_of_nonneg_ae hf hfi
 #align measure_theory.set_integral_eq_zero_iff_of_nonneg_ae MeasureTheory.set_integral_eq_zero_iff_of_nonneg_ae
 -/
 
 #print MeasureTheory.set_integral_pos_iff_support_of_nonneg_ae /-
 theorem set_integral_pos_iff_support_of_nonneg_ae {f : α → ℝ} (hf : 0 ≤ᵐ[μ.restrict s] f)
-    (hfi : IntegrableOn f s μ) : (0 < ∫ x in s, f x ∂μ) ↔ 0 < μ (support f ∩ s) :=
+    (hfi : IntegrableOn f s μ) : 0 < ∫ x in s, f x ∂μ ↔ 0 < μ (support f ∩ s) :=
   by
   rw [integral_pos_iff_support_of_nonneg_ae hf hfi, measure.restrict_apply₀]
   rw [support_eq_preimage]
@@ -633,7 +630,7 @@ theorem set_integral_gt_gt {R : ℝ} {f : α → ℝ} (hR : 0 ≤ R) (hfm : Meas
 #print MeasureTheory.set_integral_trim /-
 theorem set_integral_trim {α} {m m0 : MeasurableSpace α} {μ : Measure α} (hm : m ≤ m0) {f : α → E}
     (hf_meas : strongly_measurable[m] f) {s : Set α} (hs : measurable_set[m] s) :
-    (∫ x in s, f x ∂μ) = ∫ x in s, f x ∂μ.trim hm := by
+    ∫ x in s, f x ∂μ = ∫ x in s, f x ∂μ.trim hm := by
   rwa [integral_trim hm hf_meas, restrict_trim hm μ]
 #align measure_theory.set_integral_trim MeasureTheory.set_integral_trim
 -/
@@ -650,80 +647,80 @@ section PartialOrder
 variable [PartialOrder α] {a b : α}
 
 theorem integral_Icc_eq_integral_Ioc' (ha : μ {a} = 0) :
-    (∫ t in Icc a b, f t ∂μ) = ∫ t in Ioc a b, f t ∂μ :=
+    ∫ t in Icc a b, f t ∂μ = ∫ t in Ioc a b, f t ∂μ :=
   set_integral_congr_set_ae (Ioc_ae_eq_Icc' ha).symm
 #align measure_theory.integral_Icc_eq_integral_Ioc' MeasureTheory.integral_Icc_eq_integral_Ioc'
 
 theorem integral_Icc_eq_integral_Ico' (hb : μ {b} = 0) :
-    (∫ t in Icc a b, f t ∂μ) = ∫ t in Ico a b, f t ∂μ :=
+    ∫ t in Icc a b, f t ∂μ = ∫ t in Ico a b, f t ∂μ :=
   set_integral_congr_set_ae (Ico_ae_eq_Icc' hb).symm
 #align measure_theory.integral_Icc_eq_integral_Ico' MeasureTheory.integral_Icc_eq_integral_Ico'
 
 theorem integral_Ioc_eq_integral_Ioo' (hb : μ {b} = 0) :
-    (∫ t in Ioc a b, f t ∂μ) = ∫ t in Ioo a b, f t ∂μ :=
+    ∫ t in Ioc a b, f t ∂μ = ∫ t in Ioo a b, f t ∂μ :=
   set_integral_congr_set_ae (Ioo_ae_eq_Ioc' hb).symm
 #align measure_theory.integral_Ioc_eq_integral_Ioo' MeasureTheory.integral_Ioc_eq_integral_Ioo'
 
 theorem integral_Ico_eq_integral_Ioo' (ha : μ {a} = 0) :
-    (∫ t in Ico a b, f t ∂μ) = ∫ t in Ioo a b, f t ∂μ :=
+    ∫ t in Ico a b, f t ∂μ = ∫ t in Ioo a b, f t ∂μ :=
   set_integral_congr_set_ae (Ioo_ae_eq_Ico' ha).symm
 #align measure_theory.integral_Ico_eq_integral_Ioo' MeasureTheory.integral_Ico_eq_integral_Ioo'
 
 theorem integral_Icc_eq_integral_Ioo' (ha : μ {a} = 0) (hb : μ {b} = 0) :
-    (∫ t in Icc a b, f t ∂μ) = ∫ t in Ioo a b, f t ∂μ :=
+    ∫ t in Icc a b, f t ∂μ = ∫ t in Ioo a b, f t ∂μ :=
   set_integral_congr_set_ae (Ioo_ae_eq_Icc' ha hb).symm
 #align measure_theory.integral_Icc_eq_integral_Ioo' MeasureTheory.integral_Icc_eq_integral_Ioo'
 
 theorem integral_Iic_eq_integral_Iio' (ha : μ {a} = 0) :
-    (∫ t in Iic a, f t ∂μ) = ∫ t in Iio a, f t ∂μ :=
+    ∫ t in Iic a, f t ∂μ = ∫ t in Iio a, f t ∂μ :=
   set_integral_congr_set_ae (Iio_ae_eq_Iic' ha).symm
 #align measure_theory.integral_Iic_eq_integral_Iio' MeasureTheory.integral_Iic_eq_integral_Iio'
 
 theorem integral_Ici_eq_integral_Ioi' (ha : μ {a} = 0) :
-    (∫ t in Ici a, f t ∂μ) = ∫ t in Ioi a, f t ∂μ :=
+    ∫ t in Ici a, f t ∂μ = ∫ t in Ioi a, f t ∂μ :=
   set_integral_congr_set_ae (Ioi_ae_eq_Ici' ha).symm
 #align measure_theory.integral_Ici_eq_integral_Ioi' MeasureTheory.integral_Ici_eq_integral_Ioi'
 
 variable [NoAtoms μ]
 
 #print MeasureTheory.integral_Icc_eq_integral_Ioc /-
-theorem integral_Icc_eq_integral_Ioc : (∫ t in Icc a b, f t ∂μ) = ∫ t in Ioc a b, f t ∂μ :=
+theorem integral_Icc_eq_integral_Ioc : ∫ t in Icc a b, f t ∂μ = ∫ t in Ioc a b, f t ∂μ :=
   integral_Icc_eq_integral_Ioc' <| measure_singleton a
 #align measure_theory.integral_Icc_eq_integral_Ioc MeasureTheory.integral_Icc_eq_integral_Ioc
 -/
 
 #print MeasureTheory.integral_Icc_eq_integral_Ico /-
-theorem integral_Icc_eq_integral_Ico : (∫ t in Icc a b, f t ∂μ) = ∫ t in Ico a b, f t ∂μ :=
+theorem integral_Icc_eq_integral_Ico : ∫ t in Icc a b, f t ∂μ = ∫ t in Ico a b, f t ∂μ :=
   integral_Icc_eq_integral_Ico' <| measure_singleton b
 #align measure_theory.integral_Icc_eq_integral_Ico MeasureTheory.integral_Icc_eq_integral_Ico
 -/
 
 #print MeasureTheory.integral_Ioc_eq_integral_Ioo /-
-theorem integral_Ioc_eq_integral_Ioo : (∫ t in Ioc a b, f t ∂μ) = ∫ t in Ioo a b, f t ∂μ :=
+theorem integral_Ioc_eq_integral_Ioo : ∫ t in Ioc a b, f t ∂μ = ∫ t in Ioo a b, f t ∂μ :=
   integral_Ioc_eq_integral_Ioo' <| measure_singleton b
 #align measure_theory.integral_Ioc_eq_integral_Ioo MeasureTheory.integral_Ioc_eq_integral_Ioo
 -/
 
 #print MeasureTheory.integral_Ico_eq_integral_Ioo /-
-theorem integral_Ico_eq_integral_Ioo : (∫ t in Ico a b, f t ∂μ) = ∫ t in Ioo a b, f t ∂μ :=
+theorem integral_Ico_eq_integral_Ioo : ∫ t in Ico a b, f t ∂μ = ∫ t in Ioo a b, f t ∂μ :=
   integral_Ico_eq_integral_Ioo' <| measure_singleton a
 #align measure_theory.integral_Ico_eq_integral_Ioo MeasureTheory.integral_Ico_eq_integral_Ioo
 -/
 
 #print MeasureTheory.integral_Icc_eq_integral_Ioo /-
-theorem integral_Icc_eq_integral_Ioo : (∫ t in Icc a b, f t ∂μ) = ∫ t in Ico a b, f t ∂μ := by
+theorem integral_Icc_eq_integral_Ioo : ∫ t in Icc a b, f t ∂μ = ∫ t in Ico a b, f t ∂μ := by
   rw [integral_Icc_eq_integral_Ico, integral_Ico_eq_integral_Ioo]
 #align measure_theory.integral_Icc_eq_integral_Ioo MeasureTheory.integral_Icc_eq_integral_Ioo
 -/
 
 #print MeasureTheory.integral_Iic_eq_integral_Iio /-
-theorem integral_Iic_eq_integral_Iio : (∫ t in Iic a, f t ∂μ) = ∫ t in Iio a, f t ∂μ :=
+theorem integral_Iic_eq_integral_Iio : ∫ t in Iic a, f t ∂μ = ∫ t in Iio a, f t ∂μ :=
   integral_Iic_eq_integral_Iio' <| measure_singleton a
 #align measure_theory.integral_Iic_eq_integral_Iio MeasureTheory.integral_Iic_eq_integral_Iio
 -/
 
 #print MeasureTheory.integral_Ici_eq_integral_Ioi /-
-theorem integral_Ici_eq_integral_Ioi : (∫ t in Ici a, f t ∂μ) = ∫ t in Ioi a, f t ∂μ :=
+theorem integral_Ici_eq_integral_Ioi : ∫ t in Ici a, f t ∂μ = ∫ t in Ioi a, f t ∂μ :=
   integral_Ici_eq_integral_Ioi' <| measure_singleton a
 #align measure_theory.integral_Ici_eq_integral_Ioi MeasureTheory.integral_Ici_eq_integral_Ioi
 -/
@@ -739,17 +736,17 @@ variable {μ : Measure α} {f g : α → ℝ} {s t : Set α} (hf : IntegrableOn
 
 #print MeasureTheory.set_integral_mono_ae_restrict /-
 theorem set_integral_mono_ae_restrict (h : f ≤ᵐ[μ.restrict s] g) :
-    (∫ a in s, f a ∂μ) ≤ ∫ a in s, g a ∂μ :=
+    ∫ a in s, f a ∂μ ≤ ∫ a in s, g a ∂μ :=
   integral_mono_ae hf hg h
 #align measure_theory.set_integral_mono_ae_restrict MeasureTheory.set_integral_mono_ae_restrict
 -/
 
-theorem set_integral_mono_ae (h : f ≤ᵐ[μ] g) : (∫ a in s, f a ∂μ) ≤ ∫ a in s, g a ∂μ :=
+theorem set_integral_mono_ae (h : f ≤ᵐ[μ] g) : ∫ a in s, f a ∂μ ≤ ∫ a in s, g a ∂μ :=
   set_integral_mono_ae_restrict hf hg (ae_restrict_of_ae h)
 #align measure_theory.set_integral_mono_ae MeasureTheory.set_integral_mono_ae
 
 theorem set_integral_mono_on (hs : MeasurableSet s) (h : ∀ x ∈ s, f x ≤ g x) :
-    (∫ a in s, f a ∂μ) ≤ ∫ a in s, g a ∂μ :=
+    ∫ a in s, f a ∂μ ≤ ∫ a in s, g a ∂μ :=
   set_integral_mono_ae_restrict hf hg
     (by simp [hs, eventually_le, eventually_inf_principal, ae_of_all _ h])
 #align measure_theory.set_integral_mono_on MeasureTheory.set_integral_mono_on
@@ -758,19 +755,19 @@ include hf hg
 
 -- why do I need this include, but we don't need it in other lemmas?
 theorem set_integral_mono_on_ae (hs : MeasurableSet s) (h : ∀ᵐ x ∂μ, x ∈ s → f x ≤ g x) :
-    (∫ a in s, f a ∂μ) ≤ ∫ a in s, g a ∂μ := by refine' set_integral_mono_ae_restrict hf hg _;
+    ∫ a in s, f a ∂μ ≤ ∫ a in s, g a ∂μ := by refine' set_integral_mono_ae_restrict hf hg _;
   rwa [eventually_le, ae_restrict_iff' hs]
 #align measure_theory.set_integral_mono_on_ae MeasureTheory.set_integral_mono_on_ae
 
 omit hf hg
 
-theorem set_integral_mono (h : f ≤ g) : (∫ a in s, f a ∂μ) ≤ ∫ a in s, g a ∂μ :=
+theorem set_integral_mono (h : f ≤ g) : ∫ a in s, f a ∂μ ≤ ∫ a in s, g a ∂μ :=
   integral_mono hf hg h
 #align measure_theory.set_integral_mono MeasureTheory.set_integral_mono
 
 #print MeasureTheory.set_integral_mono_set /-
 theorem set_integral_mono_set (hfi : IntegrableOn f t μ) (hf : 0 ≤ᵐ[μ.restrict t] f)
-    (hst : s ≤ᵐ[μ] t) : (∫ x in s, f x ∂μ) ≤ ∫ x in t, f x ∂μ :=
+    (hst : s ≤ᵐ[μ] t) : ∫ x in s, f x ∂μ ≤ ∫ x in t, f x ∂μ :=
   integral_mono_measure (Measure.restrict_mono_ae hst) hf hfi
 #align measure_theory.set_integral_mono_set MeasureTheory.set_integral_mono_set
 -/
@@ -810,7 +807,7 @@ theorem set_integral_nonneg_ae (hs : MeasurableSet s) (hf : ∀ᵐ a ∂μ, a 
 #align measure_theory.set_integral_nonneg_ae MeasureTheory.set_integral_nonneg_ae
 
 theorem set_integral_le_nonneg {s : Set α} (hs : MeasurableSet s) (hf : StronglyMeasurable f)
-    (hfi : Integrable f μ) : (∫ x in s, f x ∂μ) ≤ ∫ x in {y | 0 ≤ f y}, f x ∂μ :=
+    (hfi : Integrable f μ) : ∫ x in s, f x ∂μ ≤ ∫ x in {y | 0 ≤ f y}, f x ∂μ :=
   by
   rw [← integral_indicator hs, ←
     integral_indicator (strongly_measurable_const.measurable_set_le hf)]
@@ -821,27 +818,27 @@ theorem set_integral_le_nonneg {s : Set α} (hs : MeasurableSet s) (hf : Strongl
 #align measure_theory.set_integral_le_nonneg MeasureTheory.set_integral_le_nonneg
 
 #print MeasureTheory.set_integral_nonpos_of_ae_restrict /-
-theorem set_integral_nonpos_of_ae_restrict (hf : f ≤ᵐ[μ.restrict s] 0) : (∫ a in s, f a ∂μ) ≤ 0 :=
+theorem set_integral_nonpos_of_ae_restrict (hf : f ≤ᵐ[μ.restrict s] 0) : ∫ a in s, f a ∂μ ≤ 0 :=
   integral_nonpos_of_ae hf
 #align measure_theory.set_integral_nonpos_of_ae_restrict MeasureTheory.set_integral_nonpos_of_ae_restrict
 -/
 
-theorem set_integral_nonpos_of_ae (hf : f ≤ᵐ[μ] 0) : (∫ a in s, f a ∂μ) ≤ 0 :=
+theorem set_integral_nonpos_of_ae (hf : f ≤ᵐ[μ] 0) : ∫ a in s, f a ∂μ ≤ 0 :=
   set_integral_nonpos_of_ae_restrict (ae_restrict_of_ae hf)
 #align measure_theory.set_integral_nonpos_of_ae MeasureTheory.set_integral_nonpos_of_ae
 
 theorem set_integral_nonpos (hs : MeasurableSet s) (hf : ∀ a, a ∈ s → f a ≤ 0) :
-    (∫ a in s, f a ∂μ) ≤ 0 :=
+    ∫ a in s, f a ∂μ ≤ 0 :=
   set_integral_nonpos_of_ae_restrict ((ae_restrict_iff' hs).mpr (ae_of_all μ hf))
 #align measure_theory.set_integral_nonpos MeasureTheory.set_integral_nonpos
 
 theorem set_integral_nonpos_ae (hs : MeasurableSet s) (hf : ∀ᵐ a ∂μ, a ∈ s → f a ≤ 0) :
-    (∫ a in s, f a ∂μ) ≤ 0 :=
+    ∫ a in s, f a ∂μ ≤ 0 :=
   set_integral_nonpos_of_ae_restrict <| by rwa [eventually_le, ae_restrict_iff' hs]
 #align measure_theory.set_integral_nonpos_ae MeasureTheory.set_integral_nonpos_ae
 
 theorem set_integral_nonpos_le {s : Set α} (hs : MeasurableSet s) (hf : StronglyMeasurable f)
-    (hfi : Integrable f μ) : (∫ x in {y | f y ≤ 0}, f x ∂μ) ≤ ∫ x in s, f x ∂μ :=
+    (hfi : Integrable f μ) : ∫ x in {y | f y ≤ 0}, f x ∂μ ≤ ∫ x in s, f x ∂μ :=
   by
   rw [← integral_indicator hs, ←
     integral_indicator (hf.measurable_set_le strongly_measurable_const)]
@@ -1046,9 +1043,9 @@ theorem Filter.Tendsto.integral_sub_linear_isLittleO_ae [NormedSpace ℝ E] [Com
     (hμ : μ.FiniteAtFilter l) {s : ι → Set α} {li : Filter ι} (hs : Tendsto s li l.smallSets)
     (m : ι → ℝ := fun i => (μ (s i)).toReal)
     (hsμ : (fun i => (μ (s i)).toReal) =ᶠ[li] m := by rfl) :
-    (fun i => (∫ x in s i, f x ∂μ) - m i • b) =o[li] m :=
+    (fun i => ∫ x in s i, f x ∂μ - m i • b) =o[li] m :=
   by
-  suffices : (fun s => (∫ x in s, f x ∂μ) - (μ s).toReal • b) =o[l.small_sets] fun s => (μ s).toReal
+  suffices : (fun s => ∫ x in s, f x ∂μ - (μ s).toReal • b) =o[l.small_sets] fun s => (μ s).toReal
   exact (this.comp_tendsto hs).congr' (hsμ.mono fun a ha => ha ▸ rfl) hsμ
   refine' is_o_iff.2 fun ε ε₀ => _
   have : ∀ᶠ s in l.small_sets, ∀ᶠ x in μ.ae, x ∈ s → f x ∈ closed_ball b ε :=
@@ -1077,7 +1074,7 @@ theorem ContinuousWithinAt.integral_sub_linear_isLittleO_ae [TopologicalSpace α
     (ht : MeasurableSet t) (hfm : StronglyMeasurableAtFilter f (𝓝[t] a) μ) {s : ι → Set α}
     {li : Filter ι} (hs : Tendsto s li (𝓝[t] a).smallSets) (m : ι → ℝ := fun i => (μ (s i)).toReal)
     (hsμ : (fun i => (μ (s i)).toReal) =ᶠ[li] m := by rfl) :
-    (fun i => (∫ x in s i, f x ∂μ) - m i • f a) =o[li] m :=
+    (fun i => ∫ x in s i, f x ∂μ - m i • f a) =o[li] m :=
   haveI : (𝓝[t] a).IsMeasurablyGenerated := ht.nhds_within_is_measurably_generated _
   (ha.mono_left inf_le_left).integral_sub_linear_isLittleO_ae hfm (μ.finite_at_nhds_within a t) hs m
     hsμ
@@ -1097,7 +1094,7 @@ theorem ContinuousAt.integral_sub_linear_isLittleO_ae [TopologicalSpace α] [Ope
     {f : α → E} (ha : ContinuousAt f a) (hfm : StronglyMeasurableAtFilter f (𝓝 a) μ) {s : ι → Set α}
     {li : Filter ι} (hs : Tendsto s li (𝓝 a).smallSets) (m : ι → ℝ := fun i => (μ (s i)).toReal)
     (hsμ : (fun i => (μ (s i)).toReal) =ᶠ[li] m := by rfl) :
-    (fun i => (∫ x in s i, f x ∂μ) - m i • f a) =o[li] m :=
+    (fun i => ∫ x in s i, f x ∂μ - m i • f a) =o[li] m :=
   (ha.mono_left inf_le_left).integral_sub_linear_isLittleO_ae hfm (μ.finiteAtNhds a) hs m hsμ
 #align continuous_at.integral_sub_linear_is_o_ae ContinuousAt.integral_sub_linear_isLittleO_ae
 
@@ -1115,7 +1112,7 @@ theorem ContinuousOn.integral_sub_linear_isLittleO_ae [TopologicalSpace α] [Ope
     (ht : MeasurableSet t) {s : ι → Set α} {li : Filter ι} (hs : Tendsto s li (𝓝[t] a).smallSets)
     (m : ι → ℝ := fun i => (μ (s i)).toReal)
     (hsμ : (fun i => (μ (s i)).toReal) =ᶠ[li] m := by rfl) :
-    (fun i => (∫ x in s i, f x ∂μ) - m i • f a) =o[li] m :=
+    (fun i => ∫ x in s i, f x ∂μ - m i • f a) =o[li] m :=
   (hft a ha).integral_sub_linear_isLittleO_ae ht
     ⟨t, self_mem_nhdsWithin, hft.AEStronglyMeasurable ht⟩ hs m hsμ
 #align continuous_on.integral_sub_linear_is_o_ae ContinuousOn.integral_sub_linear_isLittleO_ae
@@ -1141,13 +1138,12 @@ namespace ContinuousLinearMap
 
 variable [CompleteSpace F] [NormedSpace ℝ F]
 
-theorem integral_compLp (L : E →L[𝕜] F) (φ : Lp E p μ) :
-    (∫ a, (L.compLp φ) a ∂μ) = ∫ a, L (φ a) ∂μ :=
+theorem integral_compLp (L : E →L[𝕜] F) (φ : Lp E p μ) : ∫ a, (L.compLp φ) a ∂μ = ∫ a, L (φ a) ∂μ :=
   integral_congr_ae <| coeFn_compLp _ _
 #align continuous_linear_map.integral_comp_Lp ContinuousLinearMap.integral_compLp
 
 theorem set_integral_compLp (L : E →L[𝕜] F) (φ : Lp E p μ) {s : Set α} (hs : MeasurableSet s) :
-    (∫ a in s, (L.compLp φ) a ∂μ) = ∫ a in s, L (φ a) ∂μ :=
+    ∫ a in s, (L.compLp φ) a ∂μ = ∫ a in s, L (φ a) ∂μ :=
   set_integral_congr_ae hs ((L.coeFn_compLp φ).mono fun x hx hx2 => hx)
 #align continuous_linear_map.set_integral_comp_Lp ContinuousLinearMap.set_integral_compLp
 
@@ -1159,9 +1155,9 @@ theorem continuous_integral_comp_L1 (L : E →L[𝕜] F) :
 variable [CompleteSpace E] [NormedSpace ℝ E]
 
 theorem integral_comp_comm (L : E →L[𝕜] F) {φ : α → E} (φ_int : Integrable φ μ) :
-    (∫ a, L (φ a) ∂μ) = L (∫ a, φ a ∂μ) :=
+    ∫ a, L (φ a) ∂μ = L (∫ a, φ a ∂μ) :=
   by
-  apply integrable.induction fun φ => (∫ a, L (φ a) ∂μ) = L (∫ a, φ a ∂μ)
+  apply integrable.induction fun φ => ∫ a, L (φ a) ∂μ = L (∫ a, φ a ∂μ)
   · intro e s s_meas s_finite
     rw [integral_indicator_const e s_meas, ← @smul_one_smul E ℝ 𝕜 _ _ _ _ _ (μ s).toReal e,
       ContinuousLinearMap.map_smul, @smul_one_smul F ℝ 𝕜 _ _ _ _ _ (μ s).toReal (L e), ←
@@ -1185,7 +1181,7 @@ theorem integral_apply {H : Type _} [NormedAddCommGroup H] [NormedSpace 𝕜 H]
 #align continuous_linear_map.integral_apply ContinuousLinearMap.integral_apply
 
 theorem integral_comp_comm' (L : E →L[𝕜] F) {K} (hL : AntilipschitzWith K L) (φ : α → E) :
-    (∫ a, L (φ a) ∂μ) = L (∫ a, φ a ∂μ) :=
+    ∫ a, L (φ a) ∂μ = L (∫ a, φ a ∂μ) :=
   by
   by_cases h : integrable φ μ
   · exact integral_comp_comm L h
@@ -1194,8 +1190,7 @@ theorem integral_comp_comm' (L : E →L[𝕜] F) {K} (hL : AntilipschitzWith K L
   simp [integral_undef, h, this]
 #align continuous_linear_map.integral_comp_comm' ContinuousLinearMap.integral_comp_comm'
 
-theorem integral_comp_L1_comm (L : E →L[𝕜] F) (φ : α →₁[μ] E) :
-    (∫ a, L (φ a) ∂μ) = L (∫ a, φ a ∂μ) :=
+theorem integral_comp_L1_comm (L : E →L[𝕜] F) (φ : α →₁[μ] E) : ∫ a, L (φ a) ∂μ = L (∫ a, φ a ∂μ) :=
   L.integral_comp_comm (L1.integrable_coeFn φ)
 #align continuous_linear_map.integral_comp_L1_comm ContinuousLinearMap.integral_comp_L1_comm
 
@@ -1205,7 +1200,7 @@ namespace LinearIsometry
 
 variable [CompleteSpace F] [NormedSpace ℝ F] [CompleteSpace E] [NormedSpace ℝ E]
 
-theorem integral_comp_comm (L : E →ₗᵢ[𝕜] F) (φ : α → E) : (∫ a, L (φ a) ∂μ) = L (∫ a, φ a ∂μ) :=
+theorem integral_comp_comm (L : E →ₗᵢ[𝕜] F) (φ : α → E) : ∫ a, L (φ a) ∂μ = L (∫ a, φ a ∂μ) :=
   L.toContinuousLinearMap.integral_comp_comm' L.antilipschitz _
 #align linear_isometry.integral_comp_comm LinearIsometry.integral_comp_comm
 
@@ -1215,7 +1210,7 @@ namespace ContinuousLinearEquiv
 
 variable [CompleteSpace F] [NormedSpace ℝ F] [CompleteSpace E] [NormedSpace ℝ E]
 
-theorem integral_comp_comm (L : E ≃L[𝕜] F) (φ : α → E) : (∫ a, L (φ a) ∂μ) = L (∫ a, φ a ∂μ) :=
+theorem integral_comp_comm (L : E ≃L[𝕜] F) (φ : α → E) : ∫ a, L (φ a) ∂μ = L (∫ a, φ a ∂μ) :=
   L.toContinuousLinearMap.integral_comp_comm' L.antilipschitz _
 #align continuous_linear_equiv.integral_comp_comm ContinuousLinearEquiv.integral_comp_comm
 
@@ -1225,27 +1220,27 @@ variable [CompleteSpace E] [NormedSpace ℝ E] [CompleteSpace F] [NormedSpace 
 
 #print integral_ofReal /-
 @[norm_cast]
-theorem integral_ofReal {f : α → ℝ} : (∫ a, (f a : 𝕜) ∂μ) = ↑(∫ a, f a ∂μ) :=
+theorem integral_ofReal {f : α → ℝ} : ∫ a, (f a : 𝕜) ∂μ = ↑(∫ a, f a ∂μ) :=
   (@IsROrC.ofRealLi 𝕜 _).integral_comp_comm f
 #align integral_of_real integral_ofReal
 -/
 
 theorem integral_re {f : α → 𝕜} (hf : Integrable f μ) :
-    (∫ a, IsROrC.re (f a) ∂μ) = IsROrC.re (∫ a, f a ∂μ) :=
+    ∫ a, IsROrC.re (f a) ∂μ = IsROrC.re (∫ a, f a ∂μ) :=
   (@IsROrC.reClm 𝕜 _).integral_comp_comm hf
 #align integral_re integral_re
 
 theorem integral_im {f : α → 𝕜} (hf : Integrable f μ) :
-    (∫ a, IsROrC.im (f a) ∂μ) = IsROrC.im (∫ a, f a ∂μ) :=
+    ∫ a, IsROrC.im (f a) ∂μ = IsROrC.im (∫ a, f a ∂μ) :=
   (@IsROrC.imClm 𝕜 _).integral_comp_comm hf
 #align integral_im integral_im
 
-theorem integral_conj {f : α → 𝕜} : (∫ a, conj (f a) ∂μ) = conj (∫ a, f a ∂μ) :=
+theorem integral_conj {f : α → 𝕜} : ∫ a, conj (f a) ∂μ = conj (∫ a, f a ∂μ) :=
   (@IsROrC.conjLie 𝕜 _).toLinearIsometry.integral_comp_comm f
 #align integral_conj integral_conj
 
 theorem integral_coe_re_add_coe_im {f : α → 𝕜} (hf : Integrable f μ) :
-    (∫ x, (IsROrC.re (f x) : 𝕜) ∂μ) + (∫ x, IsROrC.im (f x) ∂μ) * IsROrC.i = ∫ x, f x ∂μ :=
+    ∫ x, (IsROrC.re (f x) : 𝕜) ∂μ + (∫ x, IsROrC.im (f x) ∂μ) * IsROrC.i = ∫ x, f x ∂μ :=
   by
   rw [mul_comm, ← smul_eq_mul, ← integral_smul, ← integral_add]
   · congr
@@ -1275,14 +1270,14 @@ theorem snd_integral {f : α → E × F} (hf : Integrable f μ) : (∫ x, f x 
 #align snd_integral snd_integral
 
 theorem integral_pair {f : α → E} {g : α → F} (hf : Integrable f μ) (hg : Integrable g μ) :
-    (∫ x, (f x, g x) ∂μ) = (∫ x, f x ∂μ, ∫ x, g x ∂μ) :=
+    ∫ x, (f x, g x) ∂μ = (∫ x, f x ∂μ, ∫ x, g x ∂μ) :=
   have := hf.prod_mk hg
   Prod.ext (fst_integral this) (snd_integral this)
 #align integral_pair integral_pair
 
 #print integral_smul_const /-
 theorem integral_smul_const {𝕜 : Type _} [IsROrC 𝕜] [NormedSpace 𝕜 E] (f : α → 𝕜) (c : E) :
-    (∫ x, f x • c ∂μ) = (∫ x, f x ∂μ) • c :=
+    ∫ x, f x • c ∂μ = (∫ x, f x ∂μ) • c :=
   by
   by_cases hf : integrable f μ
   · exact ((1 : 𝕜 →L[𝕜] 𝕜).smul_right c).integral_comp_comm hf

mathlib commit https://github.com/leanprover-community/mathlib/commit/7e5137f579de09a059a5ce98f364a04e221aabf0

@@ -191,7 +191,6 @@ theorem integral_indicator (hs : MeasurableSet s) : (∫ x, indicator s f x ∂
       (congr_arg₂ (· + ·) (integral_congr_ae (indicator_ae_eq_restrict hs))
         (integral_congr_ae (indicator_ae_eq_restrict_compl hs)))
     _ = ∫ x in s, f x ∂μ := by simp
-    
 #align measure_theory.integral_indicator MeasureTheory.integral_indicator
 
 theorem set_integral_indicator (ht : MeasurableSet t) :
@@ -209,7 +208,6 @@ theorem ofReal_set_integral_one_of_measure_ne_top {α : Type _} {m : MeasurableS
       rw [of_real_integral_norm_eq_lintegral_nnnorm (integrable_on_const.2 (Or.inr hs.lt_top))]
       simp only [nnnorm_one, ENNReal.coe_one]
     _ = μ s := set_lintegral_one _
-    
 #align measure_theory.of_real_set_integral_one_of_measure_ne_top MeasureTheory.ofReal_set_integral_one_of_measure_ne_top
 
 theorem ofReal_set_integral_one {α : Type _} {m : MeasurableSpace α} (μ : Measure α)
@@ -339,7 +337,6 @@ theorem integral_union_eq_left_of_ae (ht_eq : ∀ᵐ x ∂μ.restrict t, f x = 0
     _ = ∫ x in s, f x ∂μ :=
       integral_congr_ae
         (ae_mono (measure.restrict_mono (subset_union_left s t) le_rfl) H.1.ae_eq_mk.symm)
-    
 #align measure_theory.integral_union_eq_left_of_ae MeasureTheory.integral_union_eq_left_of_ae
 
 theorem integral_union_eq_left_of_forall₀ {f : α → E} (ht : NullMeasurableSet t μ)
@@ -379,7 +376,6 @@ theorem set_integral_eq_of_subset_of_ae_diff_eq_zero_aux (hts : s ⊆ t)
       have : ∀ x ∈ s ∩ k, f x = 0 := fun x hx => hx.2
       rw [set_integral_eq_zero_of_forall_eq_zero this, zero_add]
     _ = ∫ x in s, f x ∂μ := by rw [integral_inter_add_diff hk (h'aux.mono hts le_rfl)]
-    
 #align measure_theory.set_integral_eq_of_subset_of_ae_diff_eq_zero_aux MeasureTheory.set_integral_eq_of_subset_of_ae_diff_eq_zero_aux
 
 /-- If a function vanishes almost everywhere on `t \ s` with `s ⊆ t`, then its integrals on `s`
@@ -404,7 +400,6 @@ theorem set_integral_eq_of_subset_of_ae_diff_eq_zero (ht : NullMeasurableSet t 
       apply integral_congr_ae
       apply ae_restrict_of_ae_restrict_of_subset hts
       exact h.1.ae_eq_mk.symm
-    
 #align measure_theory.set_integral_eq_of_subset_of_ae_diff_eq_zero MeasureTheory.set_integral_eq_of_subset_of_ae_diff_eq_zero
 
 /-- If a function vanishes on `t \ s` with `s ⊆ t`, then its integrals on `s`
@@ -474,7 +469,6 @@ theorem integral_norm_eq_pos_sub_neg {f : α → ℝ} (hfi : Integrable f μ) :
       linarith
     _ = (∫ x in {x | 0 ≤ f x}, f x ∂μ) - ∫ x in {x | f x ≤ 0}, f x ∂μ := by
       rw [← set_integral_neg_eq_set_integral_nonpos hfi.1]; congr; ext1 x; simp
-    
 #align measure_theory.integral_norm_eq_pos_sub_neg MeasureTheory.integral_norm_eq_pos_sub_neg
 
 #print MeasureTheory.set_integral_const /-
@@ -502,7 +496,6 @@ theorem set_integral_indicatorConstLp {p : ℝ≥0∞} (hs : MeasurableSet s) (h
     (∫ a in s, indicatorConstLp p ht hμt x a ∂μ) = ∫ a in s, t.indicator (fun _ => x) a ∂μ := by
       rw [set_integral_congr_ae hs (indicator_const_Lp_coe_fn.mono fun x hx hxs => hx)]
     _ = (μ (t ∩ s)).toReal • x := by rw [integral_indicator_const _ ht, measure.restrict_apply ht]
-    
 #align measure_theory.set_integral_indicator_const_Lp MeasureTheory.set_integral_indicatorConstLp
 
 theorem integral_indicatorConstLp {p : ℝ≥0∞} (ht : MeasurableSet t) (hμt : μ t ≠ ∞) (x : E) :
@@ -512,7 +505,6 @@ theorem integral_indicatorConstLp {p : ℝ≥0∞} (ht : MeasurableSet t) (hμt
       rw [integral_univ]
     _ = (μ (t ∩ univ)).toReal • x := (set_integral_indicatorConstLp MeasurableSet.univ ht hμt x)
     _ = (μ t).toReal • x := by rw [inter_univ]
-    
 #align measure_theory.integral_indicator_const_Lp MeasureTheory.integral_indicatorConstLp
 
 #print MeasureTheory.set_integral_map /-
@@ -1367,7 +1359,6 @@ theorem integral_withDensity_eq_integral_smul₀ {f : α → ℝ≥0} (hf : AEMe
       apply integral_congr_ae
       filter_upwards [hf.ae_eq_mk] with x hx
       rw [hx]
-    
 #align integral_with_density_eq_integral_smul₀ integral_withDensity_eq_integral_smul₀
 
 theorem set_integral_withDensity_eq_set_integral_smul {f : α → ℝ≥0} (f_meas : Measurable f)

mathlib commit https://github.com/leanprover-community/mathlib/commit/31c24aa72e7b3e5ed97a8412470e904f82b81004

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Zhouhang Zhou, Yury Kudryashov
 
 ! This file was ported from Lean 3 source module measure_theory.integral.set_integral
-! leanprover-community/mathlib commit 24e0c85412ff6adbeca08022c25ba4876eedf37a
+! leanprover-community/mathlib commit c20927220ef87bb4962ba08bf6da2ce3cf50a6dd
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -18,6 +18,9 @@ import Mathbin.Topology.ContinuousFunction.Compact
 /-!
 # Set integral
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 In this file we prove some properties of `∫ x in s, f x ∂μ`. Recall that this notation
 is defined as `∫ x, f x ∂(μ.restrict s)`. In `integral_indicator` we prove that for a measurable
 function `f` and a measurable set `s` this definition coincides with another natural definition:

mathlib commit https://github.com/leanprover-community/mathlib/commit/58a272265b5e05f258161260dd2c5d247213cbd3

@@ -1228,11 +1228,11 @@ end ContinuousLinearEquiv
 
 variable [CompleteSpace E] [NormedSpace ℝ E] [CompleteSpace F] [NormedSpace ℝ F]
 
-#print integral_of_real /-
+#print integral_ofReal /-
 @[norm_cast]
-theorem integral_of_real {f : α → ℝ} : (∫ a, (f a : 𝕜) ∂μ) = ↑(∫ a, f a ∂μ) :=
+theorem integral_ofReal {f : α → ℝ} : (∫ a, (f a : 𝕜) ∂μ) = ↑(∫ a, f a ∂μ) :=
   (@IsROrC.ofRealLi 𝕜 _).integral_comp_comm f
-#align integral_of_real integral_of_real
+#align integral_of_real integral_ofReal
 -/
 
 theorem integral_re {f : α → 𝕜} (hf : Integrable f μ) :
@@ -1262,7 +1262,7 @@ theorem integral_coe_re_add_coe_im {f : α → 𝕜} (hf : Integrable f μ) :
 
 theorem integral_re_add_im {f : α → 𝕜} (hf : Integrable f μ) :
     ((∫ x, IsROrC.re (f x) ∂μ : ℝ) : 𝕜) + (∫ x, IsROrC.im (f x) ∂μ : ℝ) * IsROrC.i = ∫ x, f x ∂μ :=
-  by rw [← integral_of_real, ← integral_of_real, integral_coe_re_add_coe_im hf]
+  by rw [← integral_ofReal, ← integral_ofReal, integral_coe_re_add_coe_im hf]
 #align integral_re_add_im integral_re_add_im
 
 theorem set_integral_re_add_im {f : α → 𝕜} {i : Set α} (hf : IntegrableOn f i μ) :

mathlib commit https://github.com/leanprover-community/mathlib/commit/a3209ddf94136d36e5e5c624b10b2a347cc9d090

@@ -127,7 +127,7 @@ theorem integral_inter_add_diff (ht : MeasurableSet t) (hfs : IntegrableOn f s 
   integral_inter_add_diff₀ ht.NullMeasurableSet hfs
 #align measure_theory.integral_inter_add_diff MeasureTheory.integral_inter_add_diff
 
-theorem integral_finset_bUnion {ι : Type _} (t : Finset ι) {s : ι → Set α}
+theorem integral_finset_biUnion {ι : Type _} (t : Finset ι) {s : ι → Set α}
     (hs : ∀ i ∈ t, MeasurableSet (s i)) (h's : Set.Pairwise (↑t) (Disjoint on s))
     (hf : ∀ i ∈ t, IntegrableOn f (s i) μ) :
     (∫ x in ⋃ i ∈ t, s i, f x ∂μ) = ∑ i in t, ∫ x in s i, f x ∂μ :=
@@ -141,7 +141,7 @@ theorem integral_finset_bUnion {ι : Type _} (t : Finset ι) {s : ι → Set α}
     · simp only [disjoint_Union_right]
       exact fun i hi => (h's.2 i hi (ne_of_mem_of_not_mem hi hat).symm).1
     · exact Finset.measurableSet_biUnion _ hs.2
-#align measure_theory.integral_finset_bUnion MeasureTheory.integral_finset_bUnion
+#align measure_theory.integral_finset_bUnion MeasureTheory.integral_finset_biUnion
 
 theorem integral_fintype_iUnion {ι : Type _} [Fintype ι] {s : ι → Set α}
     (hs : ∀ i, MeasurableSet (s i)) (h's : Pairwise (Disjoint on s))
@@ -156,8 +156,10 @@ theorem integral_empty : (∫ x in ∅, f x ∂μ) = 0 := by
   rw [measure.restrict_empty, integral_zero_measure]
 #align measure_theory.integral_empty MeasureTheory.integral_empty
 
+#print MeasureTheory.integral_univ /-
 theorem integral_univ : (∫ x in univ, f x ∂μ) = ∫ x, f x ∂μ := by rw [measure.restrict_univ]
 #align measure_theory.integral_univ MeasureTheory.integral_univ
+-/
 
 theorem integral_add_compl₀ (hs : NullMeasurableSet s μ) (hfi : Integrable f μ) :
     ((∫ x in s, f x ∂μ) + ∫ x in sᶜ, f x ∂μ) = ∫ x, f x ∂μ := by
@@ -428,6 +430,7 @@ theorem set_integral_eq_integral_of_forall_compl_eq_zero (h : ∀ x, x ∉ s →
   set_integral_eq_integral_of_ae_compl_eq_zero (eventually_of_forall h)
 #align measure_theory.set_integral_eq_integral_of_forall_compl_eq_zero MeasureTheory.set_integral_eq_integral_of_forall_compl_eq_zero
 
+#print MeasureTheory.set_integral_neg_eq_set_integral_nonpos /-
 theorem set_integral_neg_eq_set_integral_nonpos [LinearOrder E] {f : α → E}
     (hf : AEStronglyMeasurable f μ) :
     (∫ x in {x | f x < 0}, f x ∂μ) = ∫ x in {x | f x ≤ 0}, f x ∂μ :=
@@ -441,6 +444,7 @@ theorem set_integral_neg_eq_set_integral_nonpos [LinearOrder E] {f : α → E}
   refine' integral_union_eq_left_of_ae _
   filter_upwards [ae_restrict_mem₀ B] with x hx using hx
 #align measure_theory.set_integral_neg_eq_set_integral_nonpos MeasureTheory.set_integral_neg_eq_set_integral_nonpos
+-/
 
 theorem integral_norm_eq_pos_sub_neg {f : α → ℝ} (hfi : Integrable f μ) :
     (∫ x, ‖f x‖ ∂μ) = (∫ x in {x | 0 ≤ f x}, f x ∂μ) - ∫ x in {x | f x ≤ 0}, f x ∂μ :=
@@ -470,9 +474,11 @@ theorem integral_norm_eq_pos_sub_neg {f : α → ℝ} (hfi : Integrable f μ) :
     
 #align measure_theory.integral_norm_eq_pos_sub_neg MeasureTheory.integral_norm_eq_pos_sub_neg
 
+#print MeasureTheory.set_integral_const /-
 theorem set_integral_const (c : E) : (∫ x in s, c ∂μ) = (μ s).toReal • c := by
   rw [integral_const, measure.restrict_apply_univ]
 #align measure_theory.set_integral_const MeasureTheory.set_integral_const
+-/
 
 @[simp]
 theorem integral_indicator_const (e : E) ⦃s : Set α⦄ (s_meas : MeasurableSet s) :
@@ -506,6 +512,7 @@ theorem integral_indicatorConstLp {p : ℝ≥0∞} (ht : MeasurableSet t) (hμt
     
 #align measure_theory.integral_indicator_const_Lp MeasureTheory.integral_indicatorConstLp
 
+#print MeasureTheory.set_integral_map /-
 theorem set_integral_map {β} [MeasurableSpace β] {g : α → β} {f : β → E} {s : Set β}
     (hs : MeasurableSet s) (hf : AEStronglyMeasurable f (Measure.map g μ)) (hg : AEMeasurable g μ) :
     (∫ y in s, f y ∂Measure.map g μ) = ∫ x in g ⁻¹' s, f (g x) ∂μ :=
@@ -514,6 +521,7 @@ theorem set_integral_map {β} [MeasurableSpace β] {g : α → β} {f : β → E
     integral_map (hg.mono_measure measure.restrict_le_self) (hf.mono_measure _)]
   exact measure.map_mono_of_ae_measurable measure.restrict_le_self hg
 #align measure_theory.set_integral_map MeasureTheory.set_integral_map
+-/
 
 theorem MeasurableEmbedding.set_integral_map {β} {_ : MeasurableSpace β} {f : α → β}
     (hf : MeasurableEmbedding f) (g : β → E) (s : Set β) :
@@ -584,11 +592,14 @@ theorem norm_set_integral_le_of_norm_le_const' {C : ℝ} (hs : μ s < ∞) (hsm
   norm_set_integral_le_of_norm_le_const_ae'' hs hsm <| eventually_of_forall hC
 #align measure_theory.norm_set_integral_le_of_norm_le_const' MeasureTheory.norm_set_integral_le_of_norm_le_const'
 
+#print MeasureTheory.set_integral_eq_zero_iff_of_nonneg_ae /-
 theorem set_integral_eq_zero_iff_of_nonneg_ae {f : α → ℝ} (hf : 0 ≤ᵐ[μ.restrict s] f)
     (hfi : IntegrableOn f s μ) : (∫ x in s, f x ∂μ) = 0 ↔ f =ᵐ[μ.restrict s] 0 :=
   integral_eq_zero_iff_of_nonneg_ae hf hfi
 #align measure_theory.set_integral_eq_zero_iff_of_nonneg_ae MeasureTheory.set_integral_eq_zero_iff_of_nonneg_ae
+-/
 
+#print MeasureTheory.set_integral_pos_iff_support_of_nonneg_ae /-
 theorem set_integral_pos_iff_support_of_nonneg_ae {f : α → ℝ} (hf : 0 ≤ᵐ[μ.restrict s] f)
     (hfi : IntegrableOn f s μ) : (0 < ∫ x in s, f x ∂μ) ↔ 0 < μ (support f ∩ s) :=
   by
@@ -596,6 +607,7 @@ theorem set_integral_pos_iff_support_of_nonneg_ae {f : α → ℝ} (hf : 0 ≤
   rw [support_eq_preimage]
   exact hfi.ae_strongly_measurable.ae_measurable.null_measurable (measurable_set_singleton 0).compl
 #align measure_theory.set_integral_pos_iff_support_of_nonneg_ae MeasureTheory.set_integral_pos_iff_support_of_nonneg_ae
+-/
 
 theorem set_integral_gt_gt {R : ℝ} {f : α → ℝ} (hR : 0 ≤ R) (hfm : Measurable f)
     (hfint : IntegrableOn f {x | ↑R < f x} μ) (hμ : μ {x | ↑R < f x} ≠ 0) :
@@ -623,11 +635,13 @@ theorem set_integral_gt_gt {R : ℝ} {f : α → ℝ} (hR : 0 ≤ R) (hfm : Meas
   · exact integrable.sub hfint this
 #align measure_theory.set_integral_gt_gt MeasureTheory.set_integral_gt_gt
 
+#print MeasureTheory.set_integral_trim /-
 theorem set_integral_trim {α} {m m0 : MeasurableSpace α} {μ : Measure α} (hm : m ≤ m0) {f : α → E}
     (hf_meas : strongly_measurable[m] f) {s : Set α} (hs : measurable_set[m] s) :
     (∫ x in s, f x ∂μ) = ∫ x in s, f x ∂μ.trim hm := by
   rwa [integral_trim hm hf_meas, restrict_trim hm μ]
 #align measure_theory.set_integral_trim MeasureTheory.set_integral_trim
+-/
 
 /-! ### Lemmas about adding and removing interval boundaries
 
@@ -677,33 +691,47 @@ theorem integral_Ici_eq_integral_Ioi' (ha : μ {a} = 0) :
 
 variable [NoAtoms μ]
 
+#print MeasureTheory.integral_Icc_eq_integral_Ioc /-
 theorem integral_Icc_eq_integral_Ioc : (∫ t in Icc a b, f t ∂μ) = ∫ t in Ioc a b, f t ∂μ :=
   integral_Icc_eq_integral_Ioc' <| measure_singleton a
 #align measure_theory.integral_Icc_eq_integral_Ioc MeasureTheory.integral_Icc_eq_integral_Ioc
+-/
 
+#print MeasureTheory.integral_Icc_eq_integral_Ico /-
 theorem integral_Icc_eq_integral_Ico : (∫ t in Icc a b, f t ∂μ) = ∫ t in Ico a b, f t ∂μ :=
   integral_Icc_eq_integral_Ico' <| measure_singleton b
 #align measure_theory.integral_Icc_eq_integral_Ico MeasureTheory.integral_Icc_eq_integral_Ico
+-/
 
+#print MeasureTheory.integral_Ioc_eq_integral_Ioo /-
 theorem integral_Ioc_eq_integral_Ioo : (∫ t in Ioc a b, f t ∂μ) = ∫ t in Ioo a b, f t ∂μ :=
   integral_Ioc_eq_integral_Ioo' <| measure_singleton b
 #align measure_theory.integral_Ioc_eq_integral_Ioo MeasureTheory.integral_Ioc_eq_integral_Ioo
+-/
 
+#print MeasureTheory.integral_Ico_eq_integral_Ioo /-
 theorem integral_Ico_eq_integral_Ioo : (∫ t in Ico a b, f t ∂μ) = ∫ t in Ioo a b, f t ∂μ :=
   integral_Ico_eq_integral_Ioo' <| measure_singleton a
 #align measure_theory.integral_Ico_eq_integral_Ioo MeasureTheory.integral_Ico_eq_integral_Ioo
+-/
 
+#print MeasureTheory.integral_Icc_eq_integral_Ioo /-
 theorem integral_Icc_eq_integral_Ioo : (∫ t in Icc a b, f t ∂μ) = ∫ t in Ico a b, f t ∂μ := by
   rw [integral_Icc_eq_integral_Ico, integral_Ico_eq_integral_Ioo]
 #align measure_theory.integral_Icc_eq_integral_Ioo MeasureTheory.integral_Icc_eq_integral_Ioo
+-/
 
+#print MeasureTheory.integral_Iic_eq_integral_Iio /-
 theorem integral_Iic_eq_integral_Iio : (∫ t in Iic a, f t ∂μ) = ∫ t in Iio a, f t ∂μ :=
   integral_Iic_eq_integral_Iio' <| measure_singleton a
 #align measure_theory.integral_Iic_eq_integral_Iio MeasureTheory.integral_Iic_eq_integral_Iio
+-/
 
+#print MeasureTheory.integral_Ici_eq_integral_Ioi /-
 theorem integral_Ici_eq_integral_Ioi : (∫ t in Ici a, f t ∂μ) = ∫ t in Ioi a, f t ∂μ :=
   integral_Ici_eq_integral_Ioi' <| measure_singleton a
 #align measure_theory.integral_Ici_eq_integral_Ioi MeasureTheory.integral_Ici_eq_integral_Ioi
+-/
 
 end PartialOrder
 
@@ -714,10 +742,12 @@ section Mono
 variable {μ : Measure α} {f g : α → ℝ} {s t : Set α} (hf : IntegrableOn f s μ)
   (hg : IntegrableOn g s μ)
 
+#print MeasureTheory.set_integral_mono_ae_restrict /-
 theorem set_integral_mono_ae_restrict (h : f ≤ᵐ[μ.restrict s] g) :
     (∫ a in s, f a ∂μ) ≤ ∫ a in s, g a ∂μ :=
   integral_mono_ae hf hg h
 #align measure_theory.set_integral_mono_ae_restrict MeasureTheory.set_integral_mono_ae_restrict
+-/
 
 theorem set_integral_mono_ae (h : f ≤ᵐ[μ] g) : (∫ a in s, f a ∂μ) ≤ ∫ a in s, g a ∂μ :=
   set_integral_mono_ae_restrict hf hg (ae_restrict_of_ae h)
@@ -743,10 +773,12 @@ theorem set_integral_mono (h : f ≤ g) : (∫ a in s, f a ∂μ) ≤ ∫ a in s
   integral_mono hf hg h
 #align measure_theory.set_integral_mono MeasureTheory.set_integral_mono
 
+#print MeasureTheory.set_integral_mono_set /-
 theorem set_integral_mono_set (hfi : IntegrableOn f t μ) (hf : 0 ≤ᵐ[μ.restrict t] f)
     (hst : s ≤ᵐ[μ] t) : (∫ x in s, f x ∂μ) ≤ ∫ x in t, f x ∂μ :=
   integral_mono_measure (Measure.restrict_mono_ae hst) hf hfi
 #align measure_theory.set_integral_mono_set MeasureTheory.set_integral_mono_set
+-/
 
 theorem set_integral_ge_of_const_le {c : ℝ} (hs : MeasurableSet s) (hμs : μ s ≠ ∞)
     (hf : ∀ x ∈ s, c ≤ f x) (hfint : IntegrableOn (fun x : α => f x) s μ) :
@@ -762,9 +794,11 @@ section Nonneg
 
 variable {μ : Measure α} {f : α → ℝ} {s : Set α}
 
+#print MeasureTheory.set_integral_nonneg_of_ae_restrict /-
 theorem set_integral_nonneg_of_ae_restrict (hf : 0 ≤ᵐ[μ.restrict s] f) : 0 ≤ ∫ a in s, f a ∂μ :=
   integral_nonneg_of_ae hf
 #align measure_theory.set_integral_nonneg_of_ae_restrict MeasureTheory.set_integral_nonneg_of_ae_restrict
+-/
 
 theorem set_integral_nonneg_of_ae (hf : 0 ≤ᵐ[μ] f) : 0 ≤ ∫ a in s, f a ∂μ :=
   set_integral_nonneg_of_ae_restrict (ae_restrict_of_ae hf)
@@ -791,9 +825,11 @@ theorem set_integral_le_nonneg {s : Set α} (hs : MeasurableSet s) (hf : Strongl
       (indicator_le_indicator_nonneg s f)
 #align measure_theory.set_integral_le_nonneg MeasureTheory.set_integral_le_nonneg
 
+#print MeasureTheory.set_integral_nonpos_of_ae_restrict /-
 theorem set_integral_nonpos_of_ae_restrict (hf : f ≤ᵐ[μ.restrict s] 0) : (∫ a in s, f a ∂μ) ≤ 0 :=
   integral_nonpos_of_ae hf
 #align measure_theory.set_integral_nonpos_of_ae_restrict MeasureTheory.set_integral_nonpos_of_ae_restrict
+-/
 
 theorem set_integral_nonpos_of_ae (hf : f ≤ᵐ[μ] 0) : (∫ a in s, f a ∂μ) ≤ 0 :=
   set_integral_nonpos_of_ae_restrict (ae_restrict_of_ae hf)
@@ -914,7 +950,7 @@ variable [NormedAddCommGroup E] {𝕜 : Type _} [NormedField 𝕜] [NormedAddCom
 
 /-- For `f : Lp E p μ`, we can define an element of `Lp E p (μ.restrict s)` by
 `(Lp.mem_ℒp f).restrict s).to_Lp f`. This map is additive. -/
-theorem lp_toLp_restrict_add (f g : Lp E p μ) (s : Set α) :
+theorem Lp_toLp_restrict_add (f g : Lp E p μ) (s : Set α) :
     ((Lp.memℒp (f + g)).restrict s).toLp ⇑(f + g) =
       ((Lp.memℒp f).restrict s).toLp f + ((Lp.memℒp g).restrict s).toLp g :=
   by
@@ -928,11 +964,11 @@ theorem lp_toLp_restrict_add (f g : Lp E p μ) (s : Set α) :
   refine' (mem_ℒp.coe_fn_to_Lp ((Lp.mem_ℒp g).restrict s)).mp _
   refine' (mem_ℒp.coe_fn_to_Lp ((Lp.mem_ℒp (f + g)).restrict s)).mono fun x hx1 hx2 hx3 hx4 hx5 => _
   rw [hx4, hx1, Pi.add_apply, hx2, hx3, hx5, Pi.add_apply]
-#align measure_theory.Lp_to_Lp_restrict_add MeasureTheory.lp_toLp_restrict_add
+#align measure_theory.Lp_to_Lp_restrict_add MeasureTheory.Lp_toLp_restrict_add
 
 /-- For `f : Lp E p μ`, we can define an element of `Lp E p (μ.restrict s)` by
 `(Lp.mem_ℒp f).restrict s).to_Lp f`. This map commutes with scalar multiplication. -/
-theorem lp_toLp_restrict_smul (c : 𝕜) (f : Lp F p μ) (s : Set α) :
+theorem Lp_toLp_restrict_smul (c : 𝕜) (f : Lp F p μ) (s : Set α) :
     ((Lp.memℒp (c • f)).restrict s).toLp ⇑(c • f) = c • ((Lp.memℒp f).restrict s).toLp f :=
   by
   ext1
@@ -942,39 +978,39 @@ theorem lp_toLp_restrict_smul (c : 𝕜) (f : Lp F p μ) (s : Set α) :
   refine'
     (Lp.coe_fn_smul c (mem_ℒp.to_Lp f ((Lp.mem_ℒp f).restrict s))).mono fun x hx1 hx2 hx3 hx4 => _
   rw [hx2, hx1, Pi.smul_apply, hx3, hx4, Pi.smul_apply]
-#align measure_theory.Lp_to_Lp_restrict_smul MeasureTheory.lp_toLp_restrict_smul
+#align measure_theory.Lp_to_Lp_restrict_smul MeasureTheory.Lp_toLp_restrict_smul
 
 /-- For `f : Lp E p μ`, we can define an element of `Lp E p (μ.restrict s)` by
 `(Lp.mem_ℒp f).restrict s).to_Lp f`. This map is non-expansive. -/
-theorem norm_lp_toLp_restrict_le (s : Set α) (f : Lp E p μ) :
+theorem norm_Lp_toLp_restrict_le (s : Set α) (f : Lp E p μ) :
     ‖((Lp.memℒp f).restrict s).toLp f‖ ≤ ‖f‖ :=
   by
   rw [Lp.norm_def, Lp.norm_def, ENNReal.toReal_le_toReal (Lp.snorm_ne_top _) (Lp.snorm_ne_top _)]
   refine' (le_of_eq _).trans (snorm_mono_measure _ measure.restrict_le_self)
   · exact s
   exact snorm_congr_ae (mem_ℒp.coe_fn_to_Lp _)
-#align measure_theory.norm_Lp_to_Lp_restrict_le MeasureTheory.norm_lp_toLp_restrict_le
+#align measure_theory.norm_Lp_to_Lp_restrict_le MeasureTheory.norm_Lp_toLp_restrict_le
 
 variable (α F 𝕜)
 
 /-- Continuous linear map sending a function of `Lp F p μ` to the same function in
 `Lp F p (μ.restrict s)`. -/
-def lpToLpRestrictClm (μ : Measure α) (p : ℝ≥0∞) [hp : Fact (1 ≤ p)] (s : Set α) :
+def LpToLpRestrictCLM (μ : Measure α) (p : ℝ≥0∞) [hp : Fact (1 ≤ p)] (s : Set α) :
     Lp F p μ →L[𝕜] Lp F p (μ.restrict s) :=
   @LinearMap.mkContinuous 𝕜 𝕜 (Lp F p μ) (Lp F p (μ.restrict s)) _ _ _ _ _ _ (RingHom.id 𝕜)
-    ⟨fun f => Memℒp.toLp f ((Lp.memℒp f).restrict s), fun f g => lp_toLp_restrict_add f g s,
-      fun c f => lp_toLp_restrict_smul c f s⟩
+    ⟨fun f => Memℒp.toLp f ((Lp.memℒp f).restrict s), fun f g => Lp_toLp_restrict_add f g s,
+      fun c f => Lp_toLp_restrict_smul c f s⟩
     1 (by intro f; rw [one_mul]; exact norm_Lp_to_Lp_restrict_le s f)
-#align measure_theory.Lp_to_Lp_restrict_clm MeasureTheory.lpToLpRestrictClm
+#align measure_theory.Lp_to_Lp_restrict_clm MeasureTheory.LpToLpRestrictCLM
 
 variable {α F 𝕜}
 
 variable (𝕜)
 
-theorem lpToLpRestrictClm_coeFn [hp : Fact (1 ≤ p)] (s : Set α) (f : Lp F p μ) :
-    lpToLpRestrictClm α F 𝕜 μ p s f =ᵐ[μ.restrict s] f :=
+theorem LpToLpRestrictCLM_coeFn [hp : Fact (1 ≤ p)] (s : Set α) (f : Lp F p μ) :
+    LpToLpRestrictCLM α F 𝕜 μ p s f =ᵐ[μ.restrict s] f :=
   Memℒp.coeFn_toLp ((Lp.memℒp f).restrict s)
-#align measure_theory.Lp_to_Lp_restrict_clm_coe_fn MeasureTheory.lpToLpRestrictClm_coeFn
+#align measure_theory.Lp_to_Lp_restrict_clm_coe_fn MeasureTheory.LpToLpRestrictCLM_coeFn
 
 variable {𝕜}
 
@@ -1192,10 +1228,12 @@ end ContinuousLinearEquiv
 
 variable [CompleteSpace E] [NormedSpace ℝ E] [CompleteSpace F] [NormedSpace ℝ F]
 
+#print integral_of_real /-
 @[norm_cast]
 theorem integral_of_real {f : α → ℝ} : (∫ a, (f a : 𝕜) ∂μ) = ↑(∫ a, f a ∂μ) :=
   (@IsROrC.ofRealLi 𝕜 _).integral_comp_comm f
 #align integral_of_real integral_of_real
+-/
 
 theorem integral_re {f : α → 𝕜} (hf : Integrable f μ) :
     (∫ a, IsROrC.re (f a) ∂μ) = IsROrC.re (∫ a, f a ∂μ) :=
@@ -1247,6 +1285,7 @@ theorem integral_pair {f : α → E} {g : α → F} (hf : Integrable f μ) (hg :
   Prod.ext (fst_integral this) (snd_integral this)
 #align integral_pair integral_pair
 
+#print integral_smul_const /-
 theorem integral_smul_const {𝕜 : Type _} [IsROrC 𝕜] [NormedSpace 𝕜 E] (f : α → 𝕜) (c : E) :
     (∫ x, f x • c ∂μ) = (∫ x, f x ∂μ) • c :=
   by
@@ -1257,6 +1296,7 @@ theorem integral_smul_const {𝕜 : Type _} [IsROrC 𝕜] [NormedSpace 𝕜 E] (
     rw [integral_undef hf, integral_undef, zero_smul]
     simp_rw [integrable_smul_const hc, hf, not_false_iff]
 #align integral_smul_const integral_smul_const
+-/
 
 theorem integral_withDensity_eq_integral_smul {f : α → ℝ≥0} (f_meas : Measurable f) (g : α → E) :
     (∫ a, g a ∂μ.withDensity fun x => f x) = ∫ a, f a • g a ∂μ :=

mathlib commit https://github.com/leanprover-community/mathlib/commit/5f25c089cb34db4db112556f23c50d12da81b297

@@ -208,7 +208,7 @@ theorem ofReal_set_integral_one_of_measure_ne_top {α : Type _} {m : MeasurableS
 #align measure_theory.of_real_set_integral_one_of_measure_ne_top MeasureTheory.ofReal_set_integral_one_of_measure_ne_top
 
 theorem ofReal_set_integral_one {α : Type _} {m : MeasurableSpace α} (μ : Measure α)
-    [FiniteMeasure μ] (s : Set α) : ENNReal.ofReal (∫ x in s, (1 : ℝ) ∂μ) = μ s :=
+    [IsFiniteMeasure μ] (s : Set α) : ENNReal.ofReal (∫ x in s, (1 : ℝ) ∂μ) = μ s :=
   ofReal_set_integral_one_of_measure_ne_top (measure_ne_top μ s)
 #align measure_theory.of_real_set_integral_one MeasureTheory.ofReal_set_integral_one
 
@@ -285,7 +285,7 @@ theorem set_integral_eq_zero_of_ae_eq_zero (ht_eq : ∀ᵐ x ∂μ, x ∈ t →
     refine' integral_eq_zero_of_ae _
     rw [eventually_eq,
       ae_restrict_iff (hf.strongly_measurable_mk.measurable_set_eq_fun strongly_measurable_zero)]
-    filter_upwards [ae_imp_of_ae_restrict hf.ae_eq_mk, ht_eq]with x hx h'x h''x
+    filter_upwards [ae_imp_of_ae_restrict hf.ae_eq_mk, ht_eq] with x hx h'x h''x
     rw [← hx h''x]
     exact h'x h''x
   rw [← this]
@@ -312,7 +312,7 @@ theorem integral_union_eq_left_of_ae_aux (ht_eq : ∀ᵐ x ∂μ.restrict t, f x
   rw [union_ae_eq_right]
   apply measure_mono_null (diff_subset _ _)
   rw [measure_zero_iff_ae_nmem]
-  filter_upwards [ae_imp_of_ae_restrict ht_eq]with x hx h'x using h'x.2 (hx h'x.1)
+  filter_upwards [ae_imp_of_ae_restrict ht_eq] with x hx h'x using h'x.2 (hx h'x.1)
 #align measure_theory.integral_union_eq_left_of_ae_aux MeasureTheory.integral_union_eq_left_of_ae_aux
 
 theorem integral_union_eq_left_of_ae (ht_eq : ∀ᵐ x ∂μ.restrict t, f x = 0) :
@@ -329,7 +329,7 @@ theorem integral_union_eq_left_of_ae (ht_eq : ∀ᵐ x ∂μ.restrict t, f x = 0
       apply
         integral_union_eq_left_of_ae_aux _ H.1.stronglyMeasurable_mk (H.congr_fun_ae H.1.ae_eq_mk)
       filter_upwards [ht_eq,
-        ae_mono (measure.restrict_mono (subset_union_right s t) le_rfl) H.1.ae_eq_mk]with x hx h'x
+        ae_mono (measure.restrict_mono (subset_union_right s t) le_rfl) H.1.ae_eq_mk] with x hx h'x
       rw [← h'x, hx]
     _ = ∫ x in s, f x ∂μ :=
       integral_congr_ae
@@ -360,7 +360,7 @@ theorem set_integral_eq_of_subset_of_ae_diff_eq_zero_aux (hts : s ⊆ t)
       rw [set_integral_eq_zero_of_forall_eq_zero fun x hx => _, zero_add]; exact hx.2
     _ = ∫ x in s \ k, f x ∂μ := by
       apply set_integral_congr_set_ae
-      filter_upwards [h't]with x hx
+      filter_upwards [h't] with x hx
       change (x ∈ t \ k) = (x ∈ s \ k)
       simp only [mem_preimage, mem_singleton_iff, eq_iff_iff, and_congr_left_iff, mem_diff]
       intro h'x
@@ -393,7 +393,7 @@ theorem set_integral_eq_of_subset_of_ae_diff_eq_zero (ht : NullMeasurableSet t 
       apply
         set_integral_eq_of_subset_of_ae_diff_eq_zero_aux hts _ h.1.stronglyMeasurable_mk
           (h.congr h.1.ae_eq_mk)
-      filter_upwards [h't, ae_imp_of_ae_restrict h.1.ae_eq_mk]with x hx h'x h''x
+      filter_upwards [h't, ae_imp_of_ae_restrict h.1.ae_eq_mk] with x hx h'x h''x
       rw [← h'x h''x.1, hx h''x]
     _ = ∫ x in s, f x ∂μ := by
       apply integral_congr_ae
@@ -418,7 +418,7 @@ theorem set_integral_eq_integral_of_ae_compl_eq_zero (h : ∀ᵐ x ∂μ, x ∉
   conv_rhs => rw [← integral_univ]
   symm
   apply set_integral_eq_of_subset_of_ae_diff_eq_zero null_measurable_set_univ (subset_univ _)
-  filter_upwards [h]with x hx h'x using hx h'x.2
+  filter_upwards [h] with x hx h'x using hx h'x.2
 #align measure_theory.set_integral_eq_integral_of_ae_compl_eq_zero MeasureTheory.set_integral_eq_integral_of_ae_compl_eq_zero
 
 /-- If a function vanishes on `sᶜ`, then its integral on `s` coincides with its integral on the
@@ -430,33 +430,33 @@ theorem set_integral_eq_integral_of_forall_compl_eq_zero (h : ∀ x, x ∉ s →
 
 theorem set_integral_neg_eq_set_integral_nonpos [LinearOrder E] {f : α → E}
     (hf : AEStronglyMeasurable f μ) :
-    (∫ x in { x | f x < 0 }, f x ∂μ) = ∫ x in { x | f x ≤ 0 }, f x ∂μ :=
+    (∫ x in {x | f x < 0}, f x ∂μ) = ∫ x in {x | f x ≤ 0}, f x ∂μ :=
   by
-  have h_union : { x | f x ≤ 0 } = { x | f x < 0 } ∪ { x | f x = 0 } := by ext;
+  have h_union : {x | f x ≤ 0} = {x | f x < 0} ∪ {x | f x = 0} := by ext;
     simp_rw [Set.mem_union, Set.mem_setOf_eq]; exact le_iff_lt_or_eq
   rw [h_union]
-  have B : null_measurable_set { x | f x = 0 } μ :=
+  have B : null_measurable_set {x | f x = 0} μ :=
     hf.null_measurable_set_eq_fun ae_strongly_measurable_zero
   symm
   refine' integral_union_eq_left_of_ae _
-  filter_upwards [ae_restrict_mem₀ B]with x hx using hx
+  filter_upwards [ae_restrict_mem₀ B] with x hx using hx
 #align measure_theory.set_integral_neg_eq_set_integral_nonpos MeasureTheory.set_integral_neg_eq_set_integral_nonpos
 
 theorem integral_norm_eq_pos_sub_neg {f : α → ℝ} (hfi : Integrable f μ) :
-    (∫ x, ‖f x‖ ∂μ) = (∫ x in { x | 0 ≤ f x }, f x ∂μ) - ∫ x in { x | f x ≤ 0 }, f x ∂μ :=
-  have h_meas : NullMeasurableSet { x | 0 ≤ f x } μ :=
+    (∫ x, ‖f x‖ ∂μ) = (∫ x in {x | 0 ≤ f x}, f x ∂μ) - ∫ x in {x | f x ≤ 0}, f x ∂μ :=
+  have h_meas : NullMeasurableSet {x | 0 ≤ f x} μ :=
     aestronglyMeasurable_const.nullMeasurableSet_le hfi.1
   calc
-    (∫ x, ‖f x‖ ∂μ) = (∫ x in { x | 0 ≤ f x }, ‖f x‖ ∂μ) + ∫ x in { x | 0 ≤ f x }ᶜ, ‖f x‖ ∂μ := by
+    (∫ x, ‖f x‖ ∂μ) = (∫ x in {x | 0 ≤ f x}, ‖f x‖ ∂μ) + ∫ x in {x | 0 ≤ f x}ᶜ, ‖f x‖ ∂μ := by
       rw [← integral_add_compl₀ h_meas hfi.norm]
-    _ = (∫ x in { x | 0 ≤ f x }, f x ∂μ) + ∫ x in { x | 0 ≤ f x }ᶜ, ‖f x‖ ∂μ :=
+    _ = (∫ x in {x | 0 ≤ f x}, f x ∂μ) + ∫ x in {x | 0 ≤ f x}ᶜ, ‖f x‖ ∂μ :=
       by
       congr 1
       refine' set_integral_congr₀ h_meas fun x hx => _
       dsimp only
       rw [Real.norm_eq_abs, abs_eq_self.mpr _]
       exact hx
-    _ = (∫ x in { x | 0 ≤ f x }, f x ∂μ) - ∫ x in { x | 0 ≤ f x }ᶜ, f x ∂μ :=
+    _ = (∫ x in {x | 0 ≤ f x}, f x ∂μ) - ∫ x in {x | 0 ≤ f x}ᶜ, f x ∂μ :=
       by
       congr 1
       rw [← integral_neg]
@@ -465,7 +465,7 @@ theorem integral_norm_eq_pos_sub_neg {f : α → ℝ} (hfi : Integrable f μ) :
       rw [Real.norm_eq_abs, abs_eq_neg_self.mpr _]
       rw [Set.mem_compl_iff, Set.nmem_setOf_iff] at hx 
       linarith
-    _ = (∫ x in { x | 0 ≤ f x }, f x ∂μ) - ∫ x in { x | f x ≤ 0 }, f x ∂μ := by
+    _ = (∫ x in {x | 0 ≤ f x}, f x ∂μ) - ∫ x in {x | f x ≤ 0}, f x ∂μ := by
       rw [← set_integral_neg_eq_set_integral_nonpos hfi.1]; congr; ext1 x; simp
     
 #align measure_theory.integral_norm_eq_pos_sub_neg MeasureTheory.integral_norm_eq_pos_sub_neg
@@ -559,12 +559,12 @@ theorem norm_set_integral_le_of_norm_le_const_ae' {C : ℝ} (hs : μ s < ∞)
   apply norm_set_integral_le_of_norm_le_const_ae hs
   have A : ∀ᵐ x : α ∂μ, x ∈ s → ‖ae_strongly_measurable.mk f hfm x‖ ≤ C :=
     by
-    filter_upwards [hC, hfm.ae_mem_imp_eq_mk]with _ h1 h2 h3
+    filter_upwards [hC, hfm.ae_mem_imp_eq_mk] with _ h1 h2 h3
     rw [← h2 h3]
     exact h1 h3
-  have B : MeasurableSet { x | ‖(hfm.mk f) x‖ ≤ C } :=
+  have B : MeasurableSet {x | ‖(hfm.mk f) x‖ ≤ C} :=
     hfm.strongly_measurable_mk.norm.measurable measurableSet_Iic
-  filter_upwards [hfm.ae_eq_mk, (ae_restrict_iff B).2 A]with _ h1 _
+  filter_upwards [hfm.ae_eq_mk, (ae_restrict_iff B).2 A] with _ h1 _
   rwa [h1]
 #align measure_theory.norm_set_integral_le_of_norm_le_const_ae' MeasureTheory.norm_set_integral_le_of_norm_le_const_ae'
 
@@ -598,10 +598,10 @@ theorem set_integral_pos_iff_support_of_nonneg_ae {f : α → ℝ} (hf : 0 ≤
 #align measure_theory.set_integral_pos_iff_support_of_nonneg_ae MeasureTheory.set_integral_pos_iff_support_of_nonneg_ae
 
 theorem set_integral_gt_gt {R : ℝ} {f : α → ℝ} (hR : 0 ≤ R) (hfm : Measurable f)
-    (hfint : IntegrableOn f { x | ↑R < f x } μ) (hμ : μ { x | ↑R < f x } ≠ 0) :
-    (μ { x | ↑R < f x }).toReal * R < ∫ x in { x | ↑R < f x }, f x ∂μ :=
+    (hfint : IntegrableOn f {x | ↑R < f x} μ) (hμ : μ {x | ↑R < f x} ≠ 0) :
+    (μ {x | ↑R < f x}).toReal * R < ∫ x in {x | ↑R < f x}, f x ∂μ :=
   by
-  have : integrable_on (fun x => R) { x | ↑R < f x } μ :=
+  have : integrable_on (fun x => R) {x | ↑R < f x} μ :=
     by
     refine' ⟨ae_strongly_measurable_const, lt_of_le_of_lt _ hfint.2⟩
     refine'
@@ -781,7 +781,7 @@ theorem set_integral_nonneg_ae (hs : MeasurableSet s) (hf : ∀ᵐ a ∂μ, a 
 #align measure_theory.set_integral_nonneg_ae MeasureTheory.set_integral_nonneg_ae
 
 theorem set_integral_le_nonneg {s : Set α} (hs : MeasurableSet s) (hf : StronglyMeasurable f)
-    (hfi : Integrable f μ) : (∫ x in s, f x ∂μ) ≤ ∫ x in { y | 0 ≤ f y }, f x ∂μ :=
+    (hfi : Integrable f μ) : (∫ x in s, f x ∂μ) ≤ ∫ x in {y | 0 ≤ f y}, f x ∂μ :=
   by
   rw [← integral_indicator hs, ←
     integral_indicator (strongly_measurable_const.measurable_set_le hf)]
@@ -810,7 +810,7 @@ theorem set_integral_nonpos_ae (hs : MeasurableSet s) (hf : ∀ᵐ a ∂μ, a 
 #align measure_theory.set_integral_nonpos_ae MeasureTheory.set_integral_nonpos_ae
 
 theorem set_integral_nonpos_le {s : Set α} (hs : MeasurableSet s) (hf : StronglyMeasurable f)
-    (hfi : Integrable f μ) : (∫ x in { y | f y ≤ 0 }, f x ∂μ) ≤ ∫ x in s, f x ∂μ :=
+    (hfi : Integrable f μ) : (∫ x in {y | f y ≤ 0}, f x ∂μ) ≤ ∫ x in s, f x ∂μ :=
   by
   rw [← integral_indicator hs, ←
     integral_indicator (hf.measurable_set_le strongly_measurable_const)]
@@ -842,7 +842,7 @@ theorem integrableOn_iUnion_of_summable_integral_norm {f : α → E} {s : β →
   convert ENNReal.ofReal_lt_top
 #align measure_theory.integrable_on_Union_of_summable_integral_norm MeasureTheory.integrableOn_iUnion_of_summable_integral_norm
 
-variable [TopologicalSpace α] [BorelSpace α] [MetrizableSpace α] [LocallyFiniteMeasure μ]
+variable [TopologicalSpace α] [BorelSpace α] [MetrizableSpace α] [IsLocallyFiniteMeasure μ]
 
 /-- If `s` is a countable family of compact sets, `f` is a continuous function, and the sequence
 `‖f.restrict (s i)‖ * μ (s i)` is summable, then `f` is integrable on the union of the `s i`. -/
@@ -1042,7 +1042,7 @@ argument `m` with this formula and a proof `of `(λ i, (μ (s i)).to_real) =ᶠ[
 arguments, `m i = (μ (s i)).to_real` is used in the output. -/
 theorem ContinuousWithinAt.integral_sub_linear_isLittleO_ae [TopologicalSpace α]
     [OpensMeasurableSpace α] [NormedSpace ℝ E] [CompleteSpace E] {μ : Measure α}
-    [LocallyFiniteMeasure μ] {a : α} {t : Set α} {f : α → E} (ha : ContinuousWithinAt f t a)
+    [IsLocallyFiniteMeasure μ] {a : α} {t : Set α} {f : α → E} (ha : ContinuousWithinAt f t a)
     (ht : MeasurableSet t) (hfm : StronglyMeasurableAtFilter f (𝓝[t] a) μ) {s : ι → Set α}
     {li : Filter ι} (hs : Tendsto s li (𝓝[t] a).smallSets) (m : ι → ℝ := fun i => (μ (s i)).toReal)
     (hsμ : (fun i => (μ (s i)).toReal) =ᶠ[li] m := by rfl) :
@@ -1062,8 +1062,8 @@ Often there is a good formula for `(μ (s i)).to_real`, so the formalization can
 argument `m` with this formula and a proof `of `(λ i, (μ (s i)).to_real) =ᶠ[li] m`. Without these
 arguments, `m i = (μ (s i)).to_real` is used in the output. -/
 theorem ContinuousAt.integral_sub_linear_isLittleO_ae [TopologicalSpace α] [OpensMeasurableSpace α]
-    [NormedSpace ℝ E] [CompleteSpace E] {μ : Measure α} [LocallyFiniteMeasure μ] {a : α} {f : α → E}
-    (ha : ContinuousAt f a) (hfm : StronglyMeasurableAtFilter f (𝓝 a) μ) {s : ι → Set α}
+    [NormedSpace ℝ E] [CompleteSpace E] {μ : Measure α} [IsLocallyFiniteMeasure μ] {a : α}
+    {f : α → E} (ha : ContinuousAt f a) (hfm : StronglyMeasurableAtFilter f (𝓝 a) μ) {s : ι → Set α}
     {li : Filter ι} (hs : Tendsto s li (𝓝 a).smallSets) (m : ι → ℝ := fun i => (μ (s i)).toReal)
     (hsμ : (fun i => (μ (s i)).toReal) =ᶠ[li] m := by rfl) :
     (fun i => (∫ x in s i, f x ∂μ) - m i • f a) =o[li] m :=
@@ -1080,7 +1080,7 @@ argument `m` with this formula and a proof `of `(λ i, (μ (s i)).to_real) =ᶠ[
 arguments, `m i = (μ (s i)).to_real` is used in the output. -/
 theorem ContinuousOn.integral_sub_linear_isLittleO_ae [TopologicalSpace α] [OpensMeasurableSpace α]
     [NormedSpace ℝ E] [CompleteSpace E] [SecondCountableTopologyEither α E] {μ : Measure α}
-    [LocallyFiniteMeasure μ] {a : α} {t : Set α} {f : α → E} (hft : ContinuousOn f t) (ha : a ∈ t)
+    [IsLocallyFiniteMeasure μ] {a : α} {t : Set α} {f : α → E} (hft : ContinuousOn f t) (ha : a ∈ t)
     (ht : MeasurableSet t) {s : ι → Set α} {li : Filter ι} (hs : Tendsto s li (𝓝[t] a).smallSets)
     (m : ι → ℝ := fun i => (μ (s i)).toReal)
     (hsμ : (fun i => (μ (s i)).toReal) =ᶠ[li] m := by rfl) :
@@ -1301,7 +1301,7 @@ theorem integral_withDensity_eq_integral_smul {f : α → ℝ≥0} (f_meas : Mea
   · intro u v huv u_int hu
     rw [← integral_congr_ae huv, hu]
     apply integral_congr_ae
-    filter_upwards [(ae_with_density_iff f_meas.coe_nnreal_ennreal).1 huv]with x hx
+    filter_upwards [(ae_with_density_iff f_meas.coe_nnreal_ennreal).1 huv] with x hx
     rcases eq_or_ne (f x) 0 with (h'x | h'x)
     · simp only [h'x, zero_smul]
     · rw [hx _]
@@ -1317,12 +1317,12 @@ theorem integral_withDensity_eq_integral_smul₀ {f : α → ℝ≥0} (hf : AEMe
       by
       congr 1
       apply with_density_congr_ae
-      filter_upwards [hf.ae_eq_mk]with x hx
+      filter_upwards [hf.ae_eq_mk] with x hx
       rw [hx]
     _ = ∫ a, f' a • g a ∂μ := (integral_withDensity_eq_integral_smul hf.measurable_mk _)
     _ = ∫ a, f a • g a ∂μ := by
       apply integral_congr_ae
-      filter_upwards [hf.ae_eq_mk]with x hx
+      filter_upwards [hf.ae_eq_mk] with x hx
       rw [hx]
     
 #align integral_with_density_eq_integral_smul₀ integral_withDensity_eq_integral_smul₀

mathlib commit https://github.com/leanprover-community/mathlib/commit/cca40788df1b8755d5baf17ab2f27dacc2e17acb

@@ -111,7 +111,7 @@ theorem integral_diff (ht : MeasurableSet t) (hfs : IntegrableOn f s μ) (hts :
     (∫ x in s \ t, f x ∂μ) = (∫ x in s, f x ∂μ) - ∫ x in t, f x ∂μ :=
   by
   rw [eq_sub_iff_add_eq, ← integral_union, diff_union_of_subset hts]
-  exacts[disjoint_sdiff_self_left, ht, hfs.mono_set (diff_subset _ _), hfs.mono_set hts]
+  exacts [disjoint_sdiff_self_left, ht, hfs.mono_set (diff_subset _ _), hfs.mono_set hts]
 #align measure_theory.integral_diff MeasureTheory.integral_diff
 
 theorem integral_inter_add_diff₀ (ht : NullMeasurableSet t μ) (hfs : IntegrableOn f s μ) :
@@ -135,7 +135,7 @@ theorem integral_finset_bUnion {ι : Type _} (t : Finset ι) {s : ι → Set α}
   induction' t using Finset.induction_on with a t hat IH hs h's
   · simp
   · simp only [Finset.coe_insert, Finset.forall_mem_insert, Set.pairwise_insert,
-      Finset.set_biUnion_insert] at hs hf h's⊢
+      Finset.set_biUnion_insert] at hs hf h's ⊢
     rw [integral_union _ _ hf.1 (integrable_on_finset_Union.2 hf.2)]
     · rw [Finset.sum_insert hat, IH hs.2 h's.1 hf.2]
     · simp only [disjoint_Union_right]
@@ -229,7 +229,7 @@ theorem tendsto_set_integral_of_monotone {ι : Type _} [Countable ι] [Semilatti
   set S := ⋃ i, s i
   have hSm : MeasurableSet S := MeasurableSet.iUnion hsm
   have hsub : ∀ {i}, s i ⊆ S := subset_Union s
-  rw [← with_density_apply _ hSm] at hfi'
+  rw [← with_density_apply _ hSm] at hfi' 
   set ν := μ.with_density fun x => ‖f x‖₊ with hν
   refine' metric.nhds_basis_closed_ball.tendsto_right_iff.2 fun ε ε0 => _
   lift ε to ℝ≥0 using ε0.le
@@ -240,7 +240,7 @@ theorem tendsto_set_integral_of_monotone {ι : Type _} [Countable ι] [Semilatti
     ENNReal.coe_le_coe]
   refine' (ennnorm_integral_le_lintegral_ennnorm _).trans _
   rw [← with_density_apply _ (hSm.diff (hsm _)), ← hν, measure_diff hsub (hsm _)]
-  exacts[tsub_le_iff_tsub_le.mp hi.1,
+  exacts [tsub_le_iff_tsub_le.mp hi.1,
     (hi.2.trans_lt <| ENNReal.add_lt_top.2 ⟨hfi', ENNReal.coe_lt_top⟩).Ne]
 #align measure_theory.tendsto_set_integral_of_monotone MeasureTheory.tendsto_set_integral_of_monotone
 
@@ -249,7 +249,7 @@ theorem hasSum_integral_iUnion_ae {ι : Type _} [Countable ι] {s : ι → Set 
     (hfi : IntegrableOn f (⋃ i, s i) μ) :
     HasSum (fun n => ∫ a in s n, f a ∂μ) (∫ a in ⋃ n, s n, f a ∂μ) :=
   by
-  simp only [integrable_on, measure.restrict_Union_ae hd hm] at hfi⊢
+  simp only [integrable_on, measure.restrict_Union_ae hd hm] at hfi ⊢
   exact has_sum_integral_measure hfi
 #align measure_theory.has_sum_integral_Union_ae MeasureTheory.hasSum_integral_iUnion_ae
 
@@ -463,10 +463,10 @@ theorem integral_norm_eq_pos_sub_neg {f : α → ℝ} (hfi : Integrable f μ) :
       refine' set_integral_congr₀ h_meas.compl fun x hx => _
       dsimp only
       rw [Real.norm_eq_abs, abs_eq_neg_self.mpr _]
-      rw [Set.mem_compl_iff, Set.nmem_setOf_iff] at hx
+      rw [Set.mem_compl_iff, Set.nmem_setOf_iff] at hx 
       linarith
     _ = (∫ x in { x | 0 ≤ f x }, f x ∂μ) - ∫ x in { x | f x ≤ 0 }, f x ∂μ := by
-      rw [← set_integral_neg_eq_set_integral_nonpos hfi.1]; congr ; ext1 x; simp
+      rw [← set_integral_neg_eq_set_integral_nonpos hfi.1]; congr; ext1 x; simp
     
 #align measure_theory.integral_norm_eq_pos_sub_neg MeasureTheory.integral_norm_eq_pos_sub_neg
 
@@ -613,7 +613,7 @@ theorem set_integral_gt_gt {R : ℝ} {f : α → ℝ} (hR : 0 ≤ R) (hfm : Meas
       exact le_of_lt hx
   rw [← sub_pos, ← smul_eq_mul, ← set_integral_const, ← integral_sub hfint this,
     set_integral_pos_iff_support_of_nonneg_ae]
-  · rw [← zero_lt_iff] at hμ
+  · rw [← zero_lt_iff] at hμ 
     rwa [Set.inter_eq_self_of_subset_right]
     exact fun x hx => Ne.symm (ne_of_lt <| sub_pos.2 hx)
   · change ∀ᵐ x ∂μ.restrict _, _
@@ -838,7 +838,7 @@ theorem integrableOn_iUnion_of_summable_integral_norm {f : α → E} {s : β →
         NNReal) :=
     by rw [← NNReal.summable_coe]; exact h
   have S'' := ENNReal.tsum_coe_eq S'.has_sum
-  simp_rw [ENNReal.coe_nnreal_eq, NNReal.coe_mk, coe_nnnorm] at S''
+  simp_rw [ENNReal.coe_nnreal_eq, NNReal.coe_mk, coe_nnnorm] at S'' 
   convert ENNReal.ofReal_lt_top
 #align measure_theory.integrable_on_Union_of_summable_integral_norm MeasureTheory.integrableOn_iUnion_of_summable_integral_norm
 
@@ -1273,7 +1273,7 @@ theorem integral_withDensity_eq_integral_smul {f : α → ℝ≥0} (f_meas : Mea
     · rfl
     · exact integral_nonneg fun x => NNReal.coe_nonneg _
     · refine' ⟨f_meas.coe_nnreal_real.AEMeasurable.AEStronglyMeasurable, _⟩
-      rw [with_density_apply _ s_meas] at hs
+      rw [with_density_apply _ s_meas] at hs 
       rw [has_finite_integral]
       convert hs
       ext1 x

mathlib commit https://github.com/leanprover-community/mathlib/commit/cca40788df1b8755d5baf17ab2f27dacc2e17acb

@@ -914,9 +914,9 @@ variable [NormedAddCommGroup E] {𝕜 : Type _} [NormedField 𝕜] [NormedAddCom
 
 /-- For `f : Lp E p μ`, we can define an element of `Lp E p (μ.restrict s)` by
 `(Lp.mem_ℒp f).restrict s).to_Lp f`. This map is additive. -/
-theorem lp_toLp_restrict_add (f g : lp E p μ) (s : Set α) :
-    ((lp.memℒp (f + g)).restrict s).toLp ⇑(f + g) =
-      ((lp.memℒp f).restrict s).toLp f + ((lp.memℒp g).restrict s).toLp g :=
+theorem lp_toLp_restrict_add (f g : Lp E p μ) (s : Set α) :
+    ((Lp.memℒp (f + g)).restrict s).toLp ⇑(f + g) =
+      ((Lp.memℒp f).restrict s).toLp f + ((Lp.memℒp g).restrict s).toLp g :=
   by
   ext1
   refine' (ae_restrict_of_ae (Lp.coe_fn_add f g)).mp _
@@ -932,8 +932,8 @@ theorem lp_toLp_restrict_add (f g : lp E p μ) (s : Set α) :
 
 /-- For `f : Lp E p μ`, we can define an element of `Lp E p (μ.restrict s)` by
 `(Lp.mem_ℒp f).restrict s).to_Lp f`. This map commutes with scalar multiplication. -/
-theorem lp_toLp_restrict_smul (c : 𝕜) (f : lp F p μ) (s : Set α) :
-    ((lp.memℒp (c • f)).restrict s).toLp ⇑(c • f) = c • ((lp.memℒp f).restrict s).toLp f :=
+theorem lp_toLp_restrict_smul (c : 𝕜) (f : Lp F p μ) (s : Set α) :
+    ((Lp.memℒp (c • f)).restrict s).toLp ⇑(c • f) = c • ((Lp.memℒp f).restrict s).toLp f :=
   by
   ext1
   refine' (ae_restrict_of_ae (Lp.coe_fn_smul c f)).mp _
@@ -946,8 +946,8 @@ theorem lp_toLp_restrict_smul (c : 𝕜) (f : lp F p μ) (s : Set α) :
 
 /-- For `f : Lp E p μ`, we can define an element of `Lp E p (μ.restrict s)` by
 `(Lp.mem_ℒp f).restrict s).to_Lp f`. This map is non-expansive. -/
-theorem norm_lp_toLp_restrict_le (s : Set α) (f : lp E p μ) :
-    ‖((lp.memℒp f).restrict s).toLp f‖ ≤ ‖f‖ :=
+theorem norm_lp_toLp_restrict_le (s : Set α) (f : Lp E p μ) :
+    ‖((Lp.memℒp f).restrict s).toLp f‖ ≤ ‖f‖ :=
   by
   rw [Lp.norm_def, Lp.norm_def, ENNReal.toReal_le_toReal (Lp.snorm_ne_top _) (Lp.snorm_ne_top _)]
   refine' (le_of_eq _).trans (snorm_mono_measure _ measure.restrict_le_self)
@@ -960,9 +960,9 @@ variable (α F 𝕜)
 /-- Continuous linear map sending a function of `Lp F p μ` to the same function in
 `Lp F p (μ.restrict s)`. -/
 def lpToLpRestrictClm (μ : Measure α) (p : ℝ≥0∞) [hp : Fact (1 ≤ p)] (s : Set α) :
-    lp F p μ →L[𝕜] lp F p (μ.restrict s) :=
-  @LinearMap.mkContinuous 𝕜 𝕜 (lp F p μ) (lp F p (μ.restrict s)) _ _ _ _ _ _ (RingHom.id 𝕜)
-    ⟨fun f => Memℒp.toLp f ((lp.memℒp f).restrict s), fun f g => lp_toLp_restrict_add f g s,
+    Lp F p μ →L[𝕜] Lp F p (μ.restrict s) :=
+  @LinearMap.mkContinuous 𝕜 𝕜 (Lp F p μ) (Lp F p (μ.restrict s)) _ _ _ _ _ _ (RingHom.id 𝕜)
+    ⟨fun f => Memℒp.toLp f ((Lp.memℒp f).restrict s), fun f g => lp_toLp_restrict_add f g s,
       fun c f => lp_toLp_restrict_smul c f s⟩
     1 (by intro f; rw [one_mul]; exact norm_Lp_to_Lp_restrict_le s f)
 #align measure_theory.Lp_to_Lp_restrict_clm MeasureTheory.lpToLpRestrictClm
@@ -971,9 +971,9 @@ variable {α F 𝕜}
 
 variable (𝕜)
 
-theorem lpToLpRestrictClm_coeFn [hp : Fact (1 ≤ p)] (s : Set α) (f : lp F p μ) :
+theorem lpToLpRestrictClm_coeFn [hp : Fact (1 ≤ p)] (s : Set α) (f : Lp F p μ) :
     lpToLpRestrictClm α F 𝕜 μ p s f =ᵐ[μ.restrict s] f :=
-  Memℒp.coeFn_toLp ((lp.memℒp f).restrict s)
+  Memℒp.coeFn_toLp ((Lp.memℒp f).restrict s)
 #align measure_theory.Lp_to_Lp_restrict_clm_coe_fn MeasureTheory.lpToLpRestrictClm_coeFn
 
 variable {𝕜}
@@ -1110,12 +1110,12 @@ namespace ContinuousLinearMap
 
 variable [CompleteSpace F] [NormedSpace ℝ F]
 
-theorem integral_compLp (L : E →L[𝕜] F) (φ : lp E p μ) :
+theorem integral_compLp (L : E →L[𝕜] F) (φ : Lp E p μ) :
     (∫ a, (L.compLp φ) a ∂μ) = ∫ a, L (φ a) ∂μ :=
   integral_congr_ae <| coeFn_compLp _ _
 #align continuous_linear_map.integral_comp_Lp ContinuousLinearMap.integral_compLp
 
-theorem set_integral_compLp (L : E →L[𝕜] F) (φ : lp E p μ) {s : Set α} (hs : MeasurableSet s) :
+theorem set_integral_compLp (L : E →L[𝕜] F) (φ : Lp E p μ) {s : Set α} (hs : MeasurableSet s) :
     (∫ a in s, (L.compLp φ) a ∂μ) = ∫ a in s, L (φ a) ∂μ :=
   set_integral_congr_ae hs ((L.coeFn_compLp φ).mono fun x hx hx2 => hx)
 #align continuous_linear_map.set_integral_comp_Lp ContinuousLinearMap.set_integral_compLp

mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb

@@ -60,7 +60,7 @@ noncomputable section
 
 open Set Filter TopologicalSpace MeasureTheory Function
 
-open Classical Topology Interval BigOperators Filter ENNReal NNReal MeasureTheory
+open scoped Classical Topology Interval BigOperators Filter ENNReal NNReal MeasureTheory
 
 variable {α β E F : Type _} [MeasurableSpace α]
 
@@ -1101,7 +1101,7 @@ as `continuous_linear_map.comp_Lp`. We take advantage of this construction here.
 -/
 
 
-open ComplexConjugate
+open scoped ComplexConjugate
 
 variable {μ : Measure α} {𝕜 : Type _} [IsROrC 𝕜] [NormedSpace 𝕜 E] [NormedAddCommGroup F]
   [NormedSpace 𝕜 F] {p : ENNReal}

mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb

@@ -276,8 +276,7 @@ theorem integral_iUnion_ae {ι : Type _} [Countable ι] {s : ι → Set α}
 theorem set_integral_eq_zero_of_ae_eq_zero (ht_eq : ∀ᵐ x ∂μ, x ∈ t → f x = 0) :
     (∫ x in t, f x ∂μ) = 0 :=
   by
-  by_cases hf : ae_strongly_measurable f (μ.restrict t)
-  swap
+  by_cases hf : ae_strongly_measurable f (μ.restrict t); swap
   · rw [integral_undef]
     contrapose! hf
     exact hf.1
@@ -303,9 +302,7 @@ theorem integral_union_eq_left_of_ae_aux (ht_eq : ∀ᵐ x ∂μ.restrict t, f x
     (∫ x in s ∪ t, f x ∂μ) = ∫ x in s, f x ∂μ :=
   by
   let k := f ⁻¹' {0}
-  have hk : MeasurableSet k := by
-    borelize E
-    exact haux.measurable (measurable_set_singleton _)
+  have hk : MeasurableSet k := by borelize E; exact haux.measurable (measurable_set_singleton _)
   have h's : integrable_on f s μ := H.mono (subset_union_left _ _) le_rfl
   have A : ∀ u : Set α, (∫ x in u ∩ k, f x ∂μ) = 0 := fun u =>
     set_integral_eq_zero_of_forall_eq_zero fun x hx => hx.2
@@ -321,15 +318,9 @@ theorem integral_union_eq_left_of_ae_aux (ht_eq : ∀ᵐ x ∂μ.restrict t, f x
 theorem integral_union_eq_left_of_ae (ht_eq : ∀ᵐ x ∂μ.restrict t, f x = 0) :
     (∫ x in s ∪ t, f x ∂μ) = ∫ x in s, f x ∂μ :=
   by
-  have ht : integrable_on f t μ :=
-    by
-    apply integrable_on_zero.congr_fun_ae
-    symm
-    exact ht_eq
-  by_cases H : integrable_on f (s ∪ t) μ
-  swap
-  · rw [integral_undef H, integral_undef]
-    simpa [integrable_on_union, ht] using H
+  have ht : integrable_on f t μ := by apply integrable_on_zero.congr_fun_ae; symm; exact ht_eq
+  by_cases H : integrable_on f (s ∪ t) μ; swap
+  · rw [integral_undef H, integral_undef]; simpa [integrable_on_union, ht] using H
   let f' := H.1.mk f
   calc
     (∫ x : α in s ∪ t, f x ∂μ) = ∫ x : α in s ∪ t, f' x ∂μ := integral_congr_ae H.1.ae_eq_mk
@@ -361,16 +352,12 @@ theorem set_integral_eq_of_subset_of_ae_diff_eq_zero_aux (hts : s ⊆ t)
     (h'aux : IntegrableOn f t μ) : (∫ x in t, f x ∂μ) = ∫ x in s, f x ∂μ :=
   by
   let k := f ⁻¹' {0}
-  have hk : MeasurableSet k := by
-    borelize E
-    exact haux.measurable (measurable_set_singleton _)
+  have hk : MeasurableSet k := by borelize E; exact haux.measurable (measurable_set_singleton _)
   calc
     (∫ x in t, f x ∂μ) = (∫ x in t ∩ k, f x ∂μ) + ∫ x in t \ k, f x ∂μ := by
       rw [integral_inter_add_diff hk h'aux]
-    _ = ∫ x in t \ k, f x ∂μ :=
-      by
-      rw [set_integral_eq_zero_of_forall_eq_zero fun x hx => _, zero_add]
-      exact hx.2
+    _ = ∫ x in t \ k, f x ∂μ := by
+      rw [set_integral_eq_zero_of_forall_eq_zero fun x hx => _, zero_add]; exact hx.2
     _ = ∫ x in s \ k, f x ∂μ := by
       apply set_integral_congr_set_ae
       filter_upwards [h't]with x hx
@@ -445,11 +432,8 @@ theorem set_integral_neg_eq_set_integral_nonpos [LinearOrder E] {f : α → E}
     (hf : AEStronglyMeasurable f μ) :
     (∫ x in { x | f x < 0 }, f x ∂μ) = ∫ x in { x | f x ≤ 0 }, f x ∂μ :=
   by
-  have h_union : { x | f x ≤ 0 } = { x | f x < 0 } ∪ { x | f x = 0 } :=
-    by
-    ext
-    simp_rw [Set.mem_union, Set.mem_setOf_eq]
-    exact le_iff_lt_or_eq
+  have h_union : { x | f x ≤ 0 } = { x | f x < 0 } ∪ { x | f x = 0 } := by ext;
+    simp_rw [Set.mem_union, Set.mem_setOf_eq]; exact le_iff_lt_or_eq
   rw [h_union]
   have B : null_measurable_set { x | f x = 0 } μ :=
     hf.null_measurable_set_eq_fun ae_strongly_measurable_zero
@@ -481,12 +465,8 @@ theorem integral_norm_eq_pos_sub_neg {f : α → ℝ} (hfi : Integrable f μ) :
       rw [Real.norm_eq_abs, abs_eq_neg_self.mpr _]
       rw [Set.mem_compl_iff, Set.nmem_setOf_iff] at hx
       linarith
-    _ = (∫ x in { x | 0 ≤ f x }, f x ∂μ) - ∫ x in { x | f x ≤ 0 }, f x ∂μ :=
-      by
-      rw [← set_integral_neg_eq_set_integral_nonpos hfi.1]
-      congr
-      ext1 x
-      simp
+    _ = (∫ x in { x | 0 ≤ f x }, f x ∂μ) - ∫ x in { x | f x ≤ 0 }, f x ∂μ := by
+      rw [← set_integral_neg_eq_set_integral_nonpos hfi.1]; congr ; ext1 x; simp
     
 #align measure_theory.integral_norm_eq_pos_sub_neg MeasureTheory.integral_norm_eq_pos_sub_neg
 
@@ -753,9 +733,7 @@ include hf hg
 
 -- why do I need this include, but we don't need it in other lemmas?
 theorem set_integral_mono_on_ae (hs : MeasurableSet s) (h : ∀ᵐ x ∂μ, x ∈ s → f x ≤ g x) :
-    (∫ a in s, f a ∂μ) ≤ ∫ a in s, g a ∂μ :=
-  by
-  refine' set_integral_mono_ae_restrict hf hg _
+    (∫ a in s, f a ∂μ) ≤ ∫ a in s, g a ∂μ := by refine' set_integral_mono_ae_restrict hf hg _;
   rwa [eventually_le, ae_restrict_iff' hs]
 #align measure_theory.set_integral_mono_on_ae MeasureTheory.set_integral_mono_on_ae
 
@@ -858,9 +836,7 @@ theorem integrableOn_iUnion_of_summable_integral_norm {f : α → E} {s : β →
     Summable fun b : β =>
       (⟨∫ a : α in s b, ‖f a‖₊ ∂μ, set_integral_nonneg (hs b) fun a ha => NNReal.coe_nonneg _⟩ :
         NNReal) :=
-    by
-    rw [← NNReal.summable_coe]
-    exact h
+    by rw [← NNReal.summable_coe]; exact h
   have S'' := ENNReal.tsum_coe_eq S'.has_sum
   simp_rw [ENNReal.coe_nnreal_eq, NNReal.coe_mk, coe_nnnorm] at S''
   convert ENNReal.ofReal_lt_top
@@ -988,11 +964,7 @@ def lpToLpRestrictClm (μ : Measure α) (p : ℝ≥0∞) [hp : Fact (1 ≤ p)] (
   @LinearMap.mkContinuous 𝕜 𝕜 (lp F p μ) (lp F p (μ.restrict s)) _ _ _ _ _ _ (RingHom.id 𝕜)
     ⟨fun f => Memℒp.toLp f ((lp.memℒp f).restrict s), fun f g => lp_toLp_restrict_add f g s,
       fun c f => lp_toLp_restrict_smul c f s⟩
-    1
-    (by
-      intro f
-      rw [one_mul]
-      exact norm_Lp_to_Lp_restrict_le s f)
+    1 (by intro f; rw [one_mul]; exact norm_Lp_to_Lp_restrict_le s f)
 #align measure_theory.Lp_to_Lp_restrict_clm MeasureTheory.lpToLpRestrictClm
 
 variable {α F 𝕜}
@@ -1149,9 +1121,7 @@ theorem set_integral_compLp (L : E →L[𝕜] F) (φ : lp E p μ) {s : Set α} (
 #align continuous_linear_map.set_integral_comp_Lp ContinuousLinearMap.set_integral_compLp
 
 theorem continuous_integral_comp_L1 (L : E →L[𝕜] F) :
-    Continuous fun φ : α →₁[μ] E => ∫ a : α, L (φ a) ∂μ :=
-  by
-  rw [← funext L.integral_comp_Lp]
+    Continuous fun φ : α →₁[μ] E => ∫ a : α, L (φ a) ∂μ := by rw [← funext L.integral_comp_Lp];
   exact continuous_integral.comp (L.comp_LpL 1 μ).Continuous
 #align continuous_linear_map.continuous_integral_comp_L1 ContinuousLinearMap.continuous_integral_comp_L1
 
@@ -1423,9 +1393,7 @@ theorem Integrable.simpleFunc_mul (g : SimpleFunc β ℝ) (hf : Integrable f μ)
 #align measure_theory.integrable.simple_func_mul MeasureTheory.Integrable.simpleFunc_mul
 
 theorem Integrable.simpleFunc_mul' (hm : m ≤ m0) (g : @SimpleFunc β m ℝ) (hf : Integrable f μ) :
-    Integrable (g * f) μ :=
-  by
-  rw [← simple_func.coe_to_larger_space_eq hm g]
+    Integrable (g * f) μ := by rw [← simple_func.coe_to_larger_space_eq hm g];
   exact hf.simple_func_mul (g.to_larger_space hm)
 #align measure_theory.integrable.simple_func_mul' MeasureTheory.Integrable.simpleFunc_mul'
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/ef95945cd48c932c9e034872bd25c3c220d9c946

@@ -54,7 +54,7 @@ but we reference them here because all theorems about set integrals are in this
 -/
 
 
-assert_not_exists inner_product_space
+assert_not_exists InnerProductSpace
 
 noncomputable section
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/75e7fca56381d056096ce5d05e938f63a6567828

@@ -442,7 +442,7 @@ theorem set_integral_eq_integral_of_forall_compl_eq_zero (h : ∀ x, x ∉ s →
 #align measure_theory.set_integral_eq_integral_of_forall_compl_eq_zero MeasureTheory.set_integral_eq_integral_of_forall_compl_eq_zero
 
 theorem set_integral_neg_eq_set_integral_nonpos [LinearOrder E] {f : α → E}
-    (hf : AeStronglyMeasurable f μ) :
+    (hf : AEStronglyMeasurable f μ) :
     (∫ x in { x | f x < 0 }, f x ∂μ) = ∫ x in { x | f x ≤ 0 }, f x ∂μ :=
   by
   have h_union : { x | f x ≤ 0 } = { x | f x < 0 } ∪ { x | f x = 0 } :=
@@ -461,7 +461,7 @@ theorem set_integral_neg_eq_set_integral_nonpos [LinearOrder E] {f : α → E}
 theorem integral_norm_eq_pos_sub_neg {f : α → ℝ} (hfi : Integrable f μ) :
     (∫ x, ‖f x‖ ∂μ) = (∫ x in { x | 0 ≤ f x }, f x ∂μ) - ∫ x in { x | f x ≤ 0 }, f x ∂μ :=
   have h_meas : NullMeasurableSet { x | 0 ≤ f x } μ :=
-    aeStronglyMeasurable_const.nullMeasurableSet_le hfi.1
+    aestronglyMeasurable_const.nullMeasurableSet_le hfi.1
   calc
     (∫ x, ‖f x‖ ∂μ) = (∫ x in { x | 0 ≤ f x }, ‖f x‖ ∂μ) + ∫ x in { x | 0 ≤ f x }ᶜ, ‖f x‖ ∂μ := by
       rw [← integral_add_compl₀ h_meas hfi.norm]
@@ -527,7 +527,7 @@ theorem integral_indicatorConstLp {p : ℝ≥0∞} (ht : MeasurableSet t) (hμt
 #align measure_theory.integral_indicator_const_Lp MeasureTheory.integral_indicatorConstLp
 
 theorem set_integral_map {β} [MeasurableSpace β] {g : α → β} {f : β → E} {s : Set β}
-    (hs : MeasurableSet s) (hf : AeStronglyMeasurable f (Measure.map g μ)) (hg : AEMeasurable g μ) :
+    (hs : MeasurableSet s) (hf : AEStronglyMeasurable f (Measure.map g μ)) (hg : AEMeasurable g μ) :
     (∫ y in s, f y ∂Measure.map g μ) = ∫ x in g ⁻¹' s, f (g x) ∂μ :=
   by
   rw [measure.restrict_map_of_ae_measurable hg hs,
@@ -573,7 +573,7 @@ theorem norm_set_integral_le_of_norm_le_const_ae {C : ℝ} (hs : μ s < ∞)
 #align measure_theory.norm_set_integral_le_of_norm_le_const_ae MeasureTheory.norm_set_integral_le_of_norm_le_const_ae
 
 theorem norm_set_integral_le_of_norm_le_const_ae' {C : ℝ} (hs : μ s < ∞)
-    (hC : ∀ᵐ x ∂μ, x ∈ s → ‖f x‖ ≤ C) (hfm : AeStronglyMeasurable f (μ.restrict s)) :
+    (hC : ∀ᵐ x ∂μ, x ∈ s → ‖f x‖ ≤ C) (hfm : AEStronglyMeasurable f (μ.restrict s)) :
     ‖∫ x in s, f x ∂μ‖ ≤ C * (μ s).toReal :=
   by
   apply norm_set_integral_le_of_norm_le_const_ae hs
@@ -595,7 +595,7 @@ theorem norm_set_integral_le_of_norm_le_const_ae'' {C : ℝ} (hs : μ s < ∞) (
 #align measure_theory.norm_set_integral_le_of_norm_le_const_ae'' MeasureTheory.norm_set_integral_le_of_norm_le_const_ae''
 
 theorem norm_set_integral_le_of_norm_le_const {C : ℝ} (hs : μ s < ∞) (hC : ∀ x ∈ s, ‖f x‖ ≤ C)
-    (hfm : AeStronglyMeasurable f (μ.restrict s)) : ‖∫ x in s, f x ∂μ‖ ≤ C * (μ s).toReal :=
+    (hfm : AEStronglyMeasurable f (μ.restrict s)) : ‖∫ x in s, f x ∂μ‖ ≤ C * (μ s).toReal :=
   norm_set_integral_le_of_norm_le_const_ae' hs (eventually_of_forall hC) hfm
 #align measure_theory.norm_set_integral_le_of_norm_le_const MeasureTheory.norm_set_integral_le_of_norm_le_const
 
@@ -912,7 +912,7 @@ theorem Antitone.tendsto_set_integral (hsm : ∀ i, MeasurableSet (s i)) (h_anti
   rw [← integral_indicator (MeasurableSet.iInter hsm)]
   refine' tendsto_integral_of_dominated_convergence bound _ _ _ _
   · intro n
-    rw [aeStronglyMeasurable_indicator_iff (hsm n)]
+    rw [aestronglyMeasurable_indicator_iff (hsm n)]
     exact (integrable_on.mono_set hfi (h_anti (zero_le n))).1
   · rw [integrable_indicator_iff (hsm 0)]
     exact hfi.norm
@@ -1114,7 +1114,7 @@ theorem ContinuousOn.integral_sub_linear_isLittleO_ae [TopologicalSpace α] [Ope
     (hsμ : (fun i => (μ (s i)).toReal) =ᶠ[li] m := by rfl) :
     (fun i => (∫ x in s i, f x ∂μ) - m i • f a) =o[li] m :=
   (hft a ha).integral_sub_linear_isLittleO_ae ht
-    ⟨t, self_mem_nhdsWithin, hft.AeStronglyMeasurable ht⟩ hs m hsμ
+    ⟨t, self_mem_nhdsWithin, hft.AEStronglyMeasurable ht⟩ hs m hsμ
 #align continuous_on.integral_sub_linear_is_o_ae ContinuousOn.integral_sub_linear_isLittleO_ae
 
 section
@@ -1302,7 +1302,7 @@ theorem integral_withDensity_eq_integral_smul {f : α → ℝ≥0} (f_meas : Mea
     rw [lintegral_coe_eq_integral, ENNReal.toReal_ofReal, ← integral_smul_const]
     · rfl
     · exact integral_nonneg fun x => NNReal.coe_nonneg _
-    · refine' ⟨f_meas.coe_nnreal_real.AEMeasurable.AeStronglyMeasurable, _⟩
+    · refine' ⟨f_meas.coe_nnreal_real.AEMeasurable.AEStronglyMeasurable, _⟩
       rw [with_density_apply _ s_meas] at hs
       rw [has_finite_integral]
       convert hs

mathlib commit https://github.com/leanprover-community/mathlib/commit/33c67ae661dd8988516ff7f247b0be3018cdd952

@@ -625,7 +625,7 @@ theorem set_integral_gt_gt {R : ℝ} {f : α → ℝ} (hR : 0 ≤ R) (hfm : Meas
     by
     refine' ⟨ae_strongly_measurable_const, lt_of_le_of_lt _ hfint.2⟩
     refine'
-      set_lintegral_mono (Measurable.nnnorm _).coe_nNReal_eNNReal hfm.nnnorm.coe_nnreal_ennreal
+      set_lintegral_mono (Measurable.nnnorm _).coe_nnreal_ennreal hfm.nnnorm.coe_nnreal_ennreal
         fun x hx => _
     · exact measurable_const
     · simp only [ENNReal.coe_le_coe, Real.nnnorm_of_nonneg hR,

mathlib commit https://github.com/leanprover-community/mathlib/commit/95a87616d63b3cb49d3fe678d416fbe9c4217bf4

@@ -1095,7 +1095,7 @@ theorem ContinuousAt.integral_sub_linear_isLittleO_ae [TopologicalSpace α] [Ope
     {li : Filter ι} (hs : Tendsto s li (𝓝 a).smallSets) (m : ι → ℝ := fun i => (μ (s i)).toReal)
     (hsμ : (fun i => (μ (s i)).toReal) =ᶠ[li] m := by rfl) :
     (fun i => (∫ x in s i, f x ∂μ) - m i • f a) =o[li] m :=
-  (ha.mono_left inf_le_left).integral_sub_linear_isLittleO_ae hfm (μ.finite_at_nhds a) hs m hsμ
+  (ha.mono_left inf_le_left).integral_sub_linear_isLittleO_ae hfm (μ.finiteAtNhds a) hs m hsμ
 #align continuous_at.integral_sub_linear_is_o_ae ContinuousAt.integral_sub_linear_isLittleO_ae
 
 /-- Fundamental theorem of calculus for set integrals, `nhds_within` version: if `μ` is a locally

mathlib commit https://github.com/leanprover-community/mathlib/commit/0b9eaaa7686280fad8cce467f5c3c57ee6ce77f8

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Zhouhang Zhou, Yury Kudryashov
 
 ! This file was ported from Lean 3 source module measure_theory.integral.set_integral
-! leanprover-community/mathlib commit 8b8ba04e2f326f3f7cf24ad129beda58531ada61
+! leanprover-community/mathlib commit 24e0c85412ff6adbeca08022c25ba4876eedf37a
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -54,6 +54,8 @@ but we reference them here because all theorems about set integrals are in this
 -/
 
 
+assert_not_exists inner_product_space
+
 noncomputable section
 
 open Set Filter TopologicalSpace MeasureTheory Function
@@ -1286,37 +1288,6 @@ theorem integral_smul_const {𝕜 : Type _} [IsROrC 𝕜] [NormedSpace 𝕜 E] (
     simp_rw [integrable_smul_const hc, hf, not_false_iff]
 #align integral_smul_const integral_smul_const
 
-section Inner
-
-variable {E' : Type _}
-
-variable [NormedAddCommGroup E'] [InnerProductSpace 𝕜 E']
-
-variable [CompleteSpace E'] [NormedSpace ℝ E']
-
--- mathport name: «expr⟪ , ⟫»
-local notation "⟪" x ", " y "⟫" => @inner 𝕜 E' _ x y
-
-theorem integral_inner {f : α → E'} (hf : Integrable f μ) (c : E') :
-    (∫ x, ⟪c, f x⟫ ∂μ) = ⟪c, ∫ x, f x ∂μ⟫ :=
-  ((innerSL 𝕜 c).restrictScalars ℝ).integral_comp_comm hf
-#align integral_inner integral_inner
-
-variable (𝕜)
-
--- mathport name: inner_with_explicit
--- variable binder update doesn't work for lemmas which refer to `𝕜` only via the notation
-local notation "⟪" x ", " y "⟫" => @inner 𝕜 E' _ x y
-
-theorem integral_eq_zero_of_forall_integral_inner_eq_zero (f : α → E') (hf : Integrable f μ)
-    (hf_int : ∀ c : E', (∫ x, ⟪c, f x⟫ ∂μ) = 0) : (∫ x, f x ∂μ) = 0 :=
-  by
-  specialize hf_int (∫ x, f x ∂μ)
-  rwa [integral_inner hf, inner_self_eq_zero] at hf_int
-#align integral_eq_zero_of_forall_integral_inner_eq_zero integral_eq_zero_of_forall_integral_inner_eq_zero
-
-end Inner
-
 theorem integral_withDensity_eq_integral_smul {f : α → ℝ≥0} (f_meas : Measurable f) (g : α → E) :
     (∫ a, g a ∂μ.withDensity fun x => f x) = ∫ a, f a • g a ∂μ :=
   by

mathlib commit https://github.com/leanprover-community/mathlib/commit/e3fb84046afd187b710170887195d50bada934ee

@@ -133,22 +133,22 @@ theorem integral_finset_bUnion {ι : Type _} (t : Finset ι) {s : ι → Set α}
   induction' t using Finset.induction_on with a t hat IH hs h's
   · simp
   · simp only [Finset.coe_insert, Finset.forall_mem_insert, Set.pairwise_insert,
-      Finset.set_bunionᵢ_insert] at hs hf h's⊢
+      Finset.set_biUnion_insert] at hs hf h's⊢
     rw [integral_union _ _ hf.1 (integrable_on_finset_Union.2 hf.2)]
     · rw [Finset.sum_insert hat, IH hs.2 h's.1 hf.2]
     · simp only [disjoint_Union_right]
       exact fun i hi => (h's.2 i hi (ne_of_mem_of_not_mem hi hat).symm).1
-    · exact Finset.measurableSet_bunionᵢ _ hs.2
+    · exact Finset.measurableSet_biUnion _ hs.2
 #align measure_theory.integral_finset_bUnion MeasureTheory.integral_finset_bUnion
 
-theorem integral_fintype_unionᵢ {ι : Type _} [Fintype ι] {s : ι → Set α}
+theorem integral_fintype_iUnion {ι : Type _} [Fintype ι] {s : ι → Set α}
     (hs : ∀ i, MeasurableSet (s i)) (h's : Pairwise (Disjoint on s))
     (hf : ∀ i, IntegrableOn f (s i) μ) : (∫ x in ⋃ i, s i, f x ∂μ) = ∑ i, ∫ x in s i, f x ∂μ :=
   by
   convert integral_finset_bUnion Finset.univ (fun i hi => hs i) _ fun i _ => hf i
   · simp
   · simp [pairwise_univ, h's]
-#align measure_theory.integral_fintype_Union MeasureTheory.integral_fintype_unionᵢ
+#align measure_theory.integral_fintype_Union MeasureTheory.integral_fintype_iUnion
 
 theorem integral_empty : (∫ x in ∅, f x ∂μ) = 0 := by
   rw [measure.restrict_empty, integral_zero_measure]
@@ -225,7 +225,7 @@ theorem tendsto_set_integral_of_monotone {ι : Type _} [Countable ι] [Semilatti
   by
   have hfi' : (∫⁻ x in ⋃ n, s n, ‖f x‖₊ ∂μ) < ∞ := hfi.2
   set S := ⋃ i, s i
-  have hSm : MeasurableSet S := MeasurableSet.unionᵢ hsm
+  have hSm : MeasurableSet S := MeasurableSet.iUnion hsm
   have hsub : ∀ {i}, s i ⊆ S := subset_Union s
   rw [← with_density_apply _ hSm] at hfi'
   set ν := μ.with_density fun x => ‖f x‖₊ with hν
@@ -242,34 +242,34 @@ theorem tendsto_set_integral_of_monotone {ι : Type _} [Countable ι] [Semilatti
     (hi.2.trans_lt <| ENNReal.add_lt_top.2 ⟨hfi', ENNReal.coe_lt_top⟩).Ne]
 #align measure_theory.tendsto_set_integral_of_monotone MeasureTheory.tendsto_set_integral_of_monotone
 
-theorem hasSum_integral_unionᵢ_ae {ι : Type _} [Countable ι] {s : ι → Set α}
+theorem hasSum_integral_iUnion_ae {ι : Type _} [Countable ι] {s : ι → Set α}
     (hm : ∀ i, NullMeasurableSet (s i) μ) (hd : Pairwise (AEDisjoint μ on s))
     (hfi : IntegrableOn f (⋃ i, s i) μ) :
     HasSum (fun n => ∫ a in s n, f a ∂μ) (∫ a in ⋃ n, s n, f a ∂μ) :=
   by
   simp only [integrable_on, measure.restrict_Union_ae hd hm] at hfi⊢
   exact has_sum_integral_measure hfi
-#align measure_theory.has_sum_integral_Union_ae MeasureTheory.hasSum_integral_unionᵢ_ae
+#align measure_theory.has_sum_integral_Union_ae MeasureTheory.hasSum_integral_iUnion_ae
 
-theorem hasSum_integral_unionᵢ {ι : Type _} [Countable ι] {s : ι → Set α}
+theorem hasSum_integral_iUnion {ι : Type _} [Countable ι] {s : ι → Set α}
     (hm : ∀ i, MeasurableSet (s i)) (hd : Pairwise (Disjoint on s))
     (hfi : IntegrableOn f (⋃ i, s i) μ) :
     HasSum (fun n => ∫ a in s n, f a ∂μ) (∫ a in ⋃ n, s n, f a ∂μ) :=
-  hasSum_integral_unionᵢ_ae (fun i => (hm i).NullMeasurableSet) (hd.mono fun i j h => h.AEDisjoint)
+  hasSum_integral_iUnion_ae (fun i => (hm i).NullMeasurableSet) (hd.mono fun i j h => h.AEDisjoint)
     hfi
-#align measure_theory.has_sum_integral_Union MeasureTheory.hasSum_integral_unionᵢ
+#align measure_theory.has_sum_integral_Union MeasureTheory.hasSum_integral_iUnion
 
-theorem integral_unionᵢ {ι : Type _} [Countable ι] {s : ι → Set α} (hm : ∀ i, MeasurableSet (s i))
+theorem integral_iUnion {ι : Type _} [Countable ι] {s : ι → Set α} (hm : ∀ i, MeasurableSet (s i))
     (hd : Pairwise (Disjoint on s)) (hfi : IntegrableOn f (⋃ i, s i) μ) :
     (∫ a in ⋃ n, s n, f a ∂μ) = ∑' n, ∫ a in s n, f a ∂μ :=
-  (HasSum.tsum_eq (hasSum_integral_unionᵢ hm hd hfi)).symm
-#align measure_theory.integral_Union MeasureTheory.integral_unionᵢ
+  (HasSum.tsum_eq (hasSum_integral_iUnion hm hd hfi)).symm
+#align measure_theory.integral_Union MeasureTheory.integral_iUnion
 
-theorem integral_unionᵢ_ae {ι : Type _} [Countable ι] {s : ι → Set α}
+theorem integral_iUnion_ae {ι : Type _} [Countable ι] {s : ι → Set α}
     (hm : ∀ i, NullMeasurableSet (s i) μ) (hd : Pairwise (AEDisjoint μ on s))
     (hfi : IntegrableOn f (⋃ i, s i) μ) : (∫ a in ⋃ n, s n, f a ∂μ) = ∑' n, ∫ a in s n, f a ∂μ :=
-  (HasSum.tsum_eq (hasSum_integral_unionᵢ_ae hm hd hfi)).symm
-#align measure_theory.integral_Union_ae MeasureTheory.integral_unionᵢ_ae
+  (HasSum.tsum_eq (hasSum_integral_iUnion_ae hm hd hfi)).symm
+#align measure_theory.integral_Union_ae MeasureTheory.integral_iUnion_ae
 
 theorem set_integral_eq_zero_of_ae_eq_zero (ht_eq : ∀ᵐ x ∂μ, x ∈ t → f x = 0) :
     (∫ x in t, f x ∂μ) = 0 :=
@@ -845,9 +845,9 @@ section IntegrableUnion
 
 variable {μ : Measure α} [NormedAddCommGroup E] [Countable β]
 
-theorem integrableOn_unionᵢ_of_summable_integral_norm {f : α → E} {s : β → Set α}
+theorem integrableOn_iUnion_of_summable_integral_norm {f : α → E} {s : β → Set α}
     (hs : ∀ b : β, MeasurableSet (s b)) (hi : ∀ b : β, IntegrableOn f (s b) μ)
-    (h : Summable fun b : β => ∫ a : α in s b, ‖f a‖ ∂μ) : IntegrableOn f (unionᵢ s) μ :=
+    (h : Summable fun b : β => ∫ a : α in s b, ‖f a‖ ∂μ) : IntegrableOn f (iUnion s) μ :=
   by
   refine' ⟨ae_strongly_measurable.Union fun i => (hi i).1, (lintegral_Union_le _ _).trans_lt _⟩
   have B := fun b : β => lintegral_coe_eq_integral (fun a : α => ‖f a‖₊) (hi b).norm
@@ -862,13 +862,13 @@ theorem integrableOn_unionᵢ_of_summable_integral_norm {f : α → E} {s : β 
   have S'' := ENNReal.tsum_coe_eq S'.has_sum
   simp_rw [ENNReal.coe_nnreal_eq, NNReal.coe_mk, coe_nnnorm] at S''
   convert ENNReal.ofReal_lt_top
-#align measure_theory.integrable_on_Union_of_summable_integral_norm MeasureTheory.integrableOn_unionᵢ_of_summable_integral_norm
+#align measure_theory.integrable_on_Union_of_summable_integral_norm MeasureTheory.integrableOn_iUnion_of_summable_integral_norm
 
 variable [TopologicalSpace α] [BorelSpace α] [MetrizableSpace α] [LocallyFiniteMeasure μ]
 
 /-- If `s` is a countable family of compact sets, `f` is a continuous function, and the sequence
 `‖f.restrict (s i)‖ * μ (s i)` is summable, then `f` is integrable on the union of the `s i`. -/
-theorem integrableOn_unionᵢ_of_summable_norm_restrict {f : C(α, E)} {s : β → Compacts α}
+theorem integrableOn_iUnion_of_summable_norm_restrict {f : C(α, E)} {s : β → Compacts α}
     (hf : Summable fun i : β => ‖f.restrict (s i)‖ * ENNReal.toReal (μ <| s i)) :
     IntegrableOn f (⋃ i : β, s i) μ :=
   by
@@ -881,7 +881,7 @@ theorem integrableOn_unionᵢ_of_summable_norm_restrict {f : C(α, E)} {s : β 
     norm_set_integral_le_of_norm_le_const' (s i).IsCompact.measure_lt_top
       (s i).IsCompact.IsClosed.MeasurableSet fun x hx =>
       (norm_norm (f x)).symm ▸ (f.restrict ↑(s i)).norm_coe_le_norm ⟨x, hx⟩
-#align measure_theory.integrable_on_Union_of_summable_norm_restrict MeasureTheory.integrableOn_unionᵢ_of_summable_norm_restrict
+#align measure_theory.integrable_on_Union_of_summable_norm_restrict MeasureTheory.integrableOn_iUnion_of_summable_norm_restrict
 
 /-- If `s` is a countable family of compact sets covering `α`, `f` is a continuous function, and
 the sequence `‖f.restrict (s i)‖ * μ (s i)` is summable, then `f` is integrable. -/
@@ -907,7 +907,7 @@ theorem Antitone.tendsto_set_integral (hsm : ∀ i, MeasurableSet (s i)) (h_anti
   have h_int_eq : (fun i => ∫ a in s i, f a ∂μ) = fun i => ∫ a, (s i).indicator f a ∂μ :=
     funext fun i => (integral_indicator (hsm i)).symm
   rw [h_int_eq]
-  rw [← integral_indicator (MeasurableSet.interᵢ hsm)]
+  rw [← integral_indicator (MeasurableSet.iInter hsm)]
   refine' tendsto_integral_of_dominated_convergence bound _ _ _ _
   · intro n
     rw [aeStronglyMeasurable_indicator_iff (hsm n)]

mathlib commit https://github.com/leanprover-community/mathlib/commit/d4437c68c8d350fc9d4e95e1e174409db35e30d7

@@ -206,7 +206,7 @@ theorem ofReal_set_integral_one_of_measure_ne_top {α : Type _} {m : MeasurableS
 #align measure_theory.of_real_set_integral_one_of_measure_ne_top MeasureTheory.ofReal_set_integral_one_of_measure_ne_top
 
 theorem ofReal_set_integral_one {α : Type _} {m : MeasurableSpace α} (μ : Measure α)
-    [IsFiniteMeasure μ] (s : Set α) : ENNReal.ofReal (∫ x in s, (1 : ℝ) ∂μ) = μ s :=
+    [FiniteMeasure μ] (s : Set α) : ENNReal.ofReal (∫ x in s, (1 : ℝ) ∂μ) = μ s :=
   ofReal_set_integral_one_of_measure_ne_top (measure_ne_top μ s)
 #align measure_theory.of_real_set_integral_one MeasureTheory.ofReal_set_integral_one
 
@@ -693,7 +693,7 @@ theorem integral_Ici_eq_integral_Ioi' (ha : μ {a} = 0) :
   set_integral_congr_set_ae (Ioi_ae_eq_Ici' ha).symm
 #align measure_theory.integral_Ici_eq_integral_Ioi' MeasureTheory.integral_Ici_eq_integral_Ioi'
 
-variable [HasNoAtoms μ]
+variable [NoAtoms μ]
 
 theorem integral_Icc_eq_integral_Ioc : (∫ t in Icc a b, f t ∂μ) = ∫ t in Ioc a b, f t ∂μ :=
   integral_Icc_eq_integral_Ioc' <| measure_singleton a
@@ -864,7 +864,7 @@ theorem integrableOn_unionᵢ_of_summable_integral_norm {f : α → E} {s : β 
   convert ENNReal.ofReal_lt_top
 #align measure_theory.integrable_on_Union_of_summable_integral_norm MeasureTheory.integrableOn_unionᵢ_of_summable_integral_norm
 
-variable [TopologicalSpace α] [BorelSpace α] [MetrizableSpace α] [IsLocallyFiniteMeasure μ]
+variable [TopologicalSpace α] [BorelSpace α] [MetrizableSpace α] [LocallyFiniteMeasure μ]
 
 /-- If `s` is a countable family of compact sets, `f` is a continuous function, and the sequence
 `‖f.restrict (s i)‖ * μ (s i)` is summable, then `f` is integrable on the union of the `s i`. -/
@@ -1068,7 +1068,7 @@ argument `m` with this formula and a proof `of `(λ i, (μ (s i)).to_real) =ᶠ[
 arguments, `m i = (μ (s i)).to_real` is used in the output. -/
 theorem ContinuousWithinAt.integral_sub_linear_isLittleO_ae [TopologicalSpace α]
     [OpensMeasurableSpace α] [NormedSpace ℝ E] [CompleteSpace E] {μ : Measure α}
-    [IsLocallyFiniteMeasure μ] {a : α} {t : Set α} {f : α → E} (ha : ContinuousWithinAt f t a)
+    [LocallyFiniteMeasure μ] {a : α} {t : Set α} {f : α → E} (ha : ContinuousWithinAt f t a)
     (ht : MeasurableSet t) (hfm : StronglyMeasurableAtFilter f (𝓝[t] a) μ) {s : ι → Set α}
     {li : Filter ι} (hs : Tendsto s li (𝓝[t] a).smallSets) (m : ι → ℝ := fun i => (μ (s i)).toReal)
     (hsμ : (fun i => (μ (s i)).toReal) =ᶠ[li] m := by rfl) :
@@ -1088,8 +1088,8 @@ Often there is a good formula for `(μ (s i)).to_real`, so the formalization can
 argument `m` with this formula and a proof `of `(λ i, (μ (s i)).to_real) =ᶠ[li] m`. Without these
 arguments, `m i = (μ (s i)).to_real` is used in the output. -/
 theorem ContinuousAt.integral_sub_linear_isLittleO_ae [TopologicalSpace α] [OpensMeasurableSpace α]
-    [NormedSpace ℝ E] [CompleteSpace E] {μ : Measure α} [IsLocallyFiniteMeasure μ] {a : α}
-    {f : α → E} (ha : ContinuousAt f a) (hfm : StronglyMeasurableAtFilter f (𝓝 a) μ) {s : ι → Set α}
+    [NormedSpace ℝ E] [CompleteSpace E] {μ : Measure α} [LocallyFiniteMeasure μ] {a : α} {f : α → E}
+    (ha : ContinuousAt f a) (hfm : StronglyMeasurableAtFilter f (𝓝 a) μ) {s : ι → Set α}
     {li : Filter ι} (hs : Tendsto s li (𝓝 a).smallSets) (m : ι → ℝ := fun i => (μ (s i)).toReal)
     (hsμ : (fun i => (μ (s i)).toReal) =ᶠ[li] m := by rfl) :
     (fun i => (∫ x in s i, f x ∂μ) - m i • f a) =o[li] m :=
@@ -1106,7 +1106,7 @@ argument `m` with this formula and a proof `of `(λ i, (μ (s i)).to_real) =ᶠ[
 arguments, `m i = (μ (s i)).to_real` is used in the output. -/
 theorem ContinuousOn.integral_sub_linear_isLittleO_ae [TopologicalSpace α] [OpensMeasurableSpace α]
     [NormedSpace ℝ E] [CompleteSpace E] [SecondCountableTopologyEither α E] {μ : Measure α}
-    [IsLocallyFiniteMeasure μ] {a : α} {t : Set α} {f : α → E} (hft : ContinuousOn f t) (ha : a ∈ t)
+    [LocallyFiniteMeasure μ] {a : α} {t : Set α} {f : α → E} (hft : ContinuousOn f t) (ha : a ∈ t)
     (ht : MeasurableSet t) {s : ι → Set α} {li : Filter ι} (hs : Tendsto s li (𝓝[t] a).smallSets)
     (m : ι → ℝ := fun i => (μ (s i)).toReal)
     (hsμ : (fun i => (μ (s i)).toReal) =ᶠ[li] m := by rfl) :

mathlib commit https://github.com/leanprover-community/mathlib/commit/3905fa80e62c0898131285baab35559fbc4e5cda

@@ -94,7 +94,7 @@ theorem set_integral_congr_set_ae (hst : s =ᵐ[μ] t) : (∫ x in s, f x ∂μ)
   rw [measure.restrict_congr_set hst]
 #align measure_theory.set_integral_congr_set_ae MeasureTheory.set_integral_congr_set_ae
 
-theorem integral_union_ae (hst : AeDisjoint μ s t) (ht : NullMeasurableSet t μ)
+theorem integral_union_ae (hst : AEDisjoint μ s t) (ht : NullMeasurableSet t μ)
     (hfs : IntegrableOn f s μ) (hft : IntegrableOn f t μ) :
     (∫ x in s ∪ t, f x ∂μ) = (∫ x in s, f x ∂μ) + ∫ x in t, f x ∂μ := by
   simp only [integrable_on, measure.restrict_union₀ hst ht, integral_add_measure hfs hft]
@@ -102,7 +102,7 @@ theorem integral_union_ae (hst : AeDisjoint μ s t) (ht : NullMeasurableSet t μ
 
 theorem integral_union (hst : Disjoint s t) (ht : MeasurableSet t) (hfs : IntegrableOn f s μ)
     (hft : IntegrableOn f t μ) : (∫ x in s ∪ t, f x ∂μ) = (∫ x in s, f x ∂μ) + ∫ x in t, f x ∂μ :=
-  integral_union_ae hst.AeDisjoint ht.NullMeasurableSet hfs hft
+  integral_union_ae hst.AEDisjoint ht.NullMeasurableSet hfs hft
 #align measure_theory.integral_union MeasureTheory.integral_union
 
 theorem integral_diff (ht : MeasurableSet t) (hfs : IntegrableOn f s μ) (hts : t ⊆ s) :
@@ -160,7 +160,7 @@ theorem integral_univ : (∫ x in univ, f x ∂μ) = ∫ x, f x ∂μ := by rw [
 theorem integral_add_compl₀ (hs : NullMeasurableSet s μ) (hfi : Integrable f μ) :
     ((∫ x in s, f x ∂μ) + ∫ x in sᶜ, f x ∂μ) = ∫ x, f x ∂μ := by
   rw [←
-    integral_union_ae (@disjoint_compl_right (Set α) _ _).AeDisjoint hs.compl hfi.integrable_on
+    integral_union_ae (@disjoint_compl_right (Set α) _ _).AEDisjoint hs.compl hfi.integrable_on
       hfi.integrable_on,
     union_compl_self, integral_univ]
 #align measure_theory.integral_add_compl₀ MeasureTheory.integral_add_compl₀
@@ -243,7 +243,7 @@ theorem tendsto_set_integral_of_monotone {ι : Type _} [Countable ι] [Semilatti
 #align measure_theory.tendsto_set_integral_of_monotone MeasureTheory.tendsto_set_integral_of_monotone
 
 theorem hasSum_integral_unionᵢ_ae {ι : Type _} [Countable ι] {s : ι → Set α}
-    (hm : ∀ i, NullMeasurableSet (s i) μ) (hd : Pairwise (AeDisjoint μ on s))
+    (hm : ∀ i, NullMeasurableSet (s i) μ) (hd : Pairwise (AEDisjoint μ on s))
     (hfi : IntegrableOn f (⋃ i, s i) μ) :
     HasSum (fun n => ∫ a in s n, f a ∂μ) (∫ a in ⋃ n, s n, f a ∂μ) :=
   by
@@ -255,7 +255,7 @@ theorem hasSum_integral_unionᵢ {ι : Type _} [Countable ι] {s : ι → Set α
     (hm : ∀ i, MeasurableSet (s i)) (hd : Pairwise (Disjoint on s))
     (hfi : IntegrableOn f (⋃ i, s i) μ) :
     HasSum (fun n => ∫ a in s n, f a ∂μ) (∫ a in ⋃ n, s n, f a ∂μ) :=
-  hasSum_integral_unionᵢ_ae (fun i => (hm i).NullMeasurableSet) (hd.mono fun i j h => h.AeDisjoint)
+  hasSum_integral_unionᵢ_ae (fun i => (hm i).NullMeasurableSet) (hd.mono fun i j h => h.AEDisjoint)
     hfi
 #align measure_theory.has_sum_integral_Union MeasureTheory.hasSum_integral_unionᵢ
 
@@ -266,7 +266,7 @@ theorem integral_unionᵢ {ι : Type _} [Countable ι] {s : ι → Set α} (hm :
 #align measure_theory.integral_Union MeasureTheory.integral_unionᵢ
 
 theorem integral_unionᵢ_ae {ι : Type _} [Countable ι] {s : ι → Set α}
-    (hm : ∀ i, NullMeasurableSet (s i) μ) (hd : Pairwise (AeDisjoint μ on s))
+    (hm : ∀ i, NullMeasurableSet (s i) μ) (hd : Pairwise (AEDisjoint μ on s))
     (hfi : IntegrableOn f (⋃ i, s i) μ) : (∫ a in ⋃ n, s n, f a ∂μ) = ∑' n, ∫ a in s n, f a ∂μ :=
   (HasSum.tsum_eq (hasSum_integral_unionᵢ_ae hm hd hfi)).symm
 #align measure_theory.integral_Union_ae MeasureTheory.integral_unionᵢ_ae

mathlib commit https://github.com/leanprover-community/mathlib/commit/92c69b77c5a7dc0f7eeddb552508633305157caa

@@ -394,7 +394,7 @@ theorem set_integral_eq_of_subset_of_ae_diff_eq_zero (ht : NullMeasurableSet t 
     (h't : ∀ᵐ x ∂μ, x ∈ t \ s → f x = 0) : (∫ x in t, f x ∂μ) = ∫ x in s, f x ∂μ :=
   by
   by_cases h : integrable_on f t μ; swap
-  · have : ¬integrable_on f s μ := fun H => h (H.ofAeDiffEqZero ht h't)
+  · have : ¬integrable_on f s μ := fun H => h (H.of_ae_diff_eq_zero ht h't)
     rw [integral_undef h, integral_undef this]
   let f' := h.1.mk f
   calc
@@ -459,7 +459,7 @@ theorem set_integral_neg_eq_set_integral_nonpos [LinearOrder E] {f : α → E}
 theorem integral_norm_eq_pos_sub_neg {f : α → ℝ} (hfi : Integrable f μ) :
     (∫ x, ‖f x‖ ∂μ) = (∫ x in { x | 0 ≤ f x }, f x ∂μ) - ∫ x in { x | f x ≤ 0 }, f x ∂μ :=
   have h_meas : NullMeasurableSet { x | 0 ≤ f x } μ :=
-    aeStronglyMeasurableConst.nullMeasurableSetLe hfi.1
+    aeStronglyMeasurable_const.nullMeasurableSet_le hfi.1
   calc
     (∫ x, ‖f x‖ ∂μ) = (∫ x in { x | 0 ≤ f x }, ‖f x‖ ∂μ) + ∫ x in { x | 0 ≤ f x }ᶜ, ‖f x‖ ∂μ := by
       rw [← integral_add_compl₀ h_meas hfi.norm]
@@ -525,7 +525,7 @@ theorem integral_indicatorConstLp {p : ℝ≥0∞} (ht : MeasurableSet t) (hμt
 #align measure_theory.integral_indicator_const_Lp MeasureTheory.integral_indicatorConstLp
 
 theorem set_integral_map {β} [MeasurableSpace β] {g : α → β} {f : β → E} {s : Set β}
-    (hs : MeasurableSet s) (hf : AeStronglyMeasurable f (Measure.map g μ)) (hg : AeMeasurable g μ) :
+    (hs : MeasurableSet s) (hf : AeStronglyMeasurable f (Measure.map g μ)) (hg : AEMeasurable g μ) :
     (∫ y in s, f y ∂Measure.map g μ) = ∫ x in g ⁻¹' s, f (g x) ∂μ :=
   by
   rw [measure.restrict_map_of_ae_measurable hg hs,
@@ -548,13 +548,13 @@ theorem ClosedEmbedding.set_integral_map [TopologicalSpace α] [BorelSpace α] {
 theorem MeasurePreserving.set_integral_preimage_emb {β} {_ : MeasurableSpace β} {f : α → β} {ν}
     (h₁ : MeasurePreserving f μ ν) (h₂ : MeasurableEmbedding f) (g : β → E) (s : Set β) :
     (∫ x in f ⁻¹' s, g (f x) ∂μ) = ∫ y in s, g y ∂ν :=
-  (h₁.restrictPreimageEmb h₂ s).integral_comp h₂ _
+  (h₁.restrict_preimage_emb h₂ s).integral_comp h₂ _
 #align measure_theory.measure_preserving.set_integral_preimage_emb MeasureTheory.MeasurePreserving.set_integral_preimage_emb
 
 theorem MeasurePreserving.set_integral_image_emb {β} {_ : MeasurableSpace β} {f : α → β} {ν}
     (h₁ : MeasurePreserving f μ ν) (h₂ : MeasurableEmbedding f) (g : β → E) (s : Set α) :
     (∫ y in f '' s, g y ∂ν) = ∫ x in s, g (f x) ∂μ :=
-  Eq.symm <| (h₁.restrictImageEmb h₂ s).integral_comp h₂ _
+  Eq.symm <| (h₁.restrict_image_emb h₂ s).integral_comp h₂ _
 #align measure_theory.measure_preserving.set_integral_image_emb MeasureTheory.MeasurePreserving.set_integral_image_emb
 
 theorem set_integral_map_equiv {β} [MeasurableSpace β] (e : α ≃ᵐ β) (f : β → E) (s : Set β) :
@@ -845,7 +845,7 @@ section IntegrableUnion
 
 variable {μ : Measure α} [NormedAddCommGroup E] [Countable β]
 
-theorem integrableOnUnionOfSummableIntegralNorm {f : α → E} {s : β → Set α}
+theorem integrableOn_unionᵢ_of_summable_integral_norm {f : α → E} {s : β → Set α}
     (hs : ∀ b : β, MeasurableSet (s b)) (hi : ∀ b : β, IntegrableOn f (s b) μ)
     (h : Summable fun b : β => ∫ a : α in s b, ‖f a‖ ∂μ) : IntegrableOn f (unionᵢ s) μ :=
   by
@@ -862,34 +862,34 @@ theorem integrableOnUnionOfSummableIntegralNorm {f : α → E} {s : β → Set 
   have S'' := ENNReal.tsum_coe_eq S'.has_sum
   simp_rw [ENNReal.coe_nnreal_eq, NNReal.coe_mk, coe_nnnorm] at S''
   convert ENNReal.ofReal_lt_top
-#align measure_theory.integrable_on_Union_of_summable_integral_norm MeasureTheory.integrableOnUnionOfSummableIntegralNorm
+#align measure_theory.integrable_on_Union_of_summable_integral_norm MeasureTheory.integrableOn_unionᵢ_of_summable_integral_norm
 
 variable [TopologicalSpace α] [BorelSpace α] [MetrizableSpace α] [IsLocallyFiniteMeasure μ]
 
 /-- If `s` is a countable family of compact sets, `f` is a continuous function, and the sequence
 `‖f.restrict (s i)‖ * μ (s i)` is summable, then `f` is integrable on the union of the `s i`. -/
-theorem integrableOnUnionOfSummableNormRestrict {f : C(α, E)} {s : β → Compacts α}
+theorem integrableOn_unionᵢ_of_summable_norm_restrict {f : C(α, E)} {s : β → Compacts α}
     (hf : Summable fun i : β => ‖f.restrict (s i)‖ * ENNReal.toReal (μ <| s i)) :
     IntegrableOn f (⋃ i : β, s i) μ :=
   by
   refine'
     integrable_on_Union_of_summable_integral_norm (fun i => (s i).IsCompact.IsClosed.MeasurableSet)
-      (fun i => (map_continuous f).ContinuousOn.integrableOnCompact (s i).IsCompact)
+      (fun i => (map_continuous f).ContinuousOn.integrableOn_compact (s i).IsCompact)
       (summable_of_nonneg_of_le (fun ι => integral_nonneg fun x => norm_nonneg _) (fun i => _) hf)
   rw [← (Real.norm_of_nonneg (integral_nonneg fun a => norm_nonneg _) : ‖_‖ = ∫ x in s i, ‖f x‖ ∂μ)]
   exact
     norm_set_integral_le_of_norm_le_const' (s i).IsCompact.measure_lt_top
       (s i).IsCompact.IsClosed.MeasurableSet fun x hx =>
       (norm_norm (f x)).symm ▸ (f.restrict ↑(s i)).norm_coe_le_norm ⟨x, hx⟩
-#align measure_theory.integrable_on_Union_of_summable_norm_restrict MeasureTheory.integrableOnUnionOfSummableNormRestrict
+#align measure_theory.integrable_on_Union_of_summable_norm_restrict MeasureTheory.integrableOn_unionᵢ_of_summable_norm_restrict
 
 /-- If `s` is a countable family of compact sets covering `α`, `f` is a continuous function, and
 the sequence `‖f.restrict (s i)‖ * μ (s i)` is summable, then `f` is integrable. -/
-theorem integrableOfSummableNormRestrict {f : C(α, E)} {s : β → Compacts α}
+theorem integrable_of_summable_norm_restrict {f : C(α, E)} {s : β → Compacts α}
     (hf : Summable fun i : β => ‖f.restrict (s i)‖ * ENNReal.toReal (μ <| s i))
     (hs : (⋃ i : β, ↑(s i)) = (univ : Set α)) : Integrable f μ := by
   simpa only [hs, integrable_on_univ] using integrable_on_Union_of_summable_norm_restrict hf
-#align measure_theory.integrable_of_summable_norm_restrict MeasureTheory.integrableOfSummableNormRestrict
+#align measure_theory.integrable_of_summable_norm_restrict MeasureTheory.integrable_of_summable_norm_restrict
 
 end IntegrableUnion
 
@@ -1093,7 +1093,7 @@ theorem ContinuousAt.integral_sub_linear_isLittleO_ae [TopologicalSpace α] [Ope
     {li : Filter ι} (hs : Tendsto s li (𝓝 a).smallSets) (m : ι → ℝ := fun i => (μ (s i)).toReal)
     (hsμ : (fun i => (μ (s i)).toReal) =ᶠ[li] m := by rfl) :
     (fun i => (∫ x in s i, f x ∂μ) - m i • f a) =o[li] m :=
-  (ha.mono_left inf_le_left).integral_sub_linear_isLittleO_ae hfm (μ.finiteAtNhds a) hs m hsμ
+  (ha.mono_left inf_le_left).integral_sub_linear_isLittleO_ae hfm (μ.finite_at_nhds a) hs m hsμ
 #align continuous_at.integral_sub_linear_is_o_ae ContinuousAt.integral_sub_linear_isLittleO_ae
 
 /-- Fundamental theorem of calculus for set integrals, `nhds_within` version: if `μ` is a locally
@@ -1193,7 +1193,7 @@ theorem integral_comp_comm' (L : E →L[𝕜] F) {K} (hL : AntilipschitzWith K L
 
 theorem integral_comp_L1_comm (L : E →L[𝕜] F) (φ : α →₁[μ] E) :
     (∫ a, L (φ a) ∂μ) = L (∫ a, φ a ∂μ) :=
-  L.integral_comp_comm (L1.integrableCoeFn φ)
+  L.integral_comp_comm (L1.integrable_coeFn φ)
 #align continuous_linear_map.integral_comp_L1_comm ContinuousLinearMap.integral_comp_L1_comm
 
 end ContinuousLinearMap
@@ -1331,7 +1331,7 @@ theorem integral_withDensity_eq_integral_smul {f : α → ℝ≥0} (f_meas : Mea
     rw [lintegral_coe_eq_integral, ENNReal.toReal_ofReal, ← integral_smul_const]
     · rfl
     · exact integral_nonneg fun x => NNReal.coe_nonneg _
-    · refine' ⟨f_meas.coe_nnreal_real.AeMeasurable.AeStronglyMeasurable, _⟩
+    · refine' ⟨f_meas.coe_nnreal_real.AEMeasurable.AeStronglyMeasurable, _⟩
       rw [with_density_apply _ s_meas] at hs
       rw [has_finite_integral]
       convert hs
@@ -1367,7 +1367,7 @@ theorem integral_withDensity_eq_integral_smul {f : α → ℝ≥0} (f_meas : Mea
       simpa only [Ne.def, ENNReal.coe_eq_zero] using h'x
 #align integral_with_density_eq_integral_smul integral_withDensity_eq_integral_smul
 
-theorem integral_withDensity_eq_integral_smul₀ {f : α → ℝ≥0} (hf : AeMeasurable f μ) (g : α → E) :
+theorem integral_withDensity_eq_integral_smul₀ {f : α → ℝ≥0} (hf : AEMeasurable f μ) (g : α → E) :
     (∫ a, g a ∂μ.withDensity fun x => f x) = ∫ a, f a • g a ∂μ :=
   by
   let f' := hf.mk _
@@ -1393,7 +1393,7 @@ theorem set_integral_withDensity_eq_set_integral_smul {f : α → ℝ≥0} (f_me
 #align set_integral_with_density_eq_set_integral_smul set_integral_withDensity_eq_set_integral_smul
 
 theorem set_integral_withDensity_eq_set_integral_smul₀ {f : α → ℝ≥0} {s : Set α}
-    (hf : AeMeasurable f (μ.restrict s)) (g : α → E) (hs : MeasurableSet s) :
+    (hf : AEMeasurable f (μ.restrict s)) (g : α → E) (hs : MeasurableSet s) :
     (∫ a in s, g a ∂μ.withDensity fun x => f x) = ∫ a in s, f a • g a ∂μ := by
   rw [restrict_with_density hs, integral_withDensity_eq_integral_smul₀ hf]
 #align set_integral_with_density_eq_set_integral_smul₀ set_integral_withDensity_eq_set_integral_smul₀
@@ -1431,7 +1431,7 @@ namespace MeasureTheory
 
 variable {f : β → ℝ} {m m0 : MeasurableSpace β} {μ : Measure β}
 
-theorem Integrable.simpleFuncMul (g : SimpleFunc β ℝ) (hf : Integrable f μ) :
+theorem Integrable.simpleFunc_mul (g : SimpleFunc β ℝ) (hf : Integrable f μ) :
     Integrable (g * f) μ :=
   by
   refine'
@@ -1449,14 +1449,14 @@ theorem Integrable.simpleFuncMul (g : SimpleFunc β ℝ) (hf : Integrable f μ)
     · simp only [hx, Pi.mul_apply, Set.indicator_of_not_mem, not_false_iff, MulZeroClass.zero_mul]
   rw [this, integrable_indicator_iff hs]
   exact (hf.smul c).IntegrableOn
-#align measure_theory.integrable.simple_func_mul MeasureTheory.Integrable.simpleFuncMul
+#align measure_theory.integrable.simple_func_mul MeasureTheory.Integrable.simpleFunc_mul
 
-theorem Integrable.simpleFuncMul' (hm : m ≤ m0) (g : @SimpleFunc β m ℝ) (hf : Integrable f μ) :
+theorem Integrable.simpleFunc_mul' (hm : m ≤ m0) (g : @SimpleFunc β m ℝ) (hf : Integrable f μ) :
     Integrable (g * f) μ :=
   by
   rw [← simple_func.coe_to_larger_space_eq hm g]
   exact hf.simple_func_mul (g.to_larger_space hm)
-#align measure_theory.integrable.simple_func_mul' MeasureTheory.Integrable.simpleFuncMul'
+#align measure_theory.integrable.simple_func_mul' MeasureTheory.Integrable.simpleFunc_mul'
 
 end MeasureTheory
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/8b8ba04e2f326f3f7cf24ad129beda58531ada61

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Zhouhang Zhou, Yury Kudryashov
 
 ! This file was ported from Lean 3 source module measure_theory.integral.set_integral
-! leanprover-community/mathlib commit 08a4542bec7242a5c60f179e4e49de8c0d677b1b
+! leanprover-community/mathlib commit 8b8ba04e2f326f3f7cf24ad129beda58531ada61
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -647,26 +647,84 @@ theorem set_integral_trim {α} {m m0 : MeasurableSpace α} {μ : Measure α} (hm
   rwa [integral_trim hm hf_meas, restrict_trim hm μ]
 #align measure_theory.set_integral_trim MeasureTheory.set_integral_trim
 
-theorem integral_Icc_eq_integral_Ioc' [PartialOrder α] {f : α → E} {a b : α} (ha : μ {a} = 0) :
+/-! ### Lemmas about adding and removing interval boundaries
+
+The primed lemmas take explicit arguments about the endpoint having zero measure, while the
+unprimed ones use `[has_no_atoms μ]`.
+-/
+
+
+section PartialOrder
+
+variable [PartialOrder α] {a b : α}
+
+theorem integral_Icc_eq_integral_Ioc' (ha : μ {a} = 0) :
     (∫ t in Icc a b, f t ∂μ) = ∫ t in Ioc a b, f t ∂μ :=
   set_integral_congr_set_ae (Ioc_ae_eq_Icc' ha).symm
 #align measure_theory.integral_Icc_eq_integral_Ioc' MeasureTheory.integral_Icc_eq_integral_Ioc'
 
-theorem integral_Ioc_eq_integral_Ioo' [PartialOrder α] {f : α → E} {a b : α} (hb : μ {b} = 0) :
+theorem integral_Icc_eq_integral_Ico' (hb : μ {b} = 0) :
+    (∫ t in Icc a b, f t ∂μ) = ∫ t in Ico a b, f t ∂μ :=
+  set_integral_congr_set_ae (Ico_ae_eq_Icc' hb).symm
+#align measure_theory.integral_Icc_eq_integral_Ico' MeasureTheory.integral_Icc_eq_integral_Ico'
+
+theorem integral_Ioc_eq_integral_Ioo' (hb : μ {b} = 0) :
     (∫ t in Ioc a b, f t ∂μ) = ∫ t in Ioo a b, f t ∂μ :=
   set_integral_congr_set_ae (Ioo_ae_eq_Ioc' hb).symm
 #align measure_theory.integral_Ioc_eq_integral_Ioo' MeasureTheory.integral_Ioc_eq_integral_Ioo'
 
-theorem integral_Icc_eq_integral_Ioc [PartialOrder α] {f : α → E} {a b : α} [HasNoAtoms μ] :
-    (∫ t in Icc a b, f t ∂μ) = ∫ t in Ioc a b, f t ∂μ :=
+theorem integral_Ico_eq_integral_Ioo' (ha : μ {a} = 0) :
+    (∫ t in Ico a b, f t ∂μ) = ∫ t in Ioo a b, f t ∂μ :=
+  set_integral_congr_set_ae (Ioo_ae_eq_Ico' ha).symm
+#align measure_theory.integral_Ico_eq_integral_Ioo' MeasureTheory.integral_Ico_eq_integral_Ioo'
+
+theorem integral_Icc_eq_integral_Ioo' (ha : μ {a} = 0) (hb : μ {b} = 0) :
+    (∫ t in Icc a b, f t ∂μ) = ∫ t in Ioo a b, f t ∂μ :=
+  set_integral_congr_set_ae (Ioo_ae_eq_Icc' ha hb).symm
+#align measure_theory.integral_Icc_eq_integral_Ioo' MeasureTheory.integral_Icc_eq_integral_Ioo'
+
+theorem integral_Iic_eq_integral_Iio' (ha : μ {a} = 0) :
+    (∫ t in Iic a, f t ∂μ) = ∫ t in Iio a, f t ∂μ :=
+  set_integral_congr_set_ae (Iio_ae_eq_Iic' ha).symm
+#align measure_theory.integral_Iic_eq_integral_Iio' MeasureTheory.integral_Iic_eq_integral_Iio'
+
+theorem integral_Ici_eq_integral_Ioi' (ha : μ {a} = 0) :
+    (∫ t in Ici a, f t ∂μ) = ∫ t in Ioi a, f t ∂μ :=
+  set_integral_congr_set_ae (Ioi_ae_eq_Ici' ha).symm
+#align measure_theory.integral_Ici_eq_integral_Ioi' MeasureTheory.integral_Ici_eq_integral_Ioi'
+
+variable [HasNoAtoms μ]
+
+theorem integral_Icc_eq_integral_Ioc : (∫ t in Icc a b, f t ∂μ) = ∫ t in Ioc a b, f t ∂μ :=
   integral_Icc_eq_integral_Ioc' <| measure_singleton a
 #align measure_theory.integral_Icc_eq_integral_Ioc MeasureTheory.integral_Icc_eq_integral_Ioc
 
-theorem integral_Ioc_eq_integral_Ioo [PartialOrder α] {f : α → E} {a b : α} [HasNoAtoms μ] :
-    (∫ t in Ioc a b, f t ∂μ) = ∫ t in Ioo a b, f t ∂μ :=
+theorem integral_Icc_eq_integral_Ico : (∫ t in Icc a b, f t ∂μ) = ∫ t in Ico a b, f t ∂μ :=
+  integral_Icc_eq_integral_Ico' <| measure_singleton b
+#align measure_theory.integral_Icc_eq_integral_Ico MeasureTheory.integral_Icc_eq_integral_Ico
+
+theorem integral_Ioc_eq_integral_Ioo : (∫ t in Ioc a b, f t ∂μ) = ∫ t in Ioo a b, f t ∂μ :=
   integral_Ioc_eq_integral_Ioo' <| measure_singleton b
 #align measure_theory.integral_Ioc_eq_integral_Ioo MeasureTheory.integral_Ioc_eq_integral_Ioo
 
+theorem integral_Ico_eq_integral_Ioo : (∫ t in Ico a b, f t ∂μ) = ∫ t in Ioo a b, f t ∂μ :=
+  integral_Ico_eq_integral_Ioo' <| measure_singleton a
+#align measure_theory.integral_Ico_eq_integral_Ioo MeasureTheory.integral_Ico_eq_integral_Ioo
+
+theorem integral_Icc_eq_integral_Ioo : (∫ t in Icc a b, f t ∂μ) = ∫ t in Ico a b, f t ∂μ := by
+  rw [integral_Icc_eq_integral_Ico, integral_Ico_eq_integral_Ioo]
+#align measure_theory.integral_Icc_eq_integral_Ioo MeasureTheory.integral_Icc_eq_integral_Ioo
+
+theorem integral_Iic_eq_integral_Iio : (∫ t in Iic a, f t ∂μ) = ∫ t in Iio a, f t ∂μ :=
+  integral_Iic_eq_integral_Iio' <| measure_singleton a
+#align measure_theory.integral_Iic_eq_integral_Iio MeasureTheory.integral_Iic_eq_integral_Iio
+
+theorem integral_Ici_eq_integral_Ioi : (∫ t in Ici a, f t ∂μ) = ∫ t in Ioi a, f t ∂μ :=
+  integral_Ici_eq_integral_Ioi' <| measure_singleton a
+#align measure_theory.integral_Ici_eq_integral_Ioi MeasureTheory.integral_Ici_eq_integral_Ioi
+
+end PartialOrder
+
 end NormedAddCommGroup
 
 section Mono

mathlib commit https://github.com/leanprover-community/mathlib/commit/039ef89bef6e58b32b62898dd48e9d1a4312bb65

@@ -977,7 +977,7 @@ along `li`. Since `μ (s i)` is an `ℝ≥0∞` number, we use `(μ (s i)).to_re
 Often there is a good formula for `(μ (s i)).to_real`, so the formalization can take an optional
 argument `m` with this formula and a proof `of `(λ i, (μ (s i)).to_real) =ᶠ[li] m`. Without these
 arguments, `m i = (μ (s i)).to_real` is used in the output. -/
-theorem Filter.Tendsto.integral_sub_linear_isOCat_ae [NormedSpace ℝ E] [CompleteSpace E]
+theorem Filter.Tendsto.integral_sub_linear_isLittleO_ae [NormedSpace ℝ E] [CompleteSpace E]
     {μ : Measure α} {l : Filter α} [l.IsMeasurablyGenerated] {f : α → E} {b : E}
     (h : Tendsto f (l ⊓ μ.ae) (𝓝 b)) (hfm : StronglyMeasurableAtFilter f l μ)
     (hμ : μ.FiniteAtFilter l) {s : ι → Set α} {li : Filter ι} (hs : Tendsto s li l.smallSets)
@@ -997,7 +997,7 @@ theorem Filter.Tendsto.integral_sub_linear_isOCat_ae [NormedSpace ℝ E] [Comple
   rw [← set_integral_const, ← integral_sub h_integrable (integrable_on_const.2 <| Or.inr hμs),
     Real.norm_eq_abs, abs_of_nonneg ENNReal.toReal_nonneg]
   exact norm_set_integral_le_of_norm_le_const_ae' hμs h_norm (hfm.sub ae_strongly_measurable_const)
-#align filter.tendsto.integral_sub_linear_is_o_ae Filter.Tendsto.integral_sub_linear_isOCat_ae
+#align filter.tendsto.integral_sub_linear_is_o_ae Filter.Tendsto.integral_sub_linear_isLittleO_ae
 
 /-- Fundamental theorem of calculus for set integrals, `nhds_within` version: if `μ` is a locally
 finite measure and `f` is an almost everywhere measurable function that is continuous at a point `a`
@@ -1008,7 +1008,7 @@ number, we use `(μ (s i)).to_real` in the actual statement.
 Often there is a good formula for `(μ (s i)).to_real`, so the formalization can take an optional
 argument `m` with this formula and a proof `of `(λ i, (μ (s i)).to_real) =ᶠ[li] m`. Without these
 arguments, `m i = (μ (s i)).to_real` is used in the output. -/
-theorem ContinuousWithinAt.integral_sub_linear_isOCat_ae [TopologicalSpace α]
+theorem ContinuousWithinAt.integral_sub_linear_isLittleO_ae [TopologicalSpace α]
     [OpensMeasurableSpace α] [NormedSpace ℝ E] [CompleteSpace E] {μ : Measure α}
     [IsLocallyFiniteMeasure μ] {a : α} {t : Set α} {f : α → E} (ha : ContinuousWithinAt f t a)
     (ht : MeasurableSet t) (hfm : StronglyMeasurableAtFilter f (𝓝[t] a) μ) {s : ι → Set α}
@@ -1016,9 +1016,9 @@ theorem ContinuousWithinAt.integral_sub_linear_isOCat_ae [TopologicalSpace α]
     (hsμ : (fun i => (μ (s i)).toReal) =ᶠ[li] m := by rfl) :
     (fun i => (∫ x in s i, f x ∂μ) - m i • f a) =o[li] m :=
   haveI : (𝓝[t] a).IsMeasurablyGenerated := ht.nhds_within_is_measurably_generated _
-  (ha.mono_left inf_le_left).integral_sub_linear_isOCat_ae hfm (μ.finite_at_nhds_within a t) hs m
+  (ha.mono_left inf_le_left).integral_sub_linear_isLittleO_ae hfm (μ.finite_at_nhds_within a t) hs m
     hsμ
-#align continuous_within_at.integral_sub_linear_is_o_ae ContinuousWithinAt.integral_sub_linear_isOCat_ae
+#align continuous_within_at.integral_sub_linear_is_o_ae ContinuousWithinAt.integral_sub_linear_isLittleO_ae
 
 /-- Fundamental theorem of calculus for set integrals, `nhds` version: if `μ` is a locally finite
 measure and `f` is an almost everywhere measurable function that is continuous at a point `a`, then
@@ -1029,14 +1029,14 @@ the actual statement.
 Often there is a good formula for `(μ (s i)).to_real`, so the formalization can take an optional
 argument `m` with this formula and a proof `of `(λ i, (μ (s i)).to_real) =ᶠ[li] m`. Without these
 arguments, `m i = (μ (s i)).to_real` is used in the output. -/
-theorem ContinuousAt.integral_sub_linear_isOCat_ae [TopologicalSpace α] [OpensMeasurableSpace α]
+theorem ContinuousAt.integral_sub_linear_isLittleO_ae [TopologicalSpace α] [OpensMeasurableSpace α]
     [NormedSpace ℝ E] [CompleteSpace E] {μ : Measure α} [IsLocallyFiniteMeasure μ] {a : α}
     {f : α → E} (ha : ContinuousAt f a) (hfm : StronglyMeasurableAtFilter f (𝓝 a) μ) {s : ι → Set α}
     {li : Filter ι} (hs : Tendsto s li (𝓝 a).smallSets) (m : ι → ℝ := fun i => (μ (s i)).toReal)
     (hsμ : (fun i => (μ (s i)).toReal) =ᶠ[li] m := by rfl) :
     (fun i => (∫ x in s i, f x ∂μ) - m i • f a) =o[li] m :=
-  (ha.mono_left inf_le_left).integral_sub_linear_isOCat_ae hfm (μ.finiteAtNhds a) hs m hsμ
-#align continuous_at.integral_sub_linear_is_o_ae ContinuousAt.integral_sub_linear_isOCat_ae
+  (ha.mono_left inf_le_left).integral_sub_linear_isLittleO_ae hfm (μ.finiteAtNhds a) hs m hsμ
+#align continuous_at.integral_sub_linear_is_o_ae ContinuousAt.integral_sub_linear_isLittleO_ae
 
 /-- Fundamental theorem of calculus for set integrals, `nhds_within` version: if `μ` is a locally
 finite measure, `f` is continuous on a measurable set `t`, and `a ∈ t`, then `∫ x in (s i), f x ∂μ =
@@ -1046,16 +1046,16 @@ Since `μ (s i)` is an `ℝ≥0∞` number, we use `(μ (s i)).to_real` in the a
 Often there is a good formula for `(μ (s i)).to_real`, so the formalization can take an optional
 argument `m` with this formula and a proof `of `(λ i, (μ (s i)).to_real) =ᶠ[li] m`. Without these
 arguments, `m i = (μ (s i)).to_real` is used in the output. -/
-theorem ContinuousOn.integral_sub_linear_isOCat_ae [TopologicalSpace α] [OpensMeasurableSpace α]
+theorem ContinuousOn.integral_sub_linear_isLittleO_ae [TopologicalSpace α] [OpensMeasurableSpace α]
     [NormedSpace ℝ E] [CompleteSpace E] [SecondCountableTopologyEither α E] {μ : Measure α}
     [IsLocallyFiniteMeasure μ] {a : α} {t : Set α} {f : α → E} (hft : ContinuousOn f t) (ha : a ∈ t)
     (ht : MeasurableSet t) {s : ι → Set α} {li : Filter ι} (hs : Tendsto s li (𝓝[t] a).smallSets)
     (m : ι → ℝ := fun i => (μ (s i)).toReal)
     (hsμ : (fun i => (μ (s i)).toReal) =ᶠ[li] m := by rfl) :
     (fun i => (∫ x in s i, f x ∂μ) - m i • f a) =o[li] m :=
-  (hft a ha).integral_sub_linear_isOCat_ae ht ⟨t, self_mem_nhdsWithin, hft.AeStronglyMeasurable ht⟩
-    hs m hsμ
-#align continuous_on.integral_sub_linear_is_o_ae ContinuousOn.integral_sub_linear_isOCat_ae
+  (hft a ha).integral_sub_linear_isLittleO_ae ht
+    ⟨t, self_mem_nhdsWithin, hft.AeStronglyMeasurable ht⟩ hs m hsμ
+#align continuous_on.integral_sub_linear_is_o_ae ContinuousOn.integral_sub_linear_isLittleO_ae
 
 section
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/1a4df69ca1a9a0e5e26bfe12e2b92814216016d0

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Zhouhang Zhou, Yury Kudryashov
 
 ! This file was ported from Lean 3 source module measure_theory.integral.set_integral
-! leanprover-community/mathlib commit 46b633fd842bef9469441c0209906f6dddd2b4f5
+! leanprover-community/mathlib commit 08a4542bec7242a5c60f179e4e49de8c0d677b1b
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -321,7 +321,7 @@ theorem integral_union_eq_left_of_ae (ht_eq : ∀ᵐ x ∂μ.restrict t, f x = 0
   by
   have ht : integrable_on f t μ :=
     by
-    apply integrable_on.congr_fun' integrable_on_zero
+    apply integrable_on_zero.congr_fun_ae
     symm
     exact ht_eq
   by_cases H : integrable_on f (s ∪ t) μ
@@ -333,7 +333,8 @@ theorem integral_union_eq_left_of_ae (ht_eq : ∀ᵐ x ∂μ.restrict t, f x = 0
     (∫ x : α in s ∪ t, f x ∂μ) = ∫ x : α in s ∪ t, f' x ∂μ := integral_congr_ae H.1.ae_eq_mk
     _ = ∫ x in s, f' x ∂μ :=
       by
-      apply integral_union_eq_left_of_ae_aux _ H.1.stronglyMeasurable_mk (H.congr_fun' H.1.ae_eq_mk)
+      apply
+        integral_union_eq_left_of_ae_aux _ H.1.stronglyMeasurable_mk (H.congr_fun_ae H.1.ae_eq_mk)
       filter_upwards [ht_eq,
         ae_mono (measure.restrict_mono (subset_union_right s t) le_rfl) H.1.ae_eq_mk]with x hx h'x
       rw [← h'x, hx]

mathlib commit https://github.com/leanprover-community/mathlib/commit/55d771df074d0dd020139ee1cd4b95521422df9f

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Zhouhang Zhou, Yury Kudryashov
 
 ! This file was ported from Lean 3 source module measure_theory.integral.set_integral
-! leanprover-community/mathlib commit c78cad350eb321c81e1eacf68d14e3d3ba1e17f7
+! leanprover-community/mathlib commit 46b633fd842bef9469441c0209906f6dddd2b4f5
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -1229,7 +1229,11 @@ theorem integral_smul_const {𝕜 : Type _} [IsROrC 𝕜] [NormedSpace 𝕜 E] (
 
 section Inner
 
-variable {E' : Type _} [InnerProductSpace 𝕜 E'] [CompleteSpace E'] [NormedSpace ℝ E']
+variable {E' : Type _}
+
+variable [NormedAddCommGroup E'] [InnerProductSpace 𝕜 E']
+
+variable [CompleteSpace E'] [NormedSpace ℝ E']
 
 -- mathport name: «expr⟪ , ⟫»
 local notation "⟪" x ", " y "⟫" => @inner 𝕜 E' _ x y
@@ -1239,6 +1243,12 @@ theorem integral_inner {f : α → E'} (hf : Integrable f μ) (c : E') :
   ((innerSL 𝕜 c).restrictScalars ℝ).integral_comp_comm hf
 #align integral_inner integral_inner
 
+variable (𝕜)
+
+-- mathport name: inner_with_explicit
+-- variable binder update doesn't work for lemmas which refer to `𝕜` only via the notation
+local notation "⟪" x ", " y "⟫" => @inner 𝕜 E' _ x y
+
 theorem integral_eq_zero_of_forall_integral_inner_eq_zero (f : α → E') (hf : Integrable f μ)
     (hf_int : ∀ c : E', (∫ x, ⟪c, f x⟫ ∂μ) = 0) : (∫ x, f x ∂μ) = 0 :=
   by

mathlib commit https://github.com/leanprover-community/mathlib/commit/7ec294687917cbc5c73620b4414ae9b5dd9ae1b4

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Zhouhang Zhou, Yury Kudryashov
 
 ! This file was ported from Lean 3 source module measure_theory.integral.set_integral
-! leanprover-community/mathlib commit 733fa0048f88bd38678c283c8c1bb1445ac5e23b
+! leanprover-community/mathlib commit c78cad350eb321c81e1eacf68d14e3d3ba1e17f7
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -1236,7 +1236,7 @@ local notation "⟪" x ", " y "⟫" => @inner 𝕜 E' _ x y
 
 theorem integral_inner {f : α → E'} (hf : Integrable f μ) (c : E') :
     (∫ x, ⟪c, f x⟫ ∂μ) = ⟪c, ∫ x, f x ∂μ⟫ :=
-  ((@innerSL 𝕜 E' _ _ c).restrictScalars ℝ).integral_comp_comm hf
+  ((innerSL 𝕜 c).restrictScalars ℝ).integral_comp_comm hf
 #align integral_inner integral_inner
 
 theorem integral_eq_zero_of_forall_integral_inner_eq_zero (f : α → E') (hf : Integrable f μ)

mathlib commit https://github.com/leanprover-community/mathlib/commit/3180fab693e2cee3bff62675571264cb8778b212

@@ -1377,7 +1377,7 @@ theorem Integrable.simpleFuncMul (g : SimpleFunc β ℝ) (hf : Integrable f μ)
     ext1 x
     by_cases hx : x ∈ s
     · simp only [hx, Pi.mul_apply, Set.indicator_of_mem, Pi.smul_apply, Algebra.id.smul_eq_mul]
-    · simp only [hx, Pi.mul_apply, Set.indicator_of_not_mem, not_false_iff, zero_mul]
+    · simp only [hx, Pi.mul_apply, Set.indicator_of_not_mem, not_false_iff, MulZeroClass.zero_mul]
   rw [this, integrable_indicator_iff hs]
   exact (hf.smul c).IntegrableOn
 #align measure_theory.integrable.simple_func_mul MeasureTheory.Integrable.simpleFuncMul

mathlib commit https://github.com/leanprover-community/mathlib/commit/195fcd60ff2bfe392543bceb0ec2adcdb472db4c

@@ -1333,7 +1333,7 @@ end
 
 section thickenedIndicator
 
-variable [PseudoEmetricSpace α]
+variable [PseudoEMetricSpace α]
 
 theorem measure_le_lintegral_thickenedIndicatorAux (μ : Measure α) {E : Set α}
     (E_mble : MeasurableSet E) (δ : ℝ) : μ E ≤ ∫⁻ a, (thickenedIndicatorAux δ E a : ℝ≥0∞) ∂μ :=

mathlib commit https://github.com/leanprover-community/mathlib/commit/4c586d291f189eecb9d00581aeb3dd998ac34442

@@ -181,8 +181,8 @@ theorem integral_indicator (hs : MeasurableSet s) : (∫ x, indicator s f x ∂
     (∫ x, indicator s f x ∂μ) = (∫ x in s, indicator s f x ∂μ) + ∫ x in sᶜ, indicator s f x ∂μ :=
       (integral_add_compl hs (hfi.integrable_indicator hs)).symm
     _ = (∫ x in s, f x ∂μ) + ∫ x in sᶜ, 0 ∂μ :=
-      congr_arg₂ (· + ·) (integral_congr_ae (indicator_ae_eq_restrict hs))
-        (integral_congr_ae (indicator_ae_eq_restrict_compl hs))
+      (congr_arg₂ (· + ·) (integral_congr_ae (indicator_ae_eq_restrict hs))
+        (integral_congr_ae (indicator_ae_eq_restrict_compl hs)))
     _ = ∫ x in s, f x ∂μ := by simp
     
 #align measure_theory.integral_indicator MeasureTheory.integral_indicator
@@ -518,7 +518,7 @@ theorem integral_indicatorConstLp {p : ℝ≥0∞} (ht : MeasurableSet t) (hμt
   calc
     (∫ a, indicatorConstLp p ht hμt x a ∂μ) = ∫ a in univ, indicatorConstLp p ht hμt x a ∂μ := by
       rw [integral_univ]
-    _ = (μ (t ∩ univ)).toReal • x := set_integral_indicatorConstLp MeasurableSet.univ ht hμt x
+    _ = (μ (t ∩ univ)).toReal • x := (set_integral_indicatorConstLp MeasurableSet.univ ht hμt x)
     _ = (μ t).toReal • x := by rw [inter_univ]
     
 #align measure_theory.integral_indicator_const_Lp MeasureTheory.integral_indicatorConstLp
@@ -839,7 +839,7 @@ section TendstoMono
 variable {μ : Measure α} [NormedAddCommGroup E] [CompleteSpace E] [NormedSpace ℝ E] {s : ℕ → Set α}
   {f : α → E}
 
-/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:75:38: in filter_upwards #[[], ["with", ident a], ["using", expr le_trans (h_anti.tendsto_indicator _ _ _) (pure_le_nhds _)]]: ./././Mathport/Syntax/Translate/Basic.lean:349:22: unsupported: parse error @ arg 0: next failed, no more args -/
+/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:72:38: in filter_upwards #[[], ["with", ident a], ["using", expr le_trans (h_anti.tendsto_indicator _ _ _) (pure_le_nhds _)]]: ./././Mathport/Syntax/Translate/Basic.lean:349:22: unsupported: parse error @ arg 0: next failed, no more args -/
 theorem Antitone.tendsto_set_integral (hsm : ∀ i, MeasurableSet (s i)) (h_anti : Antitone s)
     (hfi : IntegrableOn f (s 0) μ) :
     Tendsto (fun i => ∫ a in s i, f a ∂μ) atTop (𝓝 (∫ a in ⋂ n, s n, f a ∂μ)) :=
@@ -860,7 +860,7 @@ theorem Antitone.tendsto_set_integral (hsm : ∀ i, MeasurableSet (s i)) (h_anti
     exact indicator_le_indicator_of_subset (h_anti (zero_le n)) (fun a => norm_nonneg _) _
   ·
     trace
-      "./././Mathport/Syntax/Translate/Tactic/Builtin.lean:75:38: in filter_upwards #[[], [\"with\", ident a], [\"using\", expr le_trans (h_anti.tendsto_indicator _ _ _) (pure_le_nhds _)]]: ./././Mathport/Syntax/Translate/Basic.lean:349:22: unsupported: parse error @ arg 0: next failed, no more args"
+      "./././Mathport/Syntax/Translate/Tactic/Builtin.lean:72:38: in filter_upwards #[[], [\"with\", ident a], [\"using\", expr le_trans (h_anti.tendsto_indicator _ _ _) (pure_le_nhds _)]]: ./././Mathport/Syntax/Translate/Basic.lean:349:22: unsupported: parse error @ arg 0: next failed, no more args"
 #align antitone.tendsto_set_integral Antitone.tendsto_set_integral
 
 end TendstoMono
@@ -1309,7 +1309,7 @@ theorem integral_withDensity_eq_integral_smul₀ {f : α → ℝ≥0} (hf : AeMe
       apply with_density_congr_ae
       filter_upwards [hf.ae_eq_mk]with x hx
       rw [hx]
-    _ = ∫ a, f' a • g a ∂μ := integral_withDensity_eq_integral_smul hf.measurable_mk _
+    _ = ∫ a, f' a • g a ∂μ := (integral_withDensity_eq_integral_smul hf.measurable_mk _)
     _ = ∫ a, f a • g a ∂μ := by
       apply integral_congr_ae
       filter_upwards [hf.ae_eq_mk]with x hx

mathlib commit https://github.com/leanprover-community/mathlib/commit/eb0cb4511aaef0da2462207b67358a0e1fe1e2ee

@@ -58,7 +58,7 @@ noncomputable section
 
 open Set Filter TopologicalSpace MeasureTheory Function
 
-open Classical Topology Interval BigOperators Filter Ennreal NNReal MeasureTheory
+open Classical Topology Interval BigOperators Filter ENNReal NNReal MeasureTheory
 
 variable {α β E F : Type _} [MeasurableSpace α]
 
@@ -193,20 +193,20 @@ theorem set_integral_indicator (ht : MeasurableSet t) :
 #align measure_theory.set_integral_indicator MeasureTheory.set_integral_indicator
 
 theorem ofReal_set_integral_one_of_measure_ne_top {α : Type _} {m : MeasurableSpace α}
-    {μ : Measure α} {s : Set α} (hs : μ s ≠ ∞) : Ennreal.ofReal (∫ x in s, (1 : ℝ) ∂μ) = μ s :=
+    {μ : Measure α} {s : Set α} (hs : μ s ≠ ∞) : ENNReal.ofReal (∫ x in s, (1 : ℝ) ∂μ) = μ s :=
   calc
-    Ennreal.ofReal (∫ x in s, (1 : ℝ) ∂μ) = Ennreal.ofReal (∫ x in s, ‖(1 : ℝ)‖ ∂μ) := by
+    ENNReal.ofReal (∫ x in s, (1 : ℝ) ∂μ) = ENNReal.ofReal (∫ x in s, ‖(1 : ℝ)‖ ∂μ) := by
       simp only [norm_one]
     _ = ∫⁻ x in s, 1 ∂μ :=
       by
       rw [of_real_integral_norm_eq_lintegral_nnnorm (integrable_on_const.2 (Or.inr hs.lt_top))]
-      simp only [nnnorm_one, Ennreal.coe_one]
+      simp only [nnnorm_one, ENNReal.coe_one]
     _ = μ s := set_lintegral_one _
     
 #align measure_theory.of_real_set_integral_one_of_measure_ne_top MeasureTheory.ofReal_set_integral_one_of_measure_ne_top
 
 theorem ofReal_set_integral_one {α : Type _} {m : MeasurableSpace α} (μ : Measure α)
-    [IsFiniteMeasure μ] (s : Set α) : Ennreal.ofReal (∫ x in s, (1 : ℝ) ∂μ) = μ s :=
+    [IsFiniteMeasure μ] (s : Set α) : ENNReal.ofReal (∫ x in s, (1 : ℝ) ∂μ) = μ s :=
   ofReal_set_integral_one_of_measure_ne_top (measure_ne_top μ s)
 #align measure_theory.of_real_set_integral_one MeasureTheory.ofReal_set_integral_one
 
@@ -232,14 +232,14 @@ theorem tendsto_set_integral_of_monotone {ι : Type _} [Countable ι] [Semilatti
   refine' metric.nhds_basis_closed_ball.tendsto_right_iff.2 fun ε ε0 => _
   lift ε to ℝ≥0 using ε0.le
   have : ∀ᶠ i in at_top, ν (s i) ∈ Icc (ν S - ε) (ν S + ε) :=
-    tendsto_measure_Union h_mono (Ennreal.Icc_mem_nhds hfi'.ne (Ennreal.coe_pos.2 ε0).ne')
+    tendsto_measure_Union h_mono (ENNReal.Icc_mem_nhds hfi'.ne (ENNReal.coe_pos.2 ε0).ne')
   refine' this.mono fun i hi => _
   rw [mem_closedBall_iff_norm', ← integral_diff (hsm i) hfi hsub, ← coe_nnnorm, NNReal.coe_le_coe, ←
-    Ennreal.coe_le_coe]
+    ENNReal.coe_le_coe]
   refine' (ennnorm_integral_le_lintegral_ennnorm _).trans _
   rw [← with_density_apply _ (hSm.diff (hsm _)), ← hν, measure_diff hsub (hsm _)]
   exacts[tsub_le_iff_tsub_le.mp hi.1,
-    (hi.2.trans_lt <| Ennreal.add_lt_top.2 ⟨hfi', Ennreal.coe_lt_top⟩).Ne]
+    (hi.2.trans_lt <| ENNReal.add_lt_top.2 ⟨hfi', ENNReal.coe_lt_top⟩).Ne]
 #align measure_theory.tendsto_set_integral_of_monotone MeasureTheory.tendsto_set_integral_of_monotone
 
 theorem hasSum_integral_unionᵢ_ae {ι : Type _} [Countable ι] {s : ι → Set α}
@@ -622,10 +622,10 @@ theorem set_integral_gt_gt {R : ℝ} {f : α → ℝ} (hR : 0 ≤ R) (hfm : Meas
     by
     refine' ⟨ae_strongly_measurable_const, lt_of_le_of_lt _ hfint.2⟩
     refine'
-      set_lintegral_mono (Measurable.nnnorm _).coe_nNReal_ennreal hfm.nnnorm.coe_nnreal_ennreal
+      set_lintegral_mono (Measurable.nnnorm _).coe_nNReal_eNNReal hfm.nnnorm.coe_nnreal_ennreal
         fun x hx => _
     · exact measurable_const
-    · simp only [Ennreal.coe_le_coe, Real.nnnorm_of_nonneg hR,
+    · simp only [ENNReal.coe_le_coe, Real.nnnorm_of_nonneg hR,
         Real.nnnorm_of_nonneg (hR.trans <| le_of_lt hx), Subtype.mk_le_mk]
       exact le_of_lt hx
   rw [← sub_pos, ← smul_eq_mul, ← set_integral_const, ← integral_sub hfint this,
@@ -800,9 +800,9 @@ theorem integrableOnUnionOfSummableIntegralNorm {f : α → E} {s : β → Set 
     by
     rw [← NNReal.summable_coe]
     exact h
-  have S'' := Ennreal.tsum_coe_eq S'.has_sum
-  simp_rw [Ennreal.coe_nNReal_eq, NNReal.coe_mk, coe_nnnorm] at S''
-  convert Ennreal.ofReal_lt_top
+  have S'' := ENNReal.tsum_coe_eq S'.has_sum
+  simp_rw [ENNReal.coe_nnreal_eq, NNReal.coe_mk, coe_nnnorm] at S''
+  convert ENNReal.ofReal_lt_top
 #align measure_theory.integrable_on_Union_of_summable_integral_norm MeasureTheory.integrableOnUnionOfSummableIntegralNorm
 
 variable [TopologicalSpace α] [BorelSpace α] [MetrizableSpace α] [IsLocallyFiniteMeasure μ]
@@ -810,7 +810,7 @@ variable [TopologicalSpace α] [BorelSpace α] [MetrizableSpace α] [IsLocallyFi
 /-- If `s` is a countable family of compact sets, `f` is a continuous function, and the sequence
 `‖f.restrict (s i)‖ * μ (s i)` is summable, then `f` is integrable on the union of the `s i`. -/
 theorem integrableOnUnionOfSummableNormRestrict {f : C(α, E)} {s : β → Compacts α}
-    (hf : Summable fun i : β => ‖f.restrict (s i)‖ * Ennreal.toReal (μ <| s i)) :
+    (hf : Summable fun i : β => ‖f.restrict (s i)‖ * ENNReal.toReal (μ <| s i)) :
     IntegrableOn f (⋃ i : β, s i) μ :=
   by
   refine'
@@ -827,7 +827,7 @@ theorem integrableOnUnionOfSummableNormRestrict {f : C(α, E)} {s : β → Compa
 /-- If `s` is a countable family of compact sets covering `α`, `f` is a continuous function, and
 the sequence `‖f.restrict (s i)‖ * μ (s i)` is summable, then `f` is integrable. -/
 theorem integrableOfSummableNormRestrict {f : C(α, E)} {s : β → Compacts α}
-    (hf : Summable fun i : β => ‖f.restrict (s i)‖ * Ennreal.toReal (μ <| s i))
+    (hf : Summable fun i : β => ‖f.restrict (s i)‖ * ENNReal.toReal (μ <| s i))
     (hs : (⋃ i : β, ↑(s i)) = (univ : Set α)) : Integrable f μ := by
   simpa only [hs, integrable_on_univ] using integrable_on_Union_of_summable_norm_restrict hf
 #align measure_theory.integrable_of_summable_norm_restrict MeasureTheory.integrableOfSummableNormRestrict
@@ -912,7 +912,7 @@ theorem lp_toLp_restrict_smul (c : 𝕜) (f : lp F p μ) (s : Set α) :
 theorem norm_lp_toLp_restrict_le (s : Set α) (f : lp E p μ) :
     ‖((lp.memℒp f).restrict s).toLp f‖ ≤ ‖f‖ :=
   by
-  rw [Lp.norm_def, Lp.norm_def, Ennreal.toReal_le_toReal (Lp.snorm_ne_top _) (Lp.snorm_ne_top _)]
+  rw [Lp.norm_def, Lp.norm_def, ENNReal.toReal_le_toReal (Lp.snorm_ne_top _) (Lp.snorm_ne_top _)]
   refine' (le_of_eq _).trans (snorm_mono_measure _ measure.restrict_le_self)
   · exact s
   exact snorm_congr_ae (mem_ℒp.coe_fn_to_Lp _)
@@ -994,7 +994,7 @@ theorem Filter.Tendsto.integral_sub_linear_isOCat_ae [NormedSpace ℝ E] [Comple
   simp only [mem_closed_ball, dist_eq_norm]
   intro s hμs h_integrable hfm h_norm
   rw [← set_integral_const, ← integral_sub h_integrable (integrable_on_const.2 <| Or.inr hμs),
-    Real.norm_eq_abs, abs_of_nonneg Ennreal.toReal_nonneg]
+    Real.norm_eq_abs, abs_of_nonneg ENNReal.toReal_nonneg]
   exact norm_set_integral_le_of_norm_le_const_ae' hμs h_norm (hfm.sub ae_strongly_measurable_const)
 #align filter.tendsto.integral_sub_linear_is_o_ae Filter.Tendsto.integral_sub_linear_isOCat_ae
 
@@ -1071,7 +1071,7 @@ as `continuous_linear_map.comp_Lp`. We take advantage of this construction here.
 open ComplexConjugate
 
 variable {μ : Measure α} {𝕜 : Type _} [IsROrC 𝕜] [NormedSpace 𝕜 E] [NormedAddCommGroup F]
-  [NormedSpace 𝕜 F] {p : Ennreal}
+  [NormedSpace 𝕜 F] {p : ENNReal}
 
 namespace ContinuousLinearMap
 
@@ -1259,7 +1259,7 @@ theorem integral_withDensity_eq_integral_smul {f : α → ℝ≥0} (f_meas : Mea
     rw [integral_indicator s_meas]
     simp_rw [← indicator_smul_apply, integral_indicator s_meas]
     simp only [s_meas, integral_const, measure.restrict_apply', univ_inter, with_density_apply]
-    rw [lintegral_coe_eq_integral, Ennreal.toReal_ofReal, ← integral_smul_const]
+    rw [lintegral_coe_eq_integral, ENNReal.toReal_ofReal, ← integral_smul_const]
     · rfl
     · exact integral_nonneg fun x => NNReal.coe_nonneg _
     · refine' ⟨f_meas.coe_nnreal_real.AeMeasurable.AeStronglyMeasurable, _⟩
@@ -1295,7 +1295,7 @@ theorem integral_withDensity_eq_integral_smul {f : α → ℝ≥0} (f_meas : Mea
     rcases eq_or_ne (f x) 0 with (h'x | h'x)
     · simp only [h'x, zero_smul]
     · rw [hx _]
-      simpa only [Ne.def, Ennreal.coe_eq_zero] using h'x
+      simpa only [Ne.def, ENNReal.coe_eq_zero] using h'x
 #align integral_with_density_eq_integral_smul integral_withDensity_eq_integral_smul
 
 theorem integral_withDensity_eq_integral_smul₀ {f : α → ℝ≥0} (hf : AeMeasurable f μ) (g : α → E) :
@@ -1351,7 +1351,7 @@ theorem measure_le_lintegral_thickenedIndicator (μ : Measure α) {E : Set α}
   by
   convert measure_le_lintegral_thickenedIndicatorAux μ E_mble δ
   dsimp
-  simp only [thickened_indicator_aux_lt_top.ne, Ennreal.coe_toNnreal, Ne.def, not_false_iff]
+  simp only [thickened_indicator_aux_lt_top.ne, ENNReal.coe_toNNReal, Ne.def, not_false_iff]
 #align measure_le_lintegral_thickened_indicator measure_le_lintegral_thickenedIndicator
 
 end thickenedIndicator

mathlib commit https://github.com/leanprover-community/mathlib/commit/271bf175e6c51b8d31d6c0107b7bb4a967c7277e

@@ -4,14 +4,16 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Zhouhang Zhou, Yury Kudryashov
 
 ! This file was ported from Lean 3 source module measure_theory.integral.set_integral
-! leanprover-community/mathlib commit e7286cac412124bcb9114d1403c43c8a0f644f09
+! leanprover-community/mathlib commit 733fa0048f88bd38678c283c8c1bb1445ac5e23b
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
 import Mathbin.MeasureTheory.Integral.IntegrableOn
 import Mathbin.MeasureTheory.Integral.Bochner
+import Mathbin.MeasureTheory.Function.LocallyIntegrable
 import Mathbin.Order.Filter.IndicatorFunction
 import Mathbin.Topology.MetricSpace.ThickenedIndicator
+import Mathbin.Topology.ContinuousFunction.Compact
 
 /-!
 # Set integral
@@ -782,11 +784,11 @@ end Nonneg
 
 section IntegrableUnion
 
-variable {μ : Measure α} [NormedAddCommGroup E] {f : α → E} [Countable β] {s : β → Set α}
+variable {μ : Measure α} [NormedAddCommGroup E] [Countable β]
 
-theorem integrableOnUnionOfSummableIntegralNorm (hs : ∀ b : β, MeasurableSet (s b))
-    (hi : ∀ b : β, IntegrableOn f (s b) μ) (h : Summable fun b : β => ∫ a : α in s b, ‖f a‖ ∂μ) :
-    IntegrableOn f (unionᵢ s) μ :=
+theorem integrableOnUnionOfSummableIntegralNorm {f : α → E} {s : β → Set α}
+    (hs : ∀ b : β, MeasurableSet (s b)) (hi : ∀ b : β, IntegrableOn f (s b) μ)
+    (h : Summable fun b : β => ∫ a : α in s b, ‖f a‖ ∂μ) : IntegrableOn f (unionᵢ s) μ :=
   by
   refine' ⟨ae_strongly_measurable.Union fun i => (hi i).1, (lintegral_Union_le _ _).trans_lt _⟩
   have B := fun b : β => lintegral_coe_eq_integral (fun a : α => ‖f a‖₊) (hi b).norm
@@ -803,6 +805,33 @@ theorem integrableOnUnionOfSummableIntegralNorm (hs : ∀ b : β, MeasurableSet
   convert Ennreal.ofReal_lt_top
 #align measure_theory.integrable_on_Union_of_summable_integral_norm MeasureTheory.integrableOnUnionOfSummableIntegralNorm
 
+variable [TopologicalSpace α] [BorelSpace α] [MetrizableSpace α] [IsLocallyFiniteMeasure μ]
+
+/-- If `s` is a countable family of compact sets, `f` is a continuous function, and the sequence
+`‖f.restrict (s i)‖ * μ (s i)` is summable, then `f` is integrable on the union of the `s i`. -/
+theorem integrableOnUnionOfSummableNormRestrict {f : C(α, E)} {s : β → Compacts α}
+    (hf : Summable fun i : β => ‖f.restrict (s i)‖ * Ennreal.toReal (μ <| s i)) :
+    IntegrableOn f (⋃ i : β, s i) μ :=
+  by
+  refine'
+    integrable_on_Union_of_summable_integral_norm (fun i => (s i).IsCompact.IsClosed.MeasurableSet)
+      (fun i => (map_continuous f).ContinuousOn.integrableOnCompact (s i).IsCompact)
+      (summable_of_nonneg_of_le (fun ι => integral_nonneg fun x => norm_nonneg _) (fun i => _) hf)
+  rw [← (Real.norm_of_nonneg (integral_nonneg fun a => norm_nonneg _) : ‖_‖ = ∫ x in s i, ‖f x‖ ∂μ)]
+  exact
+    norm_set_integral_le_of_norm_le_const' (s i).IsCompact.measure_lt_top
+      (s i).IsCompact.IsClosed.MeasurableSet fun x hx =>
+      (norm_norm (f x)).symm ▸ (f.restrict ↑(s i)).norm_coe_le_norm ⟨x, hx⟩
+#align measure_theory.integrable_on_Union_of_summable_norm_restrict MeasureTheory.integrableOnUnionOfSummableNormRestrict
+
+/-- If `s` is a countable family of compact sets covering `α`, `f` is a continuous function, and
+the sequence `‖f.restrict (s i)‖ * μ (s i)` is summable, then `f` is integrable. -/
+theorem integrableOfSummableNormRestrict {f : C(α, E)} {s : β → Compacts α}
+    (hf : Summable fun i : β => ‖f.restrict (s i)‖ * Ennreal.toReal (μ <| s i))
+    (hs : (⋃ i : β, ↑(s i)) = (univ : Set α)) : Integrable f μ := by
+  simpa only [hs, integrable_on_univ] using integrable_on_Union_of_summable_norm_restrict hf
+#align measure_theory.integrable_of_summable_norm_restrict MeasureTheory.integrableOfSummableNormRestrict
+
 end IntegrableUnion
 
 section TendstoMono

mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc

• Changed existing proofs of some lemmas to avoid code duplication. Took out some common lines in their proofs and turned them into a lemma.
• haarScalarFactor \mu \mu = 1

Co-authored-by: Hyeokjun Kwon <86776403+Jun2M@users.noreply.github.com> Co-authored-by: Moritz Firsching <moritz.firsching@gmail.com> Co-authored-by: Dagur Tómas Ásgeirsson <dagurtomas@gmail.com> Co-authored-by: Frédéric Marbach <66742248+frederic-marbach@users.noreply.github.com> Co-authored-by: Peter Nelson <71660771+apnelson1@users.noreply.github.com> Co-authored-by: Kim Morrison <scott@tqft.net> Co-authored-by: Rémy Degenne <Remydegenne@gmail.com> Co-authored-by: Noam Atar <atarnoam@gmail.com> Co-authored-by: David Loeffler <d.loeffler.01@cantab.net> Co-authored-by: Andrew Yang <the.erd.one@gmail.com> Co-authored-by: Christopher Hoskin <christopher.hoskin@gmail.com> Co-authored-by: Christian Merten <christian@merten.dev> Co-authored-by: grunweg <rothgami@math.hu-berlin.de> Co-authored-by: Yury G. Kudryashov <urkud@urkud.name> Co-authored-by: damiano <adomani@gmail.com> Co-authored-by: Ruben Van de Velde <scott.morrison@gmail.com> Co-authored-by: Yaël Dillies <yael.dillies@gmail.com> Co-authored-by: María Inés de Frutos-Fernández <mariaines.dff@gmail.com> Co-authored-by: Jireh Loreaux <loreaujy@gmail.com> Co-authored-by: Johan Commelin <johan@commelin.net> Co-authored-by: Mitchell Lee <trivial171@gmail.com> Co-authored-by: sgouezel <sebastien.gouezel@univ-rennes1.fr> Co-authored-by: Thomas Browning <tb65536@uw.edu> Co-authored-by: Ruben Van de Velde <65514131+Ruben-VandeVelde@users.noreply.github.com>

@@ -970,6 +970,20 @@ end ContinuousSetIntegral
 
 end MeasureTheory
 
+section OpenPos
+
+open Measure
+
+variable [TopologicalSpace X] [OpensMeasurableSpace X] {μ : Measure X} [IsOpenPosMeasure μ]
+
+theorem Continuous.integral_pos_of_hasCompactSupport_nonneg_nonzero [IsFiniteMeasureOnCompacts μ]
+    {f : X → ℝ} {x : X} (f_cont : Continuous f) (f_comp : HasCompactSupport f) (f_nonneg : 0 ≤ f)
+    (f_x : f x ≠ 0) : 0 < ∫ x, f x ∂μ :=
+  integral_pos_of_integrable_nonneg_nonzero f_cont (f_cont.integrable_of_hasCompactSupport f_comp)
+    f_nonneg f_x
+
+end OpenPos
+
 /-! Fundamental theorem of calculus for set integrals -/
 section FTC
 

Co-authored-by: Moritz Firsching <firsching@google.com>

@@ -495,7 +495,7 @@ theorem integral_indicatorConstLp [CompleteSpace E]
   calc
     ∫ x, indicatorConstLp p ht hμt e x ∂μ = ∫ x in univ, indicatorConstLp p ht hμt e x ∂μ := by
       rw [integral_univ]
-    _ = (μ (t ∩ univ)).toReal • e := (set_integral_indicatorConstLp MeasurableSet.univ ht hμt e)
+    _ = (μ (t ∩ univ)).toReal • e := set_integral_indicatorConstLp MeasurableSet.univ ht hμt e
     _ = (μ t).toReal • e := by rw [inter_univ]
 set_option linter.uppercaseLean3 false in
 #align measure_theory.integral_indicator_const_Lp MeasureTheory.integral_indicatorConstLp
@@ -1334,7 +1334,7 @@ theorem integral_withDensity_eq_integral_smul₀ {f : X → ℝ≥0} (hf : AEMea
       apply withDensity_congr_ae
       filter_upwards [hf.ae_eq_mk] with x hx
       rw [hx]
-    _ = ∫ x, f' x • g x ∂μ := (integral_withDensity_eq_integral_smul hf.measurable_mk _)
+    _ = ∫ x, f' x • g x ∂μ := integral_withDensity_eq_integral_smul hf.measurable_mk _
     _ = ∫ x, f x • g x ∂μ := by
       apply integral_congr_ae
       filter_upwards [hf.ae_eq_mk] with x hx

We already have that ∫ (x : ℝ), u x * v' x = b' - a' - ∫ (x : ℝ), u' x * v x if u * v tends to a' and b' at minus infinity and infinity. Assuming morevoer that u * v is integrable, we show that it tends to 0 at minus infinity and infinity, and therefore that ∫ (x : ℝ), u x * v' x = - ∫ (x : ℝ), u' x * v x. We also give versions with a general bilinear form instead of multiplication.

@@ -222,7 +222,7 @@ theorem tendsto_set_integral_of_monotone {ι : Type*} [Countable ι] [Semilattic
   lift ε to ℝ≥0 using ε0.le
   have : ∀ᶠ i in atTop, ν (s i) ∈ Icc (ν S - ε) (ν S + ε) :=
     tendsto_measure_iUnion h_mono (ENNReal.Icc_mem_nhds hfi'.ne (ENNReal.coe_pos.2 ε0).ne')
-  refine' this.mono fun i hi => _
+  filter_upwards [this] with i hi
   rw [mem_closedBall_iff_norm', ← integral_diff (hsm i) hfi hsub, ← coe_nnnorm, NNReal.coe_le_coe, ←
     ENNReal.coe_le_coe]
   refine' (ennnorm_integral_le_lintegral_ennnorm _).trans _
@@ -231,6 +231,30 @@ theorem tendsto_set_integral_of_monotone {ι : Type*} [Countable ι] [Semilattic
     (hi.2.trans_lt <| ENNReal.add_lt_top.2 ⟨hfi', ENNReal.coe_lt_top⟩).ne]
 #align measure_theory.tendsto_set_integral_of_monotone MeasureTheory.tendsto_set_integral_of_monotone
 
+theorem tendsto_set_integral_of_antitone {ι : Type*} [Countable ι] [SemilatticeSup ι]
+    {s : ι → Set X} (hsm : ∀ i, MeasurableSet (s i)) (h_anti : Antitone s)
+    (hfi : ∃ i, IntegrableOn f (s i) μ) :
+    Tendsto (fun i ↦ ∫ x in s i, f x ∂μ) atTop (𝓝 (∫ x in ⋂ n, s n, f x ∂μ)) := by
+  set S := ⋂ i, s i
+  have hSm : MeasurableSet S := MeasurableSet.iInter hsm
+  have hsub i : S ⊆ s i := iInter_subset _ _
+  set ν := μ.withDensity fun x => ‖f x‖₊ with hν
+  refine' Metric.nhds_basis_closedBall.tendsto_right_iff.2 fun ε ε0 => _
+  lift ε to ℝ≥0 using ε0.le
+  rcases hfi with ⟨i₀, hi₀⟩
+  have νi₀ : ν (s i₀) ≠ ∞ := by
+    simpa [hsm i₀, ν, ENNReal.ofReal, norm_toNNReal] using hi₀.norm.lintegral_lt_top.ne
+  have νS : ν S ≠ ∞ := ((measure_mono (hsub i₀)).trans_lt νi₀.lt_top).ne
+  have : ∀ᶠ i in atTop, ν (s i) ∈ Icc (ν S - ε) (ν S + ε) := by
+    apply tendsto_measure_iInter hsm h_anti ⟨i₀, νi₀⟩
+    apply ENNReal.Icc_mem_nhds νS (ENNReal.coe_pos.2 ε0).ne'
+  filter_upwards [this, Ici_mem_atTop i₀] with i hi h'i
+  rw [mem_closedBall_iff_norm, ← integral_diff hSm (hi₀.mono_set (h_anti h'i)) (hsub i),
+    ← coe_nnnorm, NNReal.coe_le_coe, ← ENNReal.coe_le_coe]
+  refine' (ennnorm_integral_le_lintegral_ennnorm _).trans _
+  rw [← withDensity_apply _ ((hsm _).diff hSm), ← hν, measure_diff (hsub i) hSm νS]
+  exact tsub_le_iff_left.2 hi.2
+
 theorem hasSum_integral_iUnion_ae {ι : Type*} [Countable ι] {s : ι → Set X}
     (hm : ∀ i, NullMeasurableSet (s i) μ) (hd : Pairwise (AEDisjoint μ on s))
     (hfi : IntegrableOn f (⋃ i, s i) μ) :

When computing the integral of a function taking values in a noncomplete space, we use the junk value 0. This means that several theorems about integrals hold without completeness assumptions for trivial reasons. We use this to drop several completeness assumptions here and there in mathlib. This involves one nontrivial mathematical fact, that E →L[𝕜] F is complete iff F is complete, for which we add the missing direction (from left to right) in this PR.

@@ -8,6 +8,7 @@ import Mathlib.MeasureTheory.Integral.Bochner
 import Mathlib.MeasureTheory.Function.LocallyIntegrable
 import Mathlib.Topology.MetricSpace.ThickenedIndicator
 import Mathlib.Topology.ContinuousFunction.Compact
+import Mathlib.Analysis.NormedSpace.HahnBanach.SeparatingDual
 
 #align_import measure_theory.integral.set_integral from "leanprover-community/mathlib"@"24e0c85412ff6adbeca08022c25ba4876eedf37a"
 
@@ -1083,9 +1084,9 @@ theorem continuous_integral_comp_L1 (L : E →L[𝕜] F) :
 set_option linter.uppercaseLean3 false in
 #align continuous_linear_map.continuous_integral_comp_L1 ContinuousLinearMap.continuous_integral_comp_L1
 
-variable [CompleteSpace E] [CompleteSpace F] [NormedSpace ℝ E]
+variable [CompleteSpace F] [NormedSpace ℝ E]
 
-theorem integral_comp_comm (L : E →L[𝕜] F) {φ : X → E} (φ_int : Integrable φ μ) :
+theorem integral_comp_comm [CompleteSpace E] (L : E →L[𝕜] F) {φ : X → E} (φ_int : Integrable φ μ) :
     ∫ x, L (φ x) ∂μ = L (∫ x, φ x ∂μ) := by
   apply φ_int.induction (P := fun φ => ∫ x, L (φ x) ∂μ = L (∫ x, φ x ∂μ))
   · intro e s s_meas _
@@ -1105,10 +1106,32 @@ theorem integral_comp_comm (L : E →L[𝕜] F) {φ : X → E} (φ_int : Integra
 #align continuous_linear_map.integral_comp_comm ContinuousLinearMap.integral_comp_comm
 
 theorem integral_apply {H : Type*} [NormedAddCommGroup H] [NormedSpace 𝕜 H] {φ : X → H →L[𝕜] E}
-    (φ_int : Integrable φ μ) (v : H) : (∫ x, φ x ∂μ) v = ∫ x, φ x v ∂μ :=
-  ((ContinuousLinearMap.apply 𝕜 E v).integral_comp_comm φ_int).symm
+    (φ_int : Integrable φ μ) (v : H) : (∫ x, φ x ∂μ) v = ∫ x, φ x v ∂μ := by
+  by_cases hE : CompleteSpace E
+  · exact ((ContinuousLinearMap.apply 𝕜 E v).integral_comp_comm φ_int).symm
+  · rcases subsingleton_or_nontrivial H with hH|hH
+    · simp [Subsingleton.eq_zero v]
+    · have : ¬(CompleteSpace (H →L[𝕜] E)) := by
+        rwa [SeparatingDual.completeSpace_continuousLinearMap_iff]
+      simp [integral, hE, this]
 #align continuous_linear_map.integral_apply ContinuousLinearMap.integral_apply
 
+theorem _root_.ContinuousMultilinearMap.integral_apply {ι : Type*} [Fintype ι] {M : ι → Type*}
+    [∀ i, NormedAddCommGroup (M i)] [∀ i, NormedSpace 𝕜 (M i)]
+    {φ : X → ContinuousMultilinearMap 𝕜 M E} (φ_int : Integrable φ μ) (m : ∀ i, M i) :
+    (∫ x, φ x ∂μ) m = ∫ x, φ x m ∂μ := by
+  by_cases hE : CompleteSpace E
+  · exact ((ContinuousMultilinearMap.apply 𝕜 M E m).integral_comp_comm φ_int).symm
+  · by_cases hm : ∀ i, m i ≠ 0
+    · have : ¬ CompleteSpace (ContinuousMultilinearMap 𝕜 M E) := by
+        rwa [SeparatingDual.completeSpace_continuousMultilinearMap_iff _ _ hm]
+      simp [integral, hE, this]
+    · push_neg at hm
+      rcases hm with ⟨i, hi⟩
+      simp [ContinuousMultilinearMap.map_coord_zero _ i hi]
+
+variable [CompleteSpace E]
+
 theorem integral_comp_comm' (L : E →L[𝕜] F) {K} (hL : AntilipschitzWith K L) (φ : X → E) :
     ∫ x, L (φ x) ∂μ = L (∫ x, φ x ∂μ) := by
   by_cases h : Integrable φ μ

@@ -1275,7 +1275,7 @@ theorem integral_withDensity_eq_integral_smul {f : X → ℝ≥0} (f_meas : Meas
     rcases eq_or_ne (f x) 0 with (h'x | h'x)
     · simp only [h'x, zero_smul]
     · rw [hx _]
-      simpa only [Ne.def, ENNReal.coe_eq_zero] using h'x
+      simpa only [Ne, ENNReal.coe_eq_zero] using h'x
 #align integral_with_density_eq_integral_smul integral_withDensity_eq_integral_smul
 
 theorem integral_withDensity_eq_integral_smul₀ {f : X → ℝ≥0} (hf : AEMeasurable f μ) (g : X → E) :
@@ -1331,7 +1331,7 @@ theorem measure_le_lintegral_thickenedIndicator (μ : Measure X) {E : Set X}
     μ E ≤ ∫⁻ x, (thickenedIndicator δ_pos E x : ℝ≥0∞) ∂μ := by
   convert measure_le_lintegral_thickenedIndicatorAux μ E_mble δ
   dsimp
-  simp only [thickenedIndicatorAux_lt_top.ne, ENNReal.coe_toNNReal, Ne.def, not_false_iff]
+  simp only [thickenedIndicatorAux_lt_top.ne, ENNReal.coe_toNNReal, Ne, not_false_iff]
 #align measure_le_lintegral_thickened_indicator measure_le_lintegral_thickenedIndicator
 
 end thickenedIndicator

IsROrC contains data, which goes against the expectation that classes prefixed with Is are prop-valued. People have been complaining about this on and off, so this PR renames IsROrC to RCLike.

@@ -54,7 +54,7 @@ assert_not_exists InnerProductSpace
 
 noncomputable section
 
-open Set Filter TopologicalSpace MeasureTheory Function
+open Set Filter TopologicalSpace MeasureTheory Function RCLike
 
 open scoped Classical Topology BigOperators ENNReal NNReal
 
@@ -1058,7 +1058,7 @@ as `ContinuousLinearMap.compLp`. We take advantage of this construction here.
 
 open scoped ComplexConjugate
 
-variable {μ : Measure X} {𝕜 : Type*} [IsROrC 𝕜] [NormedAddCommGroup E] [NormedSpace 𝕜 E]
+variable {μ : Measure X} {𝕜 : Type*} [RCLike 𝕜] [NormedAddCommGroup E] [NormedSpace 𝕜 E]
   [NormedAddCommGroup F] [NormedSpace 𝕜 F] {p : ENNReal}
 
 namespace ContinuousLinearMap
@@ -1153,41 +1153,41 @@ end ContinuousLinearEquiv
 
 @[norm_cast]
 theorem integral_ofReal {f : X → ℝ} : ∫ x, (f x : 𝕜) ∂μ = ↑(∫ x, f x ∂μ) :=
-  (@IsROrC.ofRealLI 𝕜 _).integral_comp_comm f
+  (@RCLike.ofRealLI 𝕜 _).integral_comp_comm f
 #align integral_of_real integral_ofReal
 
 theorem integral_re {f : X → 𝕜} (hf : Integrable f μ) :
-    ∫ x, IsROrC.re (f x) ∂μ = IsROrC.re (∫ x, f x ∂μ) :=
-  (@IsROrC.reCLM 𝕜 _).integral_comp_comm hf
+    ∫ x, RCLike.re (f x) ∂μ = RCLike.re (∫ x, f x ∂μ) :=
+  (@RCLike.reCLM 𝕜 _).integral_comp_comm hf
 #align integral_re integral_re
 
 theorem integral_im {f : X → 𝕜} (hf : Integrable f μ) :
-    ∫ x, IsROrC.im (f x) ∂μ = IsROrC.im (∫ x, f x ∂μ) :=
-  (@IsROrC.imCLM 𝕜 _).integral_comp_comm hf
+    ∫ x, RCLike.im (f x) ∂μ = RCLike.im (∫ x, f x ∂μ) :=
+  (@RCLike.imCLM 𝕜 _).integral_comp_comm hf
 #align integral_im integral_im
 
 theorem integral_conj {f : X → 𝕜} : ∫ x, conj (f x) ∂μ = conj (∫ x, f x ∂μ) :=
-  (@IsROrC.conjLIE 𝕜 _).toLinearIsometry.integral_comp_comm f
+  (@RCLike.conjLIE 𝕜 _).toLinearIsometry.integral_comp_comm f
 #align integral_conj integral_conj
 
 theorem integral_coe_re_add_coe_im {f : X → 𝕜} (hf : Integrable f μ) :
-    ∫ x, (IsROrC.re (f x) : 𝕜) ∂μ + (∫ x, (IsROrC.im (f x) : 𝕜) ∂μ) * IsROrC.I = ∫ x, f x ∂μ := by
+    ∫ x, (re (f x) : 𝕜) ∂μ + (∫ x, (im (f x) : 𝕜) ∂μ) * RCLike.I = ∫ x, f x ∂μ := by
   rw [mul_comm, ← smul_eq_mul, ← integral_smul, ← integral_add]
   · congr
     ext1 x
-    rw [smul_eq_mul, mul_comm, IsROrC.re_add_im]
+    rw [smul_eq_mul, mul_comm, RCLike.re_add_im]
   · exact hf.re.ofReal
-  · exact hf.im.ofReal.smul (𝕜 := 𝕜) (β := 𝕜) IsROrC.I
+  · exact hf.im.ofReal.smul (𝕜 := 𝕜) (β := 𝕜) RCLike.I
 #align integral_coe_re_add_coe_im integral_coe_re_add_coe_im
 
 theorem integral_re_add_im {f : X → 𝕜} (hf : Integrable f μ) :
-    ((∫ x, IsROrC.re (f x) ∂μ : ℝ) : 𝕜) + (∫ x, IsROrC.im (f x) ∂μ : ℝ) * IsROrC.I =
+    ((∫ x, RCLike.re (f x) ∂μ : ℝ) : 𝕜) + (∫ x, RCLike.im (f x) ∂μ : ℝ) * RCLike.I =
       ∫ x, f x ∂μ := by
   rw [← integral_ofReal, ← integral_ofReal, integral_coe_re_add_coe_im hf]
 #align integral_re_add_im integral_re_add_im
 
 theorem set_integral_re_add_im {f : X → 𝕜} {i : Set X} (hf : IntegrableOn f i μ) :
-    ((∫ x in i, IsROrC.re (f x) ∂μ : ℝ) : 𝕜) + (∫ x in i, IsROrC.im (f x) ∂μ : ℝ) * IsROrC.I =
+    ((∫ x in i, RCLike.re (f x) ∂μ : ℝ) : 𝕜) + (∫ x in i, RCLike.im (f x) ∂μ : ℝ) * RCLike.I =
       ∫ x in i, f x ∂μ :=
   integral_re_add_im hf
 #align set_integral_re_add_im set_integral_re_add_im
@@ -1218,7 +1218,7 @@ theorem integral_pair [CompleteSpace E] [CompleteSpace F] {f : X → E} {g : X 
   Prod.ext (fst_integral this) (snd_integral this)
 #align integral_pair integral_pair
 
-theorem integral_smul_const {𝕜 : Type*} [IsROrC 𝕜] [NormedSpace 𝕜 E] [CompleteSpace E]
+theorem integral_smul_const {𝕜 : Type*} [RCLike 𝕜] [NormedSpace 𝕜 E] [CompleteSpace E]
     (f : X → 𝕜) (c : E) :
     ∫ x, f x • c ∂μ = (∫ x, f x ∂μ) • c := by
   by_cases hf : Integrable f μ

This is presumably not exhaustive, but covers about a hundred instances.

Style opinions (e.g., why a particular change is great/not a good idea) are very welcome; I'm still forming my own.

@@ -1455,7 +1455,7 @@ lemma continuousOn_integral_bilinear_of_locally_integrable_of_compact_support
   _ ≤ ∫ x in k, ‖L‖ * ‖g x‖ * δ ∂μ := by
       apply integral_mono_of_nonneg (eventually_of_forall (fun y ↦ by positivity))
       · exact (hg.norm.const_mul _).mul_const _
-      · apply eventually_of_forall (fun y ↦ ?_)
+      · filter_upwards with y
         by_cases hy : y ∈ k
         · dsimp only
           specialize hv p hp y hy

From the sphere eversion project.

In passing, we rename variables in one more lemma and use fun_prop in a tiny way.

@@ -1372,22 +1372,42 @@ end BilinearMap
 
 section ParametricIntegral
 
-variable {X Y F G 𝕜 : Type*} [TopologicalSpace X]
+variable {G 𝕜 : Type*} [TopologicalSpace X]
   [TopologicalSpace Y] [MeasurableSpace Y] [OpensMeasurableSpace Y] {μ : Measure Y}
   [NontriviallyNormedField 𝕜] [NormedAddCommGroup E] [NormedSpace ℝ E]
   [NormedAddCommGroup F] [NormedSpace 𝕜 F] [NormedAddCommGroup G] [NormedSpace 𝕜 G]
 
 open Metric ContinuousLinearMap
 
-/-- Consider a parameterized integral `a ↦ ∫ x, L (g x) (f a x)` where `L` is bilinear,
+/-- The parametric integral over a continuous function on a compact set is continuous,
+  under mild assumptions on the topologies involved. -/
+theorem continuous_parametric_integral_of_continuous
+    [FirstCountableTopology X] [LocallyCompactSpace X]
+    [OpensMeasurableSpace Y] [SecondCountableTopologyEither Y E] [IsLocallyFiniteMeasure μ]
+    {f : X → Y → E} (hf : Continuous f.uncurry) {s : Set Y} (hs : IsCompact s) :
+    Continuous (∫ y in s, f · y ∂μ) := by
+  rw [continuous_iff_continuousAt]
+  intro x₀
+  rcases exists_compact_mem_nhds x₀ with ⟨U, U_cpct, U_nhds⟩
+  rcases (U_cpct.prod hs).bddAbove_image hf.norm.continuousOn with ⟨M, hM⟩
+  apply continuousAt_of_dominated
+  · filter_upwards with x using Continuous.aestronglyMeasurable (by fun_prop)
+  · filter_upwards [U_nhds] with x x_in
+    rw [ae_restrict_iff]
+    · filter_upwards with t t_in using hM (mem_image_of_mem _ <| mk_mem_prod x_in t_in)
+    · exact (isClosed_le (by fun_prop) (by fun_prop)).measurableSet
+  · exact integrableOn_const.mpr (Or.inr hs.measure_lt_top)
+  · filter_upwards using (by fun_prop)
+
+/-- Consider a parameterized integral `x ↦ ∫ y, L (g y) (f x y)` where `L` is bilinear,
 `g` is locally integrable and `f` is continuous and uniformly compactly supported. Then the
-integral depends continuously on `a`. -/
+integral depends continuously on `x`. -/
 lemma continuousOn_integral_bilinear_of_locally_integrable_of_compact_support
     [NormedSpace 𝕜 E] (L : F →L[𝕜] G →L[𝕜] E)
     {f : X → Y → G} {s : Set X} {k : Set Y} {g : Y → F}
     (hk : IsCompact k) (hf : ContinuousOn f.uncurry (s ×ˢ univ))
     (hfs : ∀ p, ∀ x, p ∈ s → x ∉ k → f p x = 0) (hg : IntegrableOn g k μ) :
-    ContinuousOn (fun a ↦ ∫ x, L (g x) (f a x) ∂μ) s := by
+    ContinuousOn (fun x ↦ ∫ y, L (g y) (f x y) ∂μ) s := by
   have A : ∀ p ∈ s, Continuous (f p) := fun p hp ↦ by
     refine hf.comp_continuous (continuous_const.prod_mk continuous_id') fun y => ?_
     simpa only [prod_mk_mem_set_prod_eq, mem_univ, and_true] using hp
@@ -1403,7 +1423,7 @@ lemma continuousOn_integral_bilinear_of_locally_integrable_of_compact_support
     intro p hp
     obtain ⟨C, hC⟩ : ∃ C, ∀ y, ‖f p y‖ ≤ C := by
       have : ContinuousOn (f p) k := by
-        have : ContinuousOn (fun y ↦ (p, y)) k := (Continuous.Prod.mk p).continuousOn
+        have : ContinuousOn (fun y ↦ (p, y)) k := by fun_prop
         exact hf.comp this (by simp [MapsTo, hp])
       rcases IsCompact.exists_bound_of_continuousOn hk this with ⟨C, hC⟩
       refine ⟨max C 0, fun y ↦ ?_⟩
@@ -1448,13 +1468,13 @@ lemma continuousOn_integral_bilinear_of_locally_integrable_of_compact_support
           positivity
   _ < ε := hδ
 
-/-- Consider a parameterized integral `a ↦ ∫ x, f a x` where `f` is continuous and uniformly
-compactly supported. Then the integral depends continuously on `a`. -/
+/-- Consider a parameterized integral `x ↦ ∫ y, f x y` where `f` is continuous and uniformly
+compactly supported. Then the integral depends continuously on `x`. -/
 lemma continuousOn_integral_of_compact_support
     {f : X → Y → E} {s : Set X} {k : Set Y} [IsFiniteMeasureOnCompacts μ]
     (hk : IsCompact k) (hf : ContinuousOn f.uncurry (s ×ˢ univ))
     (hfs : ∀ p, ∀ x, p ∈ s → x ∉ k → f p x = 0) :
-    ContinuousOn (fun a ↦ ∫ x, f a x ∂μ) s := by
+    ContinuousOn (fun x ↦ ∫ y, f x y ∂μ) s := by
   simpa using continuousOn_integral_bilinear_of_locally_integrable_of_compact_support (lsmul ℝ ℝ)
     hk hf hfs (integrableOn_const.2 (Or.inr hk.measure_lt_top)) (μ := μ) (g := fun _ ↦ 1)
 

Rename measurable spaces \alpha and \beta to X and Y. Rename variables a : X and b : Y to x and y, respectively (and associated hypotheses as well).

@@ -26,7 +26,7 @@ directly. In this file we prove some theorems about dependence of `∫ x in s, f
 
 We use the property `IntegrableOn f s μ := Integrable f (μ.restrict s)`, defined in
 `MeasureTheory.IntegrableOn`. We also defined in that same file a predicate
-`IntegrableAtFilter (f : α → E) (l : Filter α) (μ : Measure α)` saying that `f` is integrable at
+`IntegrableAtFilter (f : X → E) (l : Filter X) (μ : Measure X)` saying that `f` is integrable at
 some set `s ∈ l`.
 
 Finally, we prove a version of the
@@ -41,8 +41,8 @@ theorem for a locally finite measure `μ` and a function `f` continuous at a poi
 ## Notation
 
 We provide the following notations for expressing the integral of a function on a set :
-* `∫ a in s, f a ∂μ` is `MeasureTheory.integral (μ.restrict s) f`
-* `∫ a in s, f a` is `∫ a in s, f a ∂volume`
+* `∫ x in s, f x ∂μ` is `MeasureTheory.integral (μ.restrict s) f`
+* `∫ x in s, f x` is `∫ x in s, f x ∂volume`
 
 Note that the set notations are defined in the file `Mathlib/MeasureTheory/Integral/Bochner.lean`,
 but we reference them here because all theorems about set integrals are in this file.
@@ -58,14 +58,14 @@ open Set Filter TopologicalSpace MeasureTheory Function
 
 open scoped Classical Topology BigOperators ENNReal NNReal
 
-variable {α β E F : Type*} [MeasurableSpace α]
+variable {X Y E F : Type*} [MeasurableSpace X]
 
 namespace MeasureTheory
 
 section NormedAddCommGroup
 
 variable [NormedAddCommGroup E] [NormedSpace ℝ E]
-  {f g : α → E} {s t : Set α} {μ ν : Measure α} {l l' : Filter α}
+  {f g : X → E} {s t : Set X} {μ ν : Measure X} {l l' : Filter X}
 
 theorem set_integral_congr_ae₀ (hs : NullMeasurableSet s μ) (h : ∀ᵐ x ∂μ, x ∈ s → f x = g x) :
     ∫ x in s, f x ∂μ = ∫ x in s, g x ∂μ :=
@@ -120,7 +120,7 @@ theorem integral_inter_add_diff (ht : MeasurableSet t) (hfs : IntegrableOn f s 
   integral_inter_add_diff₀ ht.nullMeasurableSet hfs
 #align measure_theory.integral_inter_add_diff MeasureTheory.integral_inter_add_diff
 
-theorem integral_finset_biUnion {ι : Type*} (t : Finset ι) {s : ι → Set α}
+theorem integral_finset_biUnion {ι : Type*} (t : Finset ι) {s : ι → Set X}
     (hs : ∀ i ∈ t, MeasurableSet (s i)) (h's : Set.Pairwise (↑t) (Disjoint on s))
     (hf : ∀ i ∈ t, IntegrableOn f (s i) μ) :
     ∫ x in ⋃ i ∈ t, s i, f x ∂μ = ∑ i in t, ∫ x in s i, f x ∂μ := by
@@ -135,7 +135,7 @@ theorem integral_finset_biUnion {ι : Type*} (t : Finset ι) {s : ι → Set α}
     · exact Finset.measurableSet_biUnion _ hs.2
 #align measure_theory.integral_finset_bUnion MeasureTheory.integral_finset_biUnion
 
-theorem integral_fintype_iUnion {ι : Type*} [Fintype ι] {s : ι → Set α}
+theorem integral_fintype_iUnion {ι : Type*} [Fintype ι] {s : ι → Set X}
     (hs : ∀ i, MeasurableSet (s i)) (h's : Pairwise (Disjoint on s))
     (hf : ∀ i, IntegrableOn f (s i) μ) : ∫ x in ⋃ i, s i, f x ∂μ = ∑ i, ∫ x in s i, f x ∂μ := by
   convert integral_finset_biUnion Finset.univ (fun i _ => hs i) _ fun i _ => hf i
@@ -183,8 +183,8 @@ theorem set_integral_indicator (ht : MeasurableSet t) :
   rw [integral_indicator ht, Measure.restrict_restrict ht, Set.inter_comm]
 #align measure_theory.set_integral_indicator MeasureTheory.set_integral_indicator
 
-theorem ofReal_set_integral_one_of_measure_ne_top {α : Type*} {m : MeasurableSpace α}
-    {μ : Measure α} {s : Set α} (hs : μ s ≠ ∞) : ENNReal.ofReal (∫ _ in s, (1 : ℝ) ∂μ) = μ s :=
+theorem ofReal_set_integral_one_of_measure_ne_top {X : Type*} {m : MeasurableSpace X}
+    {μ : Measure X} {s : Set X} (hs : μ s ≠ ∞) : ENNReal.ofReal (∫ _ in s, (1 : ℝ) ∂μ) = μ s :=
   calc
     ENNReal.ofReal (∫ _ in s, (1 : ℝ) ∂μ) = ENNReal.ofReal (∫ _ in s, ‖(1 : ℝ)‖ ∂μ) := by
       simp only [norm_one]
@@ -194,8 +194,8 @@ theorem ofReal_set_integral_one_of_measure_ne_top {α : Type*} {m : MeasurableSp
     _ = μ s := set_lintegral_one _
 #align measure_theory.of_real_set_integral_one_of_measure_ne_top MeasureTheory.ofReal_set_integral_one_of_measure_ne_top
 
-theorem ofReal_set_integral_one {α : Type*} {_ : MeasurableSpace α} (μ : Measure α)
-    [IsFiniteMeasure μ] (s : Set α) : ENNReal.ofReal (∫ _ in s, (1 : ℝ) ∂μ) = μ s :=
+theorem ofReal_set_integral_one {X : Type*} {_ : MeasurableSpace X} (μ : Measure X)
+    [IsFiniteMeasure μ] (s : Set X) : ENNReal.ofReal (∫ _ in s, (1 : ℝ) ∂μ) = μ s :=
   ofReal_set_integral_one_of_measure_ne_top (measure_ne_top μ s)
 #align measure_theory.of_real_set_integral_one MeasureTheory.ofReal_set_integral_one
 
@@ -208,9 +208,9 @@ theorem integral_piecewise [DecidablePred (· ∈ s)] (hs : MeasurableSet s) (hf
 #align measure_theory.integral_piecewise MeasureTheory.integral_piecewise
 
 theorem tendsto_set_integral_of_monotone {ι : Type*} [Countable ι] [SemilatticeSup ι]
-    {s : ι → Set α} (hsm : ∀ i, MeasurableSet (s i)) (h_mono : Monotone s)
+    {s : ι → Set X} (hsm : ∀ i, MeasurableSet (s i)) (h_mono : Monotone s)
     (hfi : IntegrableOn f (⋃ n, s n) μ) :
-    Tendsto (fun i => ∫ a in s i, f a ∂μ) atTop (𝓝 (∫ a in ⋃ n, s n, f a ∂μ)) := by
+    Tendsto (fun i => ∫ x in s i, f x ∂μ) atTop (𝓝 (∫ x in ⋃ n, s n, f x ∂μ)) := by
   have hfi' : ∫⁻ x in ⋃ n, s n, ‖f x‖₊ ∂μ < ∞ := hfi.2
   set S := ⋃ i, s i
   have hSm : MeasurableSet S := MeasurableSet.iUnion hsm
@@ -230,31 +230,31 @@ theorem tendsto_set_integral_of_monotone {ι : Type*} [Countable ι] [Semilattic
     (hi.2.trans_lt <| ENNReal.add_lt_top.2 ⟨hfi', ENNReal.coe_lt_top⟩).ne]
 #align measure_theory.tendsto_set_integral_of_monotone MeasureTheory.tendsto_set_integral_of_monotone
 
-theorem hasSum_integral_iUnion_ae {ι : Type*} [Countable ι] {s : ι → Set α}
+theorem hasSum_integral_iUnion_ae {ι : Type*} [Countable ι] {s : ι → Set X}
     (hm : ∀ i, NullMeasurableSet (s i) μ) (hd : Pairwise (AEDisjoint μ on s))
     (hfi : IntegrableOn f (⋃ i, s i) μ) :
-    HasSum (fun n => ∫ a in s n, f a ∂μ) (∫ a in ⋃ n, s n, f a ∂μ) := by
+    HasSum (fun n => ∫ x in s n, f x ∂μ) (∫ x in ⋃ n, s n, f x ∂μ) := by
   simp only [IntegrableOn, Measure.restrict_iUnion_ae hd hm] at hfi ⊢
   exact hasSum_integral_measure hfi
 #align measure_theory.has_sum_integral_Union_ae MeasureTheory.hasSum_integral_iUnion_ae
 
-theorem hasSum_integral_iUnion {ι : Type*} [Countable ι] {s : ι → Set α}
+theorem hasSum_integral_iUnion {ι : Type*} [Countable ι] {s : ι → Set X}
     (hm : ∀ i, MeasurableSet (s i)) (hd : Pairwise (Disjoint on s))
     (hfi : IntegrableOn f (⋃ i, s i) μ) :
-    HasSum (fun n => ∫ a in s n, f a ∂μ) (∫ a in ⋃ n, s n, f a ∂μ) :=
+    HasSum (fun n => ∫ x in s n, f x ∂μ) (∫ x in ⋃ n, s n, f x ∂μ) :=
   hasSum_integral_iUnion_ae (fun i => (hm i).nullMeasurableSet) (hd.mono fun _ _ h => h.aedisjoint)
     hfi
 #align measure_theory.has_sum_integral_Union MeasureTheory.hasSum_integral_iUnion
 
-theorem integral_iUnion {ι : Type*} [Countable ι] {s : ι → Set α} (hm : ∀ i, MeasurableSet (s i))
+theorem integral_iUnion {ι : Type*} [Countable ι] {s : ι → Set X} (hm : ∀ i, MeasurableSet (s i))
     (hd : Pairwise (Disjoint on s)) (hfi : IntegrableOn f (⋃ i, s i) μ) :
-    ∫ a in ⋃ n, s n, f a ∂μ = ∑' n, ∫ a in s n, f a ∂μ :=
+    ∫ x in ⋃ n, s n, f x ∂μ = ∑' n, ∫ x in s n, f x ∂μ :=
   (HasSum.tsum_eq (hasSum_integral_iUnion hm hd hfi)).symm
 #align measure_theory.integral_Union MeasureTheory.integral_iUnion
 
-theorem integral_iUnion_ae {ι : Type*} [Countable ι] {s : ι → Set α}
+theorem integral_iUnion_ae {ι : Type*} [Countable ι] {s : ι → Set X}
     (hm : ∀ i, NullMeasurableSet (s i) μ) (hd : Pairwise (AEDisjoint μ on s))
-    (hfi : IntegrableOn f (⋃ i, s i) μ) : ∫ a in ⋃ n, s n, f a ∂μ = ∑' n, ∫ a in s n, f a ∂μ :=
+    (hfi : IntegrableOn f (⋃ i, s i) μ) : ∫ x in ⋃ n, s n, f x ∂μ = ∑' n, ∫ x in s n, f x ∂μ :=
   (HasSum.tsum_eq (hasSum_integral_iUnion_ae hm hd hfi)).symm
 #align measure_theory.integral_Union_ae MeasureTheory.integral_iUnion_ae
 
@@ -286,7 +286,7 @@ theorem integral_union_eq_left_of_ae_aux (ht_eq : ∀ᵐ x ∂μ.restrict t, f x
   let k := f ⁻¹' {0}
   have hk : MeasurableSet k := by borelize E; exact haux.measurable (measurableSet_singleton _)
   have h's : IntegrableOn f s μ := H.mono (subset_union_left _ _) le_rfl
-  have A : ∀ u : Set α, ∫ x in u ∩ k, f x ∂μ = 0 := fun u =>
+  have A : ∀ u : Set X, ∫ x in u ∩ k, f x ∂μ = 0 := fun u =>
     set_integral_eq_zero_of_forall_eq_zero fun x hx => hx.2
   rw [← integral_inter_add_diff hk h's, ← integral_inter_add_diff hk H, A, A, zero_add, zero_add,
     union_diff_distrib, union_comm]
@@ -304,7 +304,7 @@ theorem integral_union_eq_left_of_ae (ht_eq : ∀ᵐ x ∂μ.restrict t, f x = 0
   · rw [integral_undef H, integral_undef]; simpa [integrableOn_union, ht] using H
   let f' := H.1.mk f
   calc
-    ∫ x : α in s ∪ t, f x ∂μ = ∫ x : α in s ∪ t, f' x ∂μ := integral_congr_ae H.1.ae_eq_mk
+    ∫ x : X in s ∪ t, f x ∂μ = ∫ x : X in s ∪ t, f' x ∂μ := integral_congr_ae H.1.ae_eq_mk
     _ = ∫ x in s, f' x ∂μ := by
       apply
         integral_union_eq_left_of_ae_aux _ H.1.stronglyMeasurable_mk (H.congr_fun_ae H.1.ae_eq_mk)
@@ -316,12 +316,12 @@ theorem integral_union_eq_left_of_ae (ht_eq : ∀ᵐ x ∂μ.restrict t, f x = 0
         (ae_mono (Measure.restrict_mono (subset_union_left s t) le_rfl) H.1.ae_eq_mk.symm)
 #align measure_theory.integral_union_eq_left_of_ae MeasureTheory.integral_union_eq_left_of_ae
 
-theorem integral_union_eq_left_of_forall₀ {f : α → E} (ht : NullMeasurableSet t μ)
+theorem integral_union_eq_left_of_forall₀ {f : X → E} (ht : NullMeasurableSet t μ)
     (ht_eq : ∀ x ∈ t, f x = 0) : ∫ x in s ∪ t, f x ∂μ = ∫ x in s, f x ∂μ :=
   integral_union_eq_left_of_ae ((ae_restrict_iff'₀ ht).2 (eventually_of_forall ht_eq))
 #align measure_theory.integral_union_eq_left_of_forall₀ MeasureTheory.integral_union_eq_left_of_forall₀
 
-theorem integral_union_eq_left_of_forall {f : α → E} (ht : MeasurableSet t)
+theorem integral_union_eq_left_of_forall {f : X → E} (ht : MeasurableSet t)
     (ht_eq : ∀ x ∈ t, f x = 0) : ∫ x in s ∪ t, f x ∂μ = ∫ x in s, f x ∂μ :=
   integral_union_eq_left_of_forall₀ ht.nullMeasurableSet ht_eq
 #align measure_theory.integral_union_eq_left_of_forall MeasureTheory.integral_union_eq_left_of_forall
@@ -400,7 +400,7 @@ theorem set_integral_eq_integral_of_forall_compl_eq_zero (h : ∀ x, x ∉ s →
   set_integral_eq_integral_of_ae_compl_eq_zero (eventually_of_forall h)
 #align measure_theory.set_integral_eq_integral_of_forall_compl_eq_zero MeasureTheory.set_integral_eq_integral_of_forall_compl_eq_zero
 
-theorem set_integral_neg_eq_set_integral_nonpos [LinearOrder E] {f : α → E}
+theorem set_integral_neg_eq_set_integral_nonpos [LinearOrder E] {f : X → E}
     (hf : AEStronglyMeasurable f μ) :
     ∫ x in {x | f x < 0}, f x ∂μ = ∫ x in {x | f x ≤ 0}, f x ∂μ := by
   have h_union : {x | f x ≤ 0} = {x | f x < 0} ∪ {x | f x = 0} := by
@@ -413,7 +413,7 @@ theorem set_integral_neg_eq_set_integral_nonpos [LinearOrder E] {f : α → E}
   filter_upwards [ae_restrict_mem₀ B] with x hx using hx
 #align measure_theory.set_integral_neg_eq_set_integral_nonpos MeasureTheory.set_integral_neg_eq_set_integral_nonpos
 
-theorem integral_norm_eq_pos_sub_neg {f : α → ℝ} (hfi : Integrable f μ) :
+theorem integral_norm_eq_pos_sub_neg {f : X → ℝ} (hfi : Integrable f μ) :
     ∫ x, ‖f x‖ ∂μ = ∫ x in {x | 0 ≤ f x}, f x ∂μ - ∫ x in {x | f x ≤ 0}, f x ∂μ :=
   have h_meas : NullMeasurableSet {x | 0 ≤ f x} μ :=
     aestronglyMeasurable_const.nullMeasurableSet_le hfi.1
@@ -443,39 +443,39 @@ theorem set_integral_const [CompleteSpace E] (c : E) : ∫ _ in s, c ∂μ = (μ
 #align measure_theory.set_integral_const MeasureTheory.set_integral_const
 
 @[simp]
-theorem integral_indicator_const [CompleteSpace E] (e : E) ⦃s : Set α⦄ (s_meas : MeasurableSet s) :
-    ∫ a : α, s.indicator (fun _ : α => e) a ∂μ = (μ s).toReal • e := by
+theorem integral_indicator_const [CompleteSpace E] (e : E) ⦃s : Set X⦄ (s_meas : MeasurableSet s) :
+    ∫ x : X, s.indicator (fun _ : X => e) x ∂μ = (μ s).toReal • e := by
   rw [integral_indicator s_meas, ← set_integral_const]
 #align measure_theory.integral_indicator_const MeasureTheory.integral_indicator_const
 
 @[simp]
-theorem integral_indicator_one ⦃s : Set α⦄ (hs : MeasurableSet s) :
-    ∫ a, s.indicator 1 a ∂μ = (μ s).toReal :=
+theorem integral_indicator_one ⦃s : Set X⦄ (hs : MeasurableSet s) :
+    ∫ x, s.indicator 1 x ∂μ = (μ s).toReal :=
   (integral_indicator_const 1 hs).trans ((smul_eq_mul _).trans (mul_one _))
 #align measure_theory.integral_indicator_one MeasureTheory.integral_indicator_one
 
 theorem set_integral_indicatorConstLp [CompleteSpace E]
-    {p : ℝ≥0∞} (hs : MeasurableSet s) (ht : MeasurableSet t) (hμt : μ t ≠ ∞) (x : E) :
-    ∫ a in s, indicatorConstLp p ht hμt x a ∂μ = (μ (t ∩ s)).toReal • x :=
+    {p : ℝ≥0∞} (hs : MeasurableSet s) (ht : MeasurableSet t) (hμt : μ t ≠ ∞) (e : E) :
+    ∫ x in s, indicatorConstLp p ht hμt e x ∂μ = (μ (t ∩ s)).toReal • e :=
   calc
-    ∫ a in s, indicatorConstLp p ht hμt x a ∂μ = ∫ a in s, t.indicator (fun _ => x) a ∂μ := by
+    ∫ x in s, indicatorConstLp p ht hμt e x ∂μ = ∫ x in s, t.indicator (fun _ => e) x ∂μ := by
       rw [set_integral_congr_ae hs (indicatorConstLp_coeFn.mono fun x hx _ => hx)]
-    _ = (μ (t ∩ s)).toReal • x := by rw [integral_indicator_const _ ht, Measure.restrict_apply ht]
+    _ = (μ (t ∩ s)).toReal • e := by rw [integral_indicator_const _ ht, Measure.restrict_apply ht]
 set_option linter.uppercaseLean3 false in
 #align measure_theory.set_integral_indicator_const_Lp MeasureTheory.set_integral_indicatorConstLp
 
 theorem integral_indicatorConstLp [CompleteSpace E]
-    {p : ℝ≥0∞} (ht : MeasurableSet t) (hμt : μ t ≠ ∞) (x : E) :
-    ∫ a, indicatorConstLp p ht hμt x a ∂μ = (μ t).toReal • x :=
+    {p : ℝ≥0∞} (ht : MeasurableSet t) (hμt : μ t ≠ ∞) (e : E) :
+    ∫ x, indicatorConstLp p ht hμt e x ∂μ = (μ t).toReal • e :=
   calc
-    ∫ a, indicatorConstLp p ht hμt x a ∂μ = ∫ a in univ, indicatorConstLp p ht hμt x a ∂μ := by
+    ∫ x, indicatorConstLp p ht hμt e x ∂μ = ∫ x in univ, indicatorConstLp p ht hμt e x ∂μ := by
       rw [integral_univ]
-    _ = (μ (t ∩ univ)).toReal • x := (set_integral_indicatorConstLp MeasurableSet.univ ht hμt x)
-    _ = (μ t).toReal • x := by rw [inter_univ]
+    _ = (μ (t ∩ univ)).toReal • e := (set_integral_indicatorConstLp MeasurableSet.univ ht hμt e)
+    _ = (μ t).toReal • e := by rw [inter_univ]
 set_option linter.uppercaseLean3 false in
 #align measure_theory.integral_indicator_const_Lp MeasureTheory.integral_indicatorConstLp
 
-theorem set_integral_map {β} [MeasurableSpace β] {g : α → β} {f : β → E} {s : Set β}
+theorem set_integral_map {Y} [MeasurableSpace Y] {g : X → Y} {f : Y → E} {s : Set Y}
     (hs : MeasurableSet s) (hf : AEStronglyMeasurable f (Measure.map g μ)) (hg : AEMeasurable g μ) :
     ∫ y in s, f y ∂Measure.map g μ = ∫ x in g ⁻¹' s, f (g x) ∂μ := by
   rw [Measure.restrict_map_of_aemeasurable hg hs,
@@ -483,31 +483,31 @@ theorem set_integral_map {β} [MeasurableSpace β] {g : α → β} {f : β → E
   exact Measure.map_mono_of_aemeasurable Measure.restrict_le_self hg
 #align measure_theory.set_integral_map MeasureTheory.set_integral_map
 
-theorem _root_.MeasurableEmbedding.set_integral_map {β} {_ : MeasurableSpace β} {f : α → β}
-    (hf : MeasurableEmbedding f) (g : β → E) (s : Set β) :
+theorem _root_.MeasurableEmbedding.set_integral_map {Y} {_ : MeasurableSpace Y} {f : X → Y}
+    (hf : MeasurableEmbedding f) (g : Y → E) (s : Set Y) :
     ∫ y in s, g y ∂Measure.map f μ = ∫ x in f ⁻¹' s, g (f x) ∂μ := by
   rw [hf.restrict_map, hf.integral_map]
 #align measurable_embedding.set_integral_map MeasurableEmbedding.set_integral_map
 
-theorem _root_.ClosedEmbedding.set_integral_map [TopologicalSpace α] [BorelSpace α] {β}
-    [MeasurableSpace β] [TopologicalSpace β] [BorelSpace β] {g : α → β} {f : β → E} (s : Set β)
+theorem _root_.ClosedEmbedding.set_integral_map [TopologicalSpace X] [BorelSpace X] {Y}
+    [MeasurableSpace Y] [TopologicalSpace Y] [BorelSpace Y] {g : X → Y} {f : Y → E} (s : Set Y)
     (hg : ClosedEmbedding g) : ∫ y in s, f y ∂Measure.map g μ = ∫ x in g ⁻¹' s, f (g x) ∂μ :=
   hg.measurableEmbedding.set_integral_map _ _
 #align closed_embedding.set_integral_map ClosedEmbedding.set_integral_map
 
-theorem MeasurePreserving.set_integral_preimage_emb {β} {_ : MeasurableSpace β} {f : α → β} {ν}
-    (h₁ : MeasurePreserving f μ ν) (h₂ : MeasurableEmbedding f) (g : β → E) (s : Set β) :
+theorem MeasurePreserving.set_integral_preimage_emb {Y} {_ : MeasurableSpace Y} {f : X → Y} {ν}
+    (h₁ : MeasurePreserving f μ ν) (h₂ : MeasurableEmbedding f) (g : Y → E) (s : Set Y) :
     ∫ x in f ⁻¹' s, g (f x) ∂μ = ∫ y in s, g y ∂ν :=
   (h₁.restrict_preimage_emb h₂ s).integral_comp h₂ _
 #align measure_theory.measure_preserving.set_integral_preimage_emb MeasureTheory.MeasurePreserving.set_integral_preimage_emb
 
-theorem MeasurePreserving.set_integral_image_emb {β} {_ : MeasurableSpace β} {f : α → β} {ν}
-    (h₁ : MeasurePreserving f μ ν) (h₂ : MeasurableEmbedding f) (g : β → E) (s : Set α) :
+theorem MeasurePreserving.set_integral_image_emb {Y} {_ : MeasurableSpace Y} {f : X → Y} {ν}
+    (h₁ : MeasurePreserving f μ ν) (h₂ : MeasurableEmbedding f) (g : Y → E) (s : Set X) :
     ∫ y in f '' s, g y ∂ν = ∫ x in s, g (f x) ∂μ :=
   Eq.symm <| (h₁.restrict_image_emb h₂ s).integral_comp h₂ _
 #align measure_theory.measure_preserving.set_integral_image_emb MeasureTheory.MeasurePreserving.set_integral_image_emb
 
-theorem set_integral_map_equiv {β} [MeasurableSpace β] (e : α ≃ᵐ β) (f : β → E) (s : Set β) :
+theorem set_integral_map_equiv {Y} [MeasurableSpace Y] (e : X ≃ᵐ Y) (f : Y → E) (s : Set Y) :
     ∫ y in s, f y ∂Measure.map e μ = ∫ x in e ⁻¹' s, f (e x) ∂μ :=
   e.measurableEmbedding.set_integral_map f s
 #align measure_theory.set_integral_map_equiv MeasureTheory.set_integral_map_equiv
@@ -523,7 +523,7 @@ theorem norm_set_integral_le_of_norm_le_const_ae' {C : ℝ} (hs : μ s < ∞)
     (hC : ∀ᵐ x ∂μ, x ∈ s → ‖f x‖ ≤ C) (hfm : AEStronglyMeasurable f (μ.restrict s)) :
     ‖∫ x in s, f x ∂μ‖ ≤ C * (μ s).toReal := by
   apply norm_set_integral_le_of_norm_le_const_ae hs
-  have A : ∀ᵐ x : α ∂μ, x ∈ s → ‖AEStronglyMeasurable.mk f hfm x‖ ≤ C := by
+  have A : ∀ᵐ x : X ∂μ, x ∈ s → ‖AEStronglyMeasurable.mk f hfm x‖ ≤ C := by
     filter_upwards [hC, hfm.ae_mem_imp_eq_mk] with _ h1 h2 h3
     rw [← h2 h3]
     exact h1 h3
@@ -549,19 +549,19 @@ theorem norm_set_integral_le_of_norm_le_const' {C : ℝ} (hs : μ s < ∞) (hsm
   norm_set_integral_le_of_norm_le_const_ae'' hs hsm <| eventually_of_forall hC
 #align measure_theory.norm_set_integral_le_of_norm_le_const' MeasureTheory.norm_set_integral_le_of_norm_le_const'
 
-theorem set_integral_eq_zero_iff_of_nonneg_ae {f : α → ℝ} (hf : 0 ≤ᵐ[μ.restrict s] f)
+theorem set_integral_eq_zero_iff_of_nonneg_ae {f : X → ℝ} (hf : 0 ≤ᵐ[μ.restrict s] f)
     (hfi : IntegrableOn f s μ) : ∫ x in s, f x ∂μ = 0 ↔ f =ᵐ[μ.restrict s] 0 :=
   integral_eq_zero_iff_of_nonneg_ae hf hfi
 #align measure_theory.set_integral_eq_zero_iff_of_nonneg_ae MeasureTheory.set_integral_eq_zero_iff_of_nonneg_ae
 
-theorem set_integral_pos_iff_support_of_nonneg_ae {f : α → ℝ} (hf : 0 ≤ᵐ[μ.restrict s] f)
+theorem set_integral_pos_iff_support_of_nonneg_ae {f : X → ℝ} (hf : 0 ≤ᵐ[μ.restrict s] f)
     (hfi : IntegrableOn f s μ) : (0 < ∫ x in s, f x ∂μ) ↔ 0 < μ (support f ∩ s) := by
   rw [integral_pos_iff_support_of_nonneg_ae hf hfi, Measure.restrict_apply₀]
   rw [support_eq_preimage]
   exact hfi.aestronglyMeasurable.aemeasurable.nullMeasurable (measurableSet_singleton 0).compl
 #align measure_theory.set_integral_pos_iff_support_of_nonneg_ae MeasureTheory.set_integral_pos_iff_support_of_nonneg_ae
 
-theorem set_integral_gt_gt {R : ℝ} {f : α → ℝ} (hR : 0 ≤ R) (hfm : Measurable f)
+theorem set_integral_gt_gt {R : ℝ} {f : X → ℝ} (hR : 0 ≤ R) (hfm : Measurable f)
     (hfint : IntegrableOn f {x | ↑R < f x} μ) (hμ : μ {x | ↑R < f x} ≠ 0) :
     (μ {x | ↑R < f x}).toReal * R < ∫ x in {x | ↑R < f x}, f x ∂μ := by
   have : IntegrableOn (fun _ => R) {x | ↑R < f x} μ := by
@@ -584,8 +584,8 @@ theorem set_integral_gt_gt {R : ℝ} {f : α → ℝ} (hR : 0 ≤ R) (hfm : Meas
   · exact Integrable.sub hfint this
 #align measure_theory.set_integral_gt_gt MeasureTheory.set_integral_gt_gt
 
-theorem set_integral_trim {α} {m m0 : MeasurableSpace α} {μ : Measure α} (hm : m ≤ m0) {f : α → E}
-    (hf_meas : StronglyMeasurable[m] f) {s : Set α} (hs : MeasurableSet[m] s) :
+theorem set_integral_trim {X} {m m0 : MeasurableSpace X} {μ : Measure X} (hm : m ≤ m0) {f : X → E}
+    (hf_meas : StronglyMeasurable[m] f) {s : Set X} (hs : MeasurableSet[m] s) :
     ∫ x in s, f x ∂μ = ∫ x in s, f x ∂μ.trim hm := by
   rwa [integral_trim hm hf_meas, restrict_trim hm μ]
 #align measure_theory.set_integral_trim MeasureTheory.set_integral_trim
@@ -599,71 +599,71 @@ unprimed ones use `[NoAtoms μ]`.
 
 section PartialOrder
 
-variable [PartialOrder α] {a b : α}
+variable [PartialOrder X] {x y : X}
 
-theorem integral_Icc_eq_integral_Ioc' (ha : μ {a} = 0) :
-    ∫ t in Icc a b, f t ∂μ = ∫ t in Ioc a b, f t ∂μ :=
-  set_integral_congr_set_ae (Ioc_ae_eq_Icc' ha).symm
+theorem integral_Icc_eq_integral_Ioc' (hx : μ {x} = 0) :
+    ∫ t in Icc x y, f t ∂μ = ∫ t in Ioc x y, f t ∂μ :=
+  set_integral_congr_set_ae (Ioc_ae_eq_Icc' hx).symm
 #align measure_theory.integral_Icc_eq_integral_Ioc' MeasureTheory.integral_Icc_eq_integral_Ioc'
 
-theorem integral_Icc_eq_integral_Ico' (hb : μ {b} = 0) :
-    ∫ t in Icc a b, f t ∂μ = ∫ t in Ico a b, f t ∂μ :=
-  set_integral_congr_set_ae (Ico_ae_eq_Icc' hb).symm
+theorem integral_Icc_eq_integral_Ico' (hy : μ {y} = 0) :
+    ∫ t in Icc x y, f t ∂μ = ∫ t in Ico x y, f t ∂μ :=
+  set_integral_congr_set_ae (Ico_ae_eq_Icc' hy).symm
 #align measure_theory.integral_Icc_eq_integral_Ico' MeasureTheory.integral_Icc_eq_integral_Ico'
 
-theorem integral_Ioc_eq_integral_Ioo' (hb : μ {b} = 0) :
-    ∫ t in Ioc a b, f t ∂μ = ∫ t in Ioo a b, f t ∂μ :=
-  set_integral_congr_set_ae (Ioo_ae_eq_Ioc' hb).symm
+theorem integral_Ioc_eq_integral_Ioo' (hy : μ {y} = 0) :
+    ∫ t in Ioc x y, f t ∂μ = ∫ t in Ioo x y, f t ∂μ :=
+  set_integral_congr_set_ae (Ioo_ae_eq_Ioc' hy).symm
 #align measure_theory.integral_Ioc_eq_integral_Ioo' MeasureTheory.integral_Ioc_eq_integral_Ioo'
 
-theorem integral_Ico_eq_integral_Ioo' (ha : μ {a} = 0) :
-    ∫ t in Ico a b, f t ∂μ = ∫ t in Ioo a b, f t ∂μ :=
-  set_integral_congr_set_ae (Ioo_ae_eq_Ico' ha).symm
+theorem integral_Ico_eq_integral_Ioo' (hx : μ {x} = 0) :
+    ∫ t in Ico x y, f t ∂μ = ∫ t in Ioo x y, f t ∂μ :=
+  set_integral_congr_set_ae (Ioo_ae_eq_Ico' hx).symm
 #align measure_theory.integral_Ico_eq_integral_Ioo' MeasureTheory.integral_Ico_eq_integral_Ioo'
 
-theorem integral_Icc_eq_integral_Ioo' (ha : μ {a} = 0) (hb : μ {b} = 0) :
-    ∫ t in Icc a b, f t ∂μ = ∫ t in Ioo a b, f t ∂μ :=
-  set_integral_congr_set_ae (Ioo_ae_eq_Icc' ha hb).symm
+theorem integral_Icc_eq_integral_Ioo' (hx : μ {x} = 0) (hy : μ {y} = 0) :
+    ∫ t in Icc x y, f t ∂μ = ∫ t in Ioo x y, f t ∂μ :=
+  set_integral_congr_set_ae (Ioo_ae_eq_Icc' hx hy).symm
 #align measure_theory.integral_Icc_eq_integral_Ioo' MeasureTheory.integral_Icc_eq_integral_Ioo'
 
-theorem integral_Iic_eq_integral_Iio' (ha : μ {a} = 0) :
-    ∫ t in Iic a, f t ∂μ = ∫ t in Iio a, f t ∂μ :=
-  set_integral_congr_set_ae (Iio_ae_eq_Iic' ha).symm
+theorem integral_Iic_eq_integral_Iio' (hx : μ {x} = 0) :
+    ∫ t in Iic x, f t ∂μ = ∫ t in Iio x, f t ∂μ :=
+  set_integral_congr_set_ae (Iio_ae_eq_Iic' hx).symm
 #align measure_theory.integral_Iic_eq_integral_Iio' MeasureTheory.integral_Iic_eq_integral_Iio'
 
-theorem integral_Ici_eq_integral_Ioi' (ha : μ {a} = 0) :
-    ∫ t in Ici a, f t ∂μ = ∫ t in Ioi a, f t ∂μ :=
-  set_integral_congr_set_ae (Ioi_ae_eq_Ici' ha).symm
+theorem integral_Ici_eq_integral_Ioi' (hx : μ {x} = 0) :
+    ∫ t in Ici x, f t ∂μ = ∫ t in Ioi x, f t ∂μ :=
+  set_integral_congr_set_ae (Ioi_ae_eq_Ici' hx).symm
 #align measure_theory.integral_Ici_eq_integral_Ioi' MeasureTheory.integral_Ici_eq_integral_Ioi'
 
 variable [NoAtoms μ]
 
-theorem integral_Icc_eq_integral_Ioc : ∫ t in Icc a b, f t ∂μ = ∫ t in Ioc a b, f t ∂μ :=
-  integral_Icc_eq_integral_Ioc' <| measure_singleton a
+theorem integral_Icc_eq_integral_Ioc : ∫ t in Icc x y, f t ∂μ = ∫ t in Ioc x y, f t ∂μ :=
+  integral_Icc_eq_integral_Ioc' <| measure_singleton x
 #align measure_theory.integral_Icc_eq_integral_Ioc MeasureTheory.integral_Icc_eq_integral_Ioc
 
-theorem integral_Icc_eq_integral_Ico : ∫ t in Icc a b, f t ∂μ = ∫ t in Ico a b, f t ∂μ :=
-  integral_Icc_eq_integral_Ico' <| measure_singleton b
+theorem integral_Icc_eq_integral_Ico : ∫ t in Icc x y, f t ∂μ = ∫ t in Ico x y, f t ∂μ :=
+  integral_Icc_eq_integral_Ico' <| measure_singleton y
 #align measure_theory.integral_Icc_eq_integral_Ico MeasureTheory.integral_Icc_eq_integral_Ico
 
-theorem integral_Ioc_eq_integral_Ioo : ∫ t in Ioc a b, f t ∂μ = ∫ t in Ioo a b, f t ∂μ :=
-  integral_Ioc_eq_integral_Ioo' <| measure_singleton b
+theorem integral_Ioc_eq_integral_Ioo : ∫ t in Ioc x y, f t ∂μ = ∫ t in Ioo x y, f t ∂μ :=
+  integral_Ioc_eq_integral_Ioo' <| measure_singleton y
 #align measure_theory.integral_Ioc_eq_integral_Ioo MeasureTheory.integral_Ioc_eq_integral_Ioo
 
-theorem integral_Ico_eq_integral_Ioo : ∫ t in Ico a b, f t ∂μ = ∫ t in Ioo a b, f t ∂μ :=
-  integral_Ico_eq_integral_Ioo' <| measure_singleton a
+theorem integral_Ico_eq_integral_Ioo : ∫ t in Ico x y, f t ∂μ = ∫ t in Ioo x y, f t ∂μ :=
+  integral_Ico_eq_integral_Ioo' <| measure_singleton x
 #align measure_theory.integral_Ico_eq_integral_Ioo MeasureTheory.integral_Ico_eq_integral_Ioo
 
-theorem integral_Icc_eq_integral_Ioo : ∫ t in Icc a b, f t ∂μ = ∫ t in Ioo a b, f t ∂μ := by
+theorem integral_Icc_eq_integral_Ioo : ∫ t in Icc x y, f t ∂μ = ∫ t in Ioo x y, f t ∂μ := by
   rw [integral_Icc_eq_integral_Ico, integral_Ico_eq_integral_Ioo]
 #align measure_theory.integral_Icc_eq_integral_Ioo MeasureTheory.integral_Icc_eq_integral_Ioo
 
-theorem integral_Iic_eq_integral_Iio : ∫ t in Iic a, f t ∂μ = ∫ t in Iio a, f t ∂μ :=
-  integral_Iic_eq_integral_Iio' <| measure_singleton a
+theorem integral_Iic_eq_integral_Iio : ∫ t in Iic x, f t ∂μ = ∫ t in Iio x, f t ∂μ :=
+  integral_Iic_eq_integral_Iio' <| measure_singleton x
 #align measure_theory.integral_Iic_eq_integral_Iio MeasureTheory.integral_Iic_eq_integral_Iio
 
-theorem integral_Ici_eq_integral_Ioi : ∫ t in Ici a, f t ∂μ = ∫ t in Ioi a, f t ∂μ :=
-  integral_Ici_eq_integral_Ioi' <| measure_singleton a
+theorem integral_Ici_eq_integral_Ioi : ∫ t in Ici x, f t ∂μ = ∫ t in Ioi x, f t ∂μ :=
+  integral_Ici_eq_integral_Ioi' <| measure_singleton x
 #align measure_theory.integral_Ici_eq_integral_Ioi MeasureTheory.integral_Ici_eq_integral_Ioi
 
 end PartialOrder
@@ -672,30 +672,30 @@ end NormedAddCommGroup
 
 section Mono
 
-variable {μ : Measure α} {f g : α → ℝ} {s t : Set α} (hf : IntegrableOn f s μ)
+variable {μ : Measure X} {f g : X → ℝ} {s t : Set X} (hf : IntegrableOn f s μ)
   (hg : IntegrableOn g s μ)
 
 theorem set_integral_mono_ae_restrict (h : f ≤ᵐ[μ.restrict s] g) :
-    ∫ a in s, f a ∂μ ≤ ∫ a in s, g a ∂μ :=
+    ∫ x in s, f x ∂μ ≤ ∫ x in s, g x ∂μ :=
   integral_mono_ae hf hg h
 #align measure_theory.set_integral_mono_ae_restrict MeasureTheory.set_integral_mono_ae_restrict
 
-theorem set_integral_mono_ae (h : f ≤ᵐ[μ] g) : ∫ a in s, f a ∂μ ≤ ∫ a in s, g a ∂μ :=
+theorem set_integral_mono_ae (h : f ≤ᵐ[μ] g) : ∫ x in s, f x ∂μ ≤ ∫ x in s, g x ∂μ :=
   set_integral_mono_ae_restrict hf hg (ae_restrict_of_ae h)
 #align measure_theory.set_integral_mono_ae MeasureTheory.set_integral_mono_ae
 
 theorem set_integral_mono_on (hs : MeasurableSet s) (h : ∀ x ∈ s, f x ≤ g x) :
-    ∫ a in s, f a ∂μ ≤ ∫ a in s, g a ∂μ :=
+    ∫ x in s, f x ∂μ ≤ ∫ x in s, g x ∂μ :=
   set_integral_mono_ae_restrict hf hg
     (by simp [hs, EventuallyLE, eventually_inf_principal, ae_of_all _ h])
 #align measure_theory.set_integral_mono_on MeasureTheory.set_integral_mono_on
 
 theorem set_integral_mono_on_ae (hs : MeasurableSet s) (h : ∀ᵐ x ∂μ, x ∈ s → f x ≤ g x) :
-    ∫ a in s, f a ∂μ ≤ ∫ a in s, g a ∂μ := by
+    ∫ x in s, f x ∂μ ≤ ∫ x in s, g x ∂μ := by
   refine' set_integral_mono_ae_restrict hf hg _; rwa [EventuallyLE, ae_restrict_iff' hs]
 #align measure_theory.set_integral_mono_on_ae MeasureTheory.set_integral_mono_on_ae
 
-theorem set_integral_mono (h : f ≤ g) : ∫ a in s, f a ∂μ ≤ ∫ a in s, g a ∂μ :=
+theorem set_integral_mono (h : f ≤ g) : ∫ x in s, f x ∂μ ≤ ∫ x in s, g x ∂μ :=
   integral_mono hf hg h
 #align measure_theory.set_integral_mono MeasureTheory.set_integral_mono
 
@@ -709,7 +709,7 @@ theorem set_integral_le_integral (hfi : Integrable f μ) (hf : 0 ≤ᵐ[μ] f) :
   integral_mono_measure (Measure.restrict_le_self) hf hfi
 
 theorem set_integral_ge_of_const_le {c : ℝ} (hs : MeasurableSet s) (hμs : μ s ≠ ∞)
-    (hf : ∀ x ∈ s, c ≤ f x) (hfint : IntegrableOn (fun x : α => f x) s μ) :
+    (hf : ∀ x ∈ s, c ≤ f x) (hfint : IntegrableOn (fun x : X => f x) s μ) :
     c * (μ s).toReal ≤ ∫ x in s, f x ∂μ := by
   rw [mul_comm, ← smul_eq_mul, ← set_integral_const c]
   exact set_integral_mono_on (integrableOn_const.2 (Or.inr hμs.lt_top)) hfint hs hf
@@ -719,27 +719,27 @@ end Mono
 
 section Nonneg
 
-variable {μ : Measure α} {f : α → ℝ} {s : Set α}
+variable {μ : Measure X} {f : X → ℝ} {s : Set X}
 
-theorem set_integral_nonneg_of_ae_restrict (hf : 0 ≤ᵐ[μ.restrict s] f) : 0 ≤ ∫ a in s, f a ∂μ :=
+theorem set_integral_nonneg_of_ae_restrict (hf : 0 ≤ᵐ[μ.restrict s] f) : 0 ≤ ∫ x in s, f x ∂μ :=
   integral_nonneg_of_ae hf
 #align measure_theory.set_integral_nonneg_of_ae_restrict MeasureTheory.set_integral_nonneg_of_ae_restrict
 
-theorem set_integral_nonneg_of_ae (hf : 0 ≤ᵐ[μ] f) : 0 ≤ ∫ a in s, f a ∂μ :=
+theorem set_integral_nonneg_of_ae (hf : 0 ≤ᵐ[μ] f) : 0 ≤ ∫ x in s, f x ∂μ :=
   set_integral_nonneg_of_ae_restrict (ae_restrict_of_ae hf)
 #align measure_theory.set_integral_nonneg_of_ae MeasureTheory.set_integral_nonneg_of_ae
 
-theorem set_integral_nonneg (hs : MeasurableSet s) (hf : ∀ a, a ∈ s → 0 ≤ f a) :
-    0 ≤ ∫ a in s, f a ∂μ :=
+theorem set_integral_nonneg (hs : MeasurableSet s) (hf : ∀ x, x ∈ s → 0 ≤ f x) :
+    0 ≤ ∫ x in s, f x ∂μ :=
   set_integral_nonneg_of_ae_restrict ((ae_restrict_iff' hs).mpr (ae_of_all μ hf))
 #align measure_theory.set_integral_nonneg MeasureTheory.set_integral_nonneg
 
-theorem set_integral_nonneg_ae (hs : MeasurableSet s) (hf : ∀ᵐ a ∂μ, a ∈ s → 0 ≤ f a) :
-    0 ≤ ∫ a in s, f a ∂μ :=
+theorem set_integral_nonneg_ae (hs : MeasurableSet s) (hf : ∀ᵐ x ∂μ, x ∈ s → 0 ≤ f x) :
+    0 ≤ ∫ x in s, f x ∂μ :=
   set_integral_nonneg_of_ae_restrict <| by rwa [EventuallyLE, ae_restrict_iff' hs]
 #align measure_theory.set_integral_nonneg_ae MeasureTheory.set_integral_nonneg_ae
 
-theorem set_integral_le_nonneg {s : Set α} (hs : MeasurableSet s) (hf : StronglyMeasurable f)
+theorem set_integral_le_nonneg {s : Set X} (hs : MeasurableSet s) (hf : StronglyMeasurable f)
     (hfi : Integrable f μ) : ∫ x in s, f x ∂μ ≤ ∫ x in {y | 0 ≤ f y}, f x ∂μ := by
   rw [← integral_indicator hs, ←
     integral_indicator (stronglyMeasurable_const.measurableSet_le hf)]
@@ -749,25 +749,25 @@ theorem set_integral_le_nonneg {s : Set α} (hs : MeasurableSet s) (hf : Strongl
       (indicator_le_indicator_nonneg s f)
 #align measure_theory.set_integral_le_nonneg MeasureTheory.set_integral_le_nonneg
 
-theorem set_integral_nonpos_of_ae_restrict (hf : f ≤ᵐ[μ.restrict s] 0) : ∫ a in s, f a ∂μ ≤ 0 :=
+theorem set_integral_nonpos_of_ae_restrict (hf : f ≤ᵐ[μ.restrict s] 0) : ∫ x in s, f x ∂μ ≤ 0 :=
   integral_nonpos_of_ae hf
 #align measure_theory.set_integral_nonpos_of_ae_restrict MeasureTheory.set_integral_nonpos_of_ae_restrict
 
-theorem set_integral_nonpos_of_ae (hf : f ≤ᵐ[μ] 0) : ∫ a in s, f a ∂μ ≤ 0 :=
+theorem set_integral_nonpos_of_ae (hf : f ≤ᵐ[μ] 0) : ∫ x in s, f x ∂μ ≤ 0 :=
   set_integral_nonpos_of_ae_restrict (ae_restrict_of_ae hf)
 #align measure_theory.set_integral_nonpos_of_ae MeasureTheory.set_integral_nonpos_of_ae
 
-theorem set_integral_nonpos_ae (hs : MeasurableSet s) (hf : ∀ᵐ a ∂μ, a ∈ s → f a ≤ 0) :
-    ∫ a in s, f a ∂μ ≤ 0 :=
+theorem set_integral_nonpos_ae (hs : MeasurableSet s) (hf : ∀ᵐ x ∂μ, x ∈ s → f x ≤ 0) :
+    ∫ x in s, f x ∂μ ≤ 0 :=
   set_integral_nonpos_of_ae_restrict <| by rwa [EventuallyLE, ae_restrict_iff' hs]
 #align measure_theory.set_integral_nonpos_ae MeasureTheory.set_integral_nonpos_ae
 
-theorem set_integral_nonpos (hs : MeasurableSet s) (hf : ∀ a, a ∈ s → f a ≤ 0) :
-    ∫ a in s, f a ∂μ ≤ 0 :=
+theorem set_integral_nonpos (hs : MeasurableSet s) (hf : ∀ x, x ∈ s → f x ≤ 0) :
+    ∫ x in s, f x ∂μ ≤ 0 :=
   set_integral_nonpos_ae hs <| ae_of_all μ hf
 #align measure_theory.set_integral_nonpos MeasureTheory.set_integral_nonpos
 
-theorem set_integral_nonpos_le {s : Set α} (hs : MeasurableSet s) (hf : StronglyMeasurable f)
+theorem set_integral_nonpos_le {s : Set X} (hs : MeasurableSet s) (hf : StronglyMeasurable f)
     (hfi : Integrable f μ) : ∫ x in {y | f y ≤ 0}, f x ∂μ ≤ ∫ x in s, f x ∂μ := by
   rw [← integral_indicator hs, ←
     integral_indicator (hf.measurableSet_le stronglyMeasurable_const)]
@@ -776,8 +776,8 @@ theorem set_integral_nonpos_le {s : Set α} (hs : MeasurableSet s) (hf : Strongl
       (hfi.indicator hs) (indicator_nonpos_le_indicator s f)
 #align measure_theory.set_integral_nonpos_le MeasureTheory.set_integral_nonpos_le
 
-lemma Integrable.measure_le_integral {f : α → ℝ} (f_int : Integrable f μ) (f_nonneg : 0 ≤ᵐ[μ] f)
-    {s : Set α} (hs : ∀ x ∈ s, 1 ≤ f x) :
+lemma Integrable.measure_le_integral {f : X → ℝ} (f_int : Integrable f μ) (f_nonneg : 0 ≤ᵐ[μ] f)
+    {s : Set X} (hs : ∀ x ∈ s, 1 ≤ f x) :
     μ s ≤ ENNReal.ofReal (∫ x, f x ∂μ) := by
   rw [ofReal_integral_eq_lintegral_ofReal f_int f_nonneg]
   apply meas_le_lintegral₀
@@ -785,7 +785,7 @@ lemma Integrable.measure_le_integral {f : α → ℝ} (f_int : Integrable f μ)
   · intro x hx
     simpa using ENNReal.ofReal_le_ofReal (hs x hx)
 
-lemma integral_le_measure {f : α → ℝ} {s : Set α}
+lemma integral_le_measure {f : X → ℝ} {s : Set X}
     (hs : ∀ x ∈ s, f x ≤ 1) (h's : ∀ x ∈ sᶜ, f x ≤ 0) :
     ENNReal.ofReal (∫ x, f x ∂μ) ≤ μ s := by
   by_cases H : Integrable f μ; swap
@@ -811,17 +811,17 @@ end Nonneg
 
 section IntegrableUnion
 
-variable {μ : Measure α} [NormedAddCommGroup E] [Countable β]
+variable {ι : Type*} [Countable ι] {μ : Measure X} [NormedAddCommGroup E]
 
-theorem integrableOn_iUnion_of_summable_integral_norm {f : α → E} {s : β → Set α}
-    (hs : ∀ b : β, MeasurableSet (s b)) (hi : ∀ b : β, IntegrableOn f (s b) μ)
-    (h : Summable fun b : β => ∫ a : α in s b, ‖f a‖ ∂μ) : IntegrableOn f (iUnion s) μ := by
+theorem integrableOn_iUnion_of_summable_integral_norm {f : X → E} {s : ι → Set X}
+    (hs : ∀ i : ι, MeasurableSet (s i)) (hi : ∀ i : ι, IntegrableOn f (s i) μ)
+    (h : Summable fun i : ι => ∫ x : X in s i, ‖f x‖ ∂μ) : IntegrableOn f (iUnion s) μ := by
   refine' ⟨AEStronglyMeasurable.iUnion fun i => (hi i).1, (lintegral_iUnion_le _ _).trans_lt _⟩
-  have B := fun b : β => lintegral_coe_eq_integral (fun a : α => ‖f a‖₊) (hi b).norm
+  have B := fun i => lintegral_coe_eq_integral (fun x : X => ‖f x‖₊) (hi i).norm
   rw [tsum_congr B]
   have S' :
-    Summable fun b : β =>
-      (⟨∫ a : α in s b, ‖f a‖₊ ∂μ, set_integral_nonneg (hs b) fun a _ => NNReal.coe_nonneg _⟩ :
+    Summable fun i : ι =>
+      (⟨∫ x : X in s i, ‖f x‖₊ ∂μ, set_integral_nonneg (hs i) fun x _ => NNReal.coe_nonneg _⟩ :
         NNReal) :=
     by rw [← NNReal.summable_coe]; exact h
   have S'' := ENNReal.tsum_coe_eq S'.hasSum
@@ -829,29 +829,29 @@ theorem integrableOn_iUnion_of_summable_integral_norm {f : α → E} {s : β →
   convert ENNReal.ofReal_lt_top
 #align measure_theory.integrable_on_Union_of_summable_integral_norm MeasureTheory.integrableOn_iUnion_of_summable_integral_norm
 
-variable [TopologicalSpace α] [BorelSpace α] [MetrizableSpace α] [IsLocallyFiniteMeasure μ]
+variable [TopologicalSpace X] [BorelSpace X] [MetrizableSpace X] [IsLocallyFiniteMeasure μ]
 
 /-- If `s` is a countable family of compact sets, `f` is a continuous function, and the sequence
 `‖f.restrict (s i)‖ * μ (s i)` is summable, then `f` is integrable on the union of the `s i`. -/
-theorem integrableOn_iUnion_of_summable_norm_restrict {f : C(α, E)} {s : β → Compacts α}
-    (hf : Summable fun i : β => ‖f.restrict (s i)‖ * ENNReal.toReal (μ <| s i)) :
-    IntegrableOn f (⋃ i : β, s i) μ := by
+theorem integrableOn_iUnion_of_summable_norm_restrict {f : C(X, E)} {s : ι → Compacts X}
+    (hf : Summable fun i : ι => ‖f.restrict (s i)‖ * ENNReal.toReal (μ <| s i)) :
+    IntegrableOn f (⋃ i : ι, s i) μ := by
   refine'
     integrableOn_iUnion_of_summable_integral_norm (fun i => (s i).isCompact.isClosed.measurableSet)
       (fun i => (map_continuous f).continuousOn.integrableOn_compact (s i).isCompact)
       (.of_nonneg_of_le (fun ι => integral_nonneg fun x => norm_nonneg _) (fun i => _) hf)
-  rw [← (Real.norm_of_nonneg (integral_nonneg fun a => norm_nonneg _) : ‖_‖ = ∫ x in s i, ‖f x‖ ∂μ)]
+  rw [← (Real.norm_of_nonneg (integral_nonneg fun x => norm_nonneg _) : ‖_‖ = ∫ x in s i, ‖f x‖ ∂μ)]
   exact
     norm_set_integral_le_of_norm_le_const' (s i).isCompact.measure_lt_top
       (s i).isCompact.isClosed.measurableSet fun x hx =>
-      (norm_norm (f x)).symm ▸ (f.restrict (s i : Set α)).norm_coe_le_norm ⟨x, hx⟩
+      (norm_norm (f x)).symm ▸ (f.restrict (s i : Set X)).norm_coe_le_norm ⟨x, hx⟩
 #align measure_theory.integrable_on_Union_of_summable_norm_restrict MeasureTheory.integrableOn_iUnion_of_summable_norm_restrict
 
-/-- If `s` is a countable family of compact sets covering `α`, `f` is a continuous function, and
+/-- If `s` is a countable family of compact sets covering `X`, `f` is a continuous function, and
 the sequence `‖f.restrict (s i)‖ * μ (s i)` is summable, then `f` is integrable. -/
-theorem integrable_of_summable_norm_restrict {f : C(α, E)} {s : β → Compacts α}
-    (hf : Summable fun i : β => ‖f.restrict (s i)‖ * ENNReal.toReal (μ <| s i))
-    (hs : ⋃ i : β, ↑(s i) = (univ : Set α)) : Integrable f μ := by
+theorem integrable_of_summable_norm_restrict {f : C(X, E)} {s : ι → Compacts X}
+    (hf : Summable fun i : ι => ‖f.restrict (s i)‖ * ENNReal.toReal (μ <| s i))
+    (hs : ⋃ i : ι, ↑(s i) = (univ : Set X)) : Integrable f μ := by
   simpa only [hs, integrableOn_univ] using integrableOn_iUnion_of_summable_norm_restrict hf
 #align measure_theory.integrable_of_summable_norm_restrict MeasureTheory.integrable_of_summable_norm_restrict
 
@@ -860,17 +860,17 @@ end IntegrableUnion
 /-! ### Continuity of the set integral
 
 We prove that for any set `s`, the function
-`fun f : α →₁[μ] E => ∫ x in s, f x ∂μ` is continuous. -/
+`fun f : X →₁[μ] E => ∫ x in s, f x ∂μ` is continuous. -/
 
 
 section ContinuousSetIntegral
 
 variable [NormedAddCommGroup E]
-  {𝕜 : Type*} [NormedField 𝕜] [NormedAddCommGroup F] [NormedSpace 𝕜 F] {p : ℝ≥0∞} {μ : Measure α}
+  {𝕜 : Type*} [NormedField 𝕜] [NormedAddCommGroup F] [NormedSpace 𝕜 F] {p : ℝ≥0∞} {μ : Measure X}
 
 /-- For `f : Lp E p μ`, we can define an element of `Lp E p (μ.restrict s)` by
 `(Lp.memℒp f).restrict s).toLp f`. This map is additive. -/
-theorem Lp_toLp_restrict_add (f g : Lp E p μ) (s : Set α) :
+theorem Lp_toLp_restrict_add (f g : Lp E p μ) (s : Set X) :
     ((Lp.memℒp (f + g)).restrict s).toLp (⇑(f + g)) =
       ((Lp.memℒp f).restrict s).toLp f + ((Lp.memℒp g).restrict s).toLp g := by
   ext1
@@ -887,7 +887,7 @@ set_option linter.uppercaseLean3 false in
 
 /-- For `f : Lp E p μ`, we can define an element of `Lp E p (μ.restrict s)` by
 `(Lp.memℒp f).restrict s).toLp f`. This map commutes with scalar multiplication. -/
-theorem Lp_toLp_restrict_smul (c : 𝕜) (f : Lp F p μ) (s : Set α) :
+theorem Lp_toLp_restrict_smul (c : 𝕜) (f : Lp F p μ) (s : Set X) :
     ((Lp.memℒp (c • f)).restrict s).toLp (⇑(c • f)) = c • ((Lp.memℒp f).restrict s).toLp f := by
   ext1
   refine' (ae_restrict_of_ae (Lp.coeFn_smul c f)).mp _
@@ -901,7 +901,7 @@ set_option linter.uppercaseLean3 false in
 
 /-- For `f : Lp E p μ`, we can define an element of `Lp E p (μ.restrict s)` by
 `(Lp.memℒp f).restrict s).toLp f`. This map is non-expansive. -/
-theorem norm_Lp_toLp_restrict_le (s : Set α) (f : Lp E p μ) :
+theorem norm_Lp_toLp_restrict_le (s : Set X) (f : Lp E p μ) :
     ‖((Lp.memℒp f).restrict s).toLp f‖ ≤ ‖f‖ := by
   rw [Lp.norm_def, Lp.norm_def, ENNReal.toReal_le_toReal (Lp.snorm_ne_top _) (Lp.snorm_ne_top _)]
   refine' (le_of_eq _).trans (snorm_mono_measure _ Measure.restrict_le_self)
@@ -909,10 +909,10 @@ theorem norm_Lp_toLp_restrict_le (s : Set α) (f : Lp E p μ) :
 set_option linter.uppercaseLean3 false in
 #align measure_theory.norm_Lp_to_Lp_restrict_le MeasureTheory.norm_Lp_toLp_restrict_le
 
-variable (α F 𝕜) in
+variable (X F 𝕜) in
 /-- Continuous linear map sending a function of `Lp F p μ` to the same function in
 `Lp F p (μ.restrict s)`. -/
-def LpToLpRestrictCLM (μ : Measure α) (p : ℝ≥0∞) [hp : Fact (1 ≤ p)] (s : Set α) :
+def LpToLpRestrictCLM (μ : Measure X) (p : ℝ≥0∞) [hp : Fact (1 ≤ p)] (s : Set X) :
     Lp F p μ →L[𝕜] Lp F p (μ.restrict s) :=
   @LinearMap.mkContinuous 𝕜 𝕜 (Lp F p μ) (Lp F p (μ.restrict s)) _ _ _ _ _ _ (RingHom.id 𝕜)
     ⟨⟨fun f => Memℒp.toLp f ((Lp.memℒp f).restrict s), fun f g => Lp_toLp_restrict_add f g s⟩,
@@ -922,23 +922,23 @@ set_option linter.uppercaseLean3 false in
 #align measure_theory.Lp_to_Lp_restrict_clm MeasureTheory.LpToLpRestrictCLM
 
 variable (𝕜) in
-theorem LpToLpRestrictCLM_coeFn [Fact (1 ≤ p)] (s : Set α) (f : Lp F p μ) :
-    LpToLpRestrictCLM α F 𝕜 μ p s f =ᵐ[μ.restrict s] f :=
+theorem LpToLpRestrictCLM_coeFn [Fact (1 ≤ p)] (s : Set X) (f : Lp F p μ) :
+    LpToLpRestrictCLM X F 𝕜 μ p s f =ᵐ[μ.restrict s] f :=
   Memℒp.coeFn_toLp ((Lp.memℒp f).restrict s)
 set_option linter.uppercaseLean3 false in
 #align measure_theory.Lp_to_Lp_restrict_clm_coe_fn MeasureTheory.LpToLpRestrictCLM_coeFn
 
 @[continuity]
-theorem continuous_set_integral [NormedSpace ℝ E] (s : Set α) :
-    Continuous fun f : α →₁[μ] E => ∫ x in s, f x ∂μ := by
+theorem continuous_set_integral [NormedSpace ℝ E] (s : Set X) :
+    Continuous fun f : X →₁[μ] E => ∫ x in s, f x ∂μ := by
   haveI : Fact ((1 : ℝ≥0∞) ≤ 1) := ⟨le_rfl⟩
   have h_comp :
-    (fun f : α →₁[μ] E => ∫ x in s, f x ∂μ) =
-      integral (μ.restrict s) ∘ fun f => LpToLpRestrictCLM α E ℝ μ 1 s f := by
+    (fun f : X →₁[μ] E => ∫ x in s, f x ∂μ) =
+      integral (μ.restrict s) ∘ fun f => LpToLpRestrictCLM X E ℝ μ 1 s f := by
     ext1 f
     rw [Function.comp_apply, integral_congr_ae (LpToLpRestrictCLM_coeFn ℝ s f)]
   rw [h_comp]
-  exact continuous_integral.comp (LpToLpRestrictCLM α E ℝ μ 1 s).continuous
+  exact continuous_integral.comp (LpToLpRestrictCLM X E ℝ μ 1 s).continuous
 #align measure_theory.continuous_set_integral MeasureTheory.continuous_set_integral
 
 end ContinuousSetIntegral
@@ -963,9 +963,9 @@ Often there is a good formula for `(μ (s i)).toReal`, so the formalization can
 argument `m` with this formula and a proof of `(fun i => (μ (s i)).toReal) =ᶠ[li] m`. Without these
 arguments, `m i = (μ (s i)).toReal` is used in the output. -/
 theorem Filter.Tendsto.integral_sub_linear_isLittleO_ae
-    {μ : Measure α} {l : Filter α} [l.IsMeasurablyGenerated] {f : α → E} {b : E}
+    {μ : Measure X} {l : Filter X} [l.IsMeasurablyGenerated] {f : X → E} {b : E}
     (h : Tendsto f (l ⊓ μ.ae) (𝓝 b)) (hfm : StronglyMeasurableAtFilter f l μ)
-    (hμ : μ.FiniteAtFilter l) {s : ι → Set α} {li : Filter ι} (hs : Tendsto s li l.smallSets)
+    (hμ : μ.FiniteAtFilter l) {s : ι → Set X} {li : Filter ι} (hs : Tendsto s li l.smallSets)
     (m : ι → ℝ := fun i => (μ (s i)).toReal)
     (hsμ : (fun i => (μ (s i)).toReal) =ᶠ[li] m := by rfl) :
     (fun i => (∫ x in s i, f x ∂μ) - m i • b) =o[li] m := by
@@ -994,15 +994,15 @@ number, we use `(μ (s i)).toReal` in the actual statement.
 Often there is a good formula for `(μ (s i)).toReal`, so the formalization can take an optional
 argument `m` with this formula and a proof of `(fun i => (μ (s i)).toReal) =ᶠ[li] m`. Without these
 arguments, `m i = (μ (s i)).toReal` is used in the output. -/
-theorem ContinuousWithinAt.integral_sub_linear_isLittleO_ae [TopologicalSpace α]
-    [OpensMeasurableSpace α] {μ : Measure α}
-    [IsLocallyFiniteMeasure μ] {a : α} {t : Set α} {f : α → E} (ha : ContinuousWithinAt f t a)
-    (ht : MeasurableSet t) (hfm : StronglyMeasurableAtFilter f (𝓝[t] a) μ) {s : ι → Set α}
-    {li : Filter ι} (hs : Tendsto s li (𝓝[t] a).smallSets) (m : ι → ℝ := fun i => (μ (s i)).toReal)
+theorem ContinuousWithinAt.integral_sub_linear_isLittleO_ae [TopologicalSpace X]
+    [OpensMeasurableSpace X] {μ : Measure X}
+    [IsLocallyFiniteMeasure μ] {x : X} {t : Set X} {f : X → E} (hx : ContinuousWithinAt f t x)
+    (ht : MeasurableSet t) (hfm : StronglyMeasurableAtFilter f (𝓝[t] x) μ) {s : ι → Set X}
+    {li : Filter ι} (hs : Tendsto s li (𝓝[t] x).smallSets) (m : ι → ℝ := fun i => (μ (s i)).toReal)
     (hsμ : (fun i => (μ (s i)).toReal) =ᶠ[li] m := by rfl) :
-    (fun i => (∫ x in s i, f x ∂μ) - m i • f a) =o[li] m :=
-  haveI : (𝓝[t] a).IsMeasurablyGenerated := ht.nhdsWithin_isMeasurablyGenerated _
-  (ha.mono_left inf_le_left).integral_sub_linear_isLittleO_ae hfm (μ.finiteAt_nhdsWithin a t) hs m
+    (fun i => (∫ x in s i, f x ∂μ) - m i • f x) =o[li] m :=
+  haveI : (𝓝[t] x).IsMeasurablyGenerated := ht.nhdsWithin_isMeasurablyGenerated _
+  (hx.mono_left inf_le_left).integral_sub_linear_isLittleO_ae hfm (μ.finiteAt_nhdsWithin x t) hs m
     hsμ
 #align continuous_within_at.integral_sub_linear_is_o_ae ContinuousWithinAt.integral_sub_linear_isLittleO_ae
 
@@ -1015,13 +1015,13 @@ the actual statement.
 Often there is a good formula for `(μ (s i)).toReal`, so the formalization can take an optional
 argument `m` with this formula and a proof of `(fun i => (μ (s i)).toReal) =ᶠ[li] m`. Without these
 arguments, `m i = (μ (s i)).toReal` is used in the output. -/
-theorem ContinuousAt.integral_sub_linear_isLittleO_ae [TopologicalSpace α] [OpensMeasurableSpace α]
-    {μ : Measure α} [IsLocallyFiniteMeasure μ] {a : α}
-    {f : α → E} (ha : ContinuousAt f a) (hfm : StronglyMeasurableAtFilter f (𝓝 a) μ) {s : ι → Set α}
-    {li : Filter ι} (hs : Tendsto s li (𝓝 a).smallSets) (m : ι → ℝ := fun i => (μ (s i)).toReal)
+theorem ContinuousAt.integral_sub_linear_isLittleO_ae [TopologicalSpace X] [OpensMeasurableSpace X]
+    {μ : Measure X} [IsLocallyFiniteMeasure μ] {x : X}
+    {f : X → E} (hx : ContinuousAt f x) (hfm : StronglyMeasurableAtFilter f (𝓝 x) μ) {s : ι → Set X}
+    {li : Filter ι} (hs : Tendsto s li (𝓝 x).smallSets) (m : ι → ℝ := fun i => (μ (s i)).toReal)
     (hsμ : (fun i => (μ (s i)).toReal) =ᶠ[li] m := by rfl) :
-    (fun i => (∫ x in s i, f x ∂μ) - m i • f a) =o[li] m :=
-  (ha.mono_left inf_le_left).integral_sub_linear_isLittleO_ae hfm (μ.finiteAt_nhds a) hs m hsμ
+    (fun i => (∫ x in s i, f x ∂μ) - m i • f x) =o[li] m :=
+  (hx.mono_left inf_le_left).integral_sub_linear_isLittleO_ae hfm (μ.finiteAt_nhds x) hs m hsμ
 #align continuous_at.integral_sub_linear_is_o_ae ContinuousAt.integral_sub_linear_isLittleO_ae
 
 /-- Fundamental theorem of calculus for set integrals, `nhdsWithin` version: if `μ` is a locally
@@ -1032,14 +1032,14 @@ Since `μ (s i)` is an `ℝ≥0∞` number, we use `(μ (s i)).toReal` in the ac
 Often there is a good formula for `(μ (s i)).toReal`, so the formalization can take an optional
 argument `m` with this formula and a proof of `(fun i => (μ (s i)).toReal) =ᶠ[li] m`. Without these
 arguments, `m i = (μ (s i)).toReal` is used in the output. -/
-theorem ContinuousOn.integral_sub_linear_isLittleO_ae [TopologicalSpace α] [OpensMeasurableSpace α]
-    [SecondCountableTopologyEither α E] {μ : Measure α}
-    [IsLocallyFiniteMeasure μ] {a : α} {t : Set α} {f : α → E} (hft : ContinuousOn f t) (ha : a ∈ t)
-    (ht : MeasurableSet t) {s : ι → Set α} {li : Filter ι} (hs : Tendsto s li (𝓝[t] a).smallSets)
+theorem ContinuousOn.integral_sub_linear_isLittleO_ae [TopologicalSpace X] [OpensMeasurableSpace X]
+    [SecondCountableTopologyEither X E] {μ : Measure X}
+    [IsLocallyFiniteMeasure μ] {x : X} {t : Set X} {f : X → E} (hft : ContinuousOn f t) (hx : x ∈ t)
+    (ht : MeasurableSet t) {s : ι → Set X} {li : Filter ι} (hs : Tendsto s li (𝓝[t] x).smallSets)
     (m : ι → ℝ := fun i => (μ (s i)).toReal)
     (hsμ : (fun i => (μ (s i)).toReal) =ᶠ[li] m := by rfl) :
-    (fun i => (∫ x in s i, f x ∂μ) - m i • f a) =o[li] m :=
-  (hft a ha).integral_sub_linear_isLittleO_ae ht
+    (fun i => (∫ x in s i, f x ∂μ) - m i • f x) =o[li] m :=
+  (hft x hx).integral_sub_linear_isLittleO_ae ht
     ⟨t, self_mem_nhdsWithin, hft.aestronglyMeasurable ht⟩ hs m hsμ
 #align continuous_on.integral_sub_linear_is_o_ae ContinuousOn.integral_sub_linear_isLittleO_ae
 
@@ -1058,7 +1058,7 @@ as `ContinuousLinearMap.compLp`. We take advantage of this construction here.
 
 open scoped ComplexConjugate
 
-variable {μ : Measure α} {𝕜 : Type*} [IsROrC 𝕜] [NormedAddCommGroup E] [NormedSpace 𝕜 E]
+variable {μ : Measure X} {𝕜 : Type*} [IsROrC 𝕜] [NormedAddCommGroup E] [NormedSpace 𝕜 E]
   [NormedAddCommGroup F] [NormedSpace 𝕜 F] {p : ENNReal}
 
 namespace ContinuousLinearMap
@@ -1066,28 +1066,28 @@ namespace ContinuousLinearMap
 variable [NormedSpace ℝ F]
 
 theorem integral_compLp (L : E →L[𝕜] F) (φ : Lp E p μ) :
-    ∫ a, (L.compLp φ) a ∂μ = ∫ a, L (φ a) ∂μ :=
+    ∫ x, (L.compLp φ) x ∂μ = ∫ x, L (φ x) ∂μ :=
   integral_congr_ae <| coeFn_compLp _ _
 set_option linter.uppercaseLean3 false in
 #align continuous_linear_map.integral_comp_Lp ContinuousLinearMap.integral_compLp
 
-theorem set_integral_compLp (L : E →L[𝕜] F) (φ : Lp E p μ) {s : Set α} (hs : MeasurableSet s) :
-    ∫ a in s, (L.compLp φ) a ∂μ = ∫ a in s, L (φ a) ∂μ :=
+theorem set_integral_compLp (L : E →L[𝕜] F) (φ : Lp E p μ) {s : Set X} (hs : MeasurableSet s) :
+    ∫ x in s, (L.compLp φ) x ∂μ = ∫ x in s, L (φ x) ∂μ :=
   set_integral_congr_ae hs ((L.coeFn_compLp φ).mono fun _x hx _ => hx)
 set_option linter.uppercaseLean3 false in
 #align continuous_linear_map.set_integral_comp_Lp ContinuousLinearMap.set_integral_compLp
 
 theorem continuous_integral_comp_L1 (L : E →L[𝕜] F) :
-    Continuous fun φ : α →₁[μ] E => ∫ a : α, L (φ a) ∂μ := by
+    Continuous fun φ : X →₁[μ] E => ∫ x : X, L (φ x) ∂μ := by
   rw [← funext L.integral_compLp]; exact continuous_integral.comp (L.compLpL 1 μ).continuous
 set_option linter.uppercaseLean3 false in
 #align continuous_linear_map.continuous_integral_comp_L1 ContinuousLinearMap.continuous_integral_comp_L1
 
 variable [CompleteSpace E] [CompleteSpace F] [NormedSpace ℝ E]
 
-theorem integral_comp_comm (L : E →L[𝕜] F) {φ : α → E} (φ_int : Integrable φ μ) :
-    ∫ a, L (φ a) ∂μ = L (∫ a, φ a ∂μ) := by
-  apply φ_int.induction (P := fun φ => ∫ a, L (φ a) ∂μ = L (∫ a, φ a ∂μ))
+theorem integral_comp_comm (L : E →L[𝕜] F) {φ : X → E} (φ_int : Integrable φ μ) :
+    ∫ x, L (φ x) ∂μ = L (∫ x, φ x ∂μ) := by
+  apply φ_int.induction (P := fun φ => ∫ x, L (φ x) ∂μ = L (∫ x, φ x ∂μ))
   · intro e s s_meas _
     rw [integral_indicator_const e s_meas, ← @smul_one_smul E ℝ 𝕜 _ _ _ _ _ (μ s).toReal e,
       ContinuousLinearMap.map_smul, @smul_one_smul F ℝ 𝕜 _ _ _ _ _ (μ s).toReal (L e), ←
@@ -1104,23 +1104,23 @@ theorem integral_comp_comm (L : E →L[𝕜] F) {φ : α → E} (φ_int : Integr
     · rw [integral_congr_ae hfg.symm]
 #align continuous_linear_map.integral_comp_comm ContinuousLinearMap.integral_comp_comm
 
-theorem integral_apply {H : Type*} [NormedAddCommGroup H] [NormedSpace 𝕜 H] {φ : α → H →L[𝕜] E}
-    (φ_int : Integrable φ μ) (v : H) : (∫ a, φ a ∂μ) v = ∫ a, φ a v ∂μ :=
+theorem integral_apply {H : Type*} [NormedAddCommGroup H] [NormedSpace 𝕜 H] {φ : X → H →L[𝕜] E}
+    (φ_int : Integrable φ μ) (v : H) : (∫ x, φ x ∂μ) v = ∫ x, φ x v ∂μ :=
   ((ContinuousLinearMap.apply 𝕜 E v).integral_comp_comm φ_int).symm
 #align continuous_linear_map.integral_apply ContinuousLinearMap.integral_apply
 
-theorem integral_comp_comm' (L : E →L[𝕜] F) {K} (hL : AntilipschitzWith K L) (φ : α → E) :
-    ∫ a, L (φ a) ∂μ = L (∫ a, φ a ∂μ) := by
+theorem integral_comp_comm' (L : E →L[𝕜] F) {K} (hL : AntilipschitzWith K L) (φ : X → E) :
+    ∫ x, L (φ x) ∂μ = L (∫ x, φ x ∂μ) := by
   by_cases h : Integrable φ μ
   · exact integral_comp_comm L h
-  have : ¬Integrable (fun a => L (φ a)) μ := by
+  have : ¬Integrable (fun x => L (φ x)) μ := by
     rwa [← Function.comp_def,
       LipschitzWith.integrable_comp_iff_of_antilipschitz L.lipschitz hL L.map_zero]
   simp [integral_undef, h, this]
 #align continuous_linear_map.integral_comp_comm' ContinuousLinearMap.integral_comp_comm'
 
-theorem integral_comp_L1_comm (L : E →L[𝕜] F) (φ : α →₁[μ] E) :
-    ∫ a, L (φ a) ∂μ = L (∫ a, φ a ∂μ) :=
+theorem integral_comp_L1_comm (L : E →L[𝕜] F) (φ : X →₁[μ] E) :
+    ∫ x, L (φ x) ∂μ = L (∫ x, φ x ∂μ) :=
   L.integral_comp_comm (L1.integrable_coeFn φ)
 set_option linter.uppercaseLean3 false in
 #align continuous_linear_map.integral_comp_L1_comm ContinuousLinearMap.integral_comp_L1_comm
@@ -1131,7 +1131,7 @@ namespace LinearIsometry
 
 variable [CompleteSpace F] [NormedSpace ℝ F] [CompleteSpace E] [NormedSpace ℝ E]
 
-theorem integral_comp_comm (L : E →ₗᵢ[𝕜] F) (φ : α → E) : ∫ a, L (φ a) ∂μ = L (∫ a, φ a ∂μ) :=
+theorem integral_comp_comm (L : E →ₗᵢ[𝕜] F) (φ : X → E) : ∫ x, L (φ x) ∂μ = L (∫ x, φ x ∂μ) :=
   L.toContinuousLinearMap.integral_comp_comm' L.antilipschitz _
 #align linear_isometry.integral_comp_comm LinearIsometry.integral_comp_comm
 
@@ -1141,7 +1141,7 @@ namespace ContinuousLinearEquiv
 
 variable [NormedSpace ℝ F] [NormedSpace ℝ E]
 
-theorem integral_comp_comm (L : E ≃L[𝕜] F) (φ : α → E) : ∫ a, L (φ a) ∂μ = L (∫ a, φ a ∂μ) := by
+theorem integral_comp_comm (L : E ≃L[𝕜] F) (φ : X → E) : ∫ x, L (φ x) ∂μ = L (∫ x, φ x ∂μ) := by
   have : CompleteSpace E ↔ CompleteSpace F :=
     completeSpace_congr (e := L.toEquiv) L.uniformEmbedding
   obtain ⟨_, _⟩|⟨_, _⟩ := iff_iff_and_or_not_and_not.mp this
@@ -1152,25 +1152,25 @@ theorem integral_comp_comm (L : E ≃L[𝕜] F) (φ : α → E) : ∫ a, L (φ a
 end ContinuousLinearEquiv
 
 @[norm_cast]
-theorem integral_ofReal {f : α → ℝ} : ∫ a, (f a : 𝕜) ∂μ = ↑(∫ a, f a ∂μ) :=
+theorem integral_ofReal {f : X → ℝ} : ∫ x, (f x : 𝕜) ∂μ = ↑(∫ x, f x ∂μ) :=
   (@IsROrC.ofRealLI 𝕜 _).integral_comp_comm f
 #align integral_of_real integral_ofReal
 
-theorem integral_re {f : α → 𝕜} (hf : Integrable f μ) :
-    ∫ a, IsROrC.re (f a) ∂μ = IsROrC.re (∫ a, f a ∂μ) :=
+theorem integral_re {f : X → 𝕜} (hf : Integrable f μ) :
+    ∫ x, IsROrC.re (f x) ∂μ = IsROrC.re (∫ x, f x ∂μ) :=
   (@IsROrC.reCLM 𝕜 _).integral_comp_comm hf
 #align integral_re integral_re
 
-theorem integral_im {f : α → 𝕜} (hf : Integrable f μ) :
-    ∫ a, IsROrC.im (f a) ∂μ = IsROrC.im (∫ a, f a ∂μ) :=
+theorem integral_im {f : X → 𝕜} (hf : Integrable f μ) :
+    ∫ x, IsROrC.im (f x) ∂μ = IsROrC.im (∫ x, f x ∂μ) :=
   (@IsROrC.imCLM 𝕜 _).integral_comp_comm hf
 #align integral_im integral_im
 
-theorem integral_conj {f : α → 𝕜} : ∫ a, conj (f a) ∂μ = conj (∫ a, f a ∂μ) :=
+theorem integral_conj {f : X → 𝕜} : ∫ x, conj (f x) ∂μ = conj (∫ x, f x ∂μ) :=
   (@IsROrC.conjLIE 𝕜 _).toLinearIsometry.integral_comp_comm f
 #align integral_conj integral_conj
 
-theorem integral_coe_re_add_coe_im {f : α → 𝕜} (hf : Integrable f μ) :
+theorem integral_coe_re_add_coe_im {f : X → 𝕜} (hf : Integrable f μ) :
     ∫ x, (IsROrC.re (f x) : 𝕜) ∂μ + (∫ x, (IsROrC.im (f x) : 𝕜) ∂μ) * IsROrC.I = ∫ x, f x ∂μ := by
   rw [mul_comm, ← smul_eq_mul, ← integral_smul, ← integral_add]
   · congr
@@ -1180,13 +1180,13 @@ theorem integral_coe_re_add_coe_im {f : α → 𝕜} (hf : Integrable f μ) :
   · exact hf.im.ofReal.smul (𝕜 := 𝕜) (β := 𝕜) IsROrC.I
 #align integral_coe_re_add_coe_im integral_coe_re_add_coe_im
 
-theorem integral_re_add_im {f : α → 𝕜} (hf : Integrable f μ) :
+theorem integral_re_add_im {f : X → 𝕜} (hf : Integrable f μ) :
     ((∫ x, IsROrC.re (f x) ∂μ : ℝ) : 𝕜) + (∫ x, IsROrC.im (f x) ∂μ : ℝ) * IsROrC.I =
       ∫ x, f x ∂μ := by
   rw [← integral_ofReal, ← integral_ofReal, integral_coe_re_add_coe_im hf]
 #align integral_re_add_im integral_re_add_im
 
-theorem set_integral_re_add_im {f : α → 𝕜} {i : Set α} (hf : IntegrableOn f i μ) :
+theorem set_integral_re_add_im {f : X → 𝕜} {i : Set X} (hf : IntegrableOn f i μ) :
     ((∫ x in i, IsROrC.re (f x) ∂μ : ℝ) : 𝕜) + (∫ x in i, IsROrC.im (f x) ∂μ : ℝ) * IsROrC.I =
       ∫ x in i, f x ∂μ :=
   integral_re_add_im hf
@@ -1194,10 +1194,10 @@ theorem set_integral_re_add_im {f : α → 𝕜} {i : Set α} (hf : IntegrableOn
 
 variable [NormedSpace ℝ E] [NormedSpace ℝ F]
 
-lemma swap_integral (f : α → E × F) : (∫ x, f x ∂μ).swap = ∫ x, (f x).swap ∂μ :=
+lemma swap_integral (f : X → E × F) : (∫ x, f x ∂μ).swap = ∫ x, (f x).swap ∂μ :=
   .symm <| (ContinuousLinearEquiv.prodComm ℝ E F).integral_comp_comm f
 
-theorem fst_integral [CompleteSpace F] {f : α → E × F} (hf : Integrable f μ) :
+theorem fst_integral [CompleteSpace F] {f : X → E × F} (hf : Integrable f μ) :
     (∫ x, f x ∂μ).1 = ∫ x, (f x).1 ∂μ := by
   by_cases hE : CompleteSpace E
   · exact ((ContinuousLinearMap.fst ℝ E F).integral_comp_comm hf).symm
@@ -1205,13 +1205,13 @@ theorem fst_integral [CompleteSpace F] {f : α → E × F} (hf : Integrable f μ
     simp [integral, *]
 #align fst_integral fst_integral
 
-theorem snd_integral [CompleteSpace E] {f : α → E × F} (hf : Integrable f μ) :
+theorem snd_integral [CompleteSpace E] {f : X → E × F} (hf : Integrable f μ) :
     (∫ x, f x ∂μ).2 = ∫ x, (f x).2 ∂μ := by
   rw [← Prod.fst_swap, swap_integral]
   exact fst_integral <| hf.snd.prod_mk hf.fst
 #align snd_integral snd_integral
 
-theorem integral_pair [CompleteSpace E] [CompleteSpace F] {f : α → E} {g : α → F}
+theorem integral_pair [CompleteSpace E] [CompleteSpace F] {f : X → E} {g : X → F}
     (hf : Integrable f μ) (hg : Integrable g μ) :
     ∫ x, (f x, g x) ∂μ = (∫ x, f x ∂μ, ∫ x, g x ∂μ) :=
   have := hf.prod_mk hg
@@ -1219,7 +1219,7 @@ theorem integral_pair [CompleteSpace E] [CompleteSpace F] {f : α → E} {g : α
 #align integral_pair integral_pair
 
 theorem integral_smul_const {𝕜 : Type*} [IsROrC 𝕜] [NormedSpace 𝕜 E] [CompleteSpace E]
-    (f : α → 𝕜) (c : E) :
+    (f : X → 𝕜) (c : E) :
     ∫ x, f x • c ∂μ = (∫ x, f x ∂μ) • c := by
   by_cases hf : Integrable f μ
   · exact ((1 : 𝕜 →L[𝕜] 𝕜).smulRight c).integral_comp_comm hf
@@ -1230,14 +1230,14 @@ theorem integral_smul_const {𝕜 : Type*} [IsROrC 𝕜] [NormedSpace 𝕜 E] [C
     simp_rw [hf, not_false_eq_true]
 #align integral_smul_const integral_smul_const
 
-theorem integral_withDensity_eq_integral_smul {f : α → ℝ≥0} (f_meas : Measurable f) (g : α → E) :
-    ∫ a, g a ∂μ.withDensity (fun x => f x) = ∫ a, f a • g a ∂μ := by
+theorem integral_withDensity_eq_integral_smul {f : X → ℝ≥0} (f_meas : Measurable f) (g : X → E) :
+    ∫ x, g x ∂μ.withDensity (fun x => f x) = ∫ x, f x • g x ∂μ := by
   by_cases hE : CompleteSpace E; swap; · simp [integral, hE]
   by_cases hg : Integrable g (μ.withDensity fun x => f x); swap
   · rw [integral_undef hg, integral_undef]
     rwa [← integrable_withDensity_iff_integrable_smul f_meas]
   refine' Integrable.induction
-    (P := fun g => ∫ a, g a ∂μ.withDensity (fun x => f x) = ∫ a, f a • g a ∂μ) _ _ _ _ hg
+    (P := fun g => ∫ x, g x ∂μ.withDensity (fun x => f x) = ∫ x, f x • g x ∂μ) _ _ _ _ hg
   · intro c s s_meas hs
     rw [integral_indicator s_meas]
     simp_rw [← indicator_smul_apply, integral_indicator s_meas]
@@ -1252,7 +1252,7 @@ theorem integral_withDensity_eq_integral_smul {f : α → ℝ≥0} (f_meas : Mea
       simp only [NNReal.nnnorm_eq]
   · intro u u' _ u_int u'_int h h'
     change
-      (∫ a : α, u a + u' a ∂μ.withDensity fun x : α => ↑(f x)) = ∫ a : α, f a • (u a + u' a) ∂μ
+      (∫ x : X, u x + u' x ∂μ.withDensity fun x : X => ↑(f x)) = ∫ x : X, f x • (u x + u' x) ∂μ
     simp_rw [smul_add]
     rw [integral_add u_int u'_int, h, h', integral_add]
     · exact (integrable_withDensity_iff_integrable_smul f_meas).1 u_int
@@ -1278,47 +1278,47 @@ theorem integral_withDensity_eq_integral_smul {f : α → ℝ≥0} (f_meas : Mea
       simpa only [Ne.def, ENNReal.coe_eq_zero] using h'x
 #align integral_with_density_eq_integral_smul integral_withDensity_eq_integral_smul
 
-theorem integral_withDensity_eq_integral_smul₀ {f : α → ℝ≥0} (hf : AEMeasurable f μ) (g : α → E) :
-    ∫ a, g a ∂μ.withDensity (fun x => f x) = ∫ a, f a • g a ∂μ := by
+theorem integral_withDensity_eq_integral_smul₀ {f : X → ℝ≥0} (hf : AEMeasurable f μ) (g : X → E) :
+    ∫ x, g x ∂μ.withDensity (fun x => f x) = ∫ x, f x • g x ∂μ := by
   let f' := hf.mk _
   calc
-    ∫ a, g a ∂μ.withDensity (fun x => f x) = ∫ a, g a ∂μ.withDensity fun x => f' x := by
+    ∫ x, g x ∂μ.withDensity (fun x => f x) = ∫ x, g x ∂μ.withDensity fun x => f' x := by
       congr 1
       apply withDensity_congr_ae
       filter_upwards [hf.ae_eq_mk] with x hx
       rw [hx]
-    _ = ∫ a, f' a • g a ∂μ := (integral_withDensity_eq_integral_smul hf.measurable_mk _)
-    _ = ∫ a, f a • g a ∂μ := by
+    _ = ∫ x, f' x • g x ∂μ := (integral_withDensity_eq_integral_smul hf.measurable_mk _)
+    _ = ∫ x, f x • g x ∂μ := by
       apply integral_congr_ae
       filter_upwards [hf.ae_eq_mk] with x hx
       rw [hx]
 #align integral_with_density_eq_integral_smul₀ integral_withDensity_eq_integral_smul₀
 
-theorem set_integral_withDensity_eq_set_integral_smul {f : α → ℝ≥0} (f_meas : Measurable f)
-    (g : α → E) {s : Set α} (hs : MeasurableSet s) :
-    ∫ a in s, g a ∂μ.withDensity (fun x => f x) = ∫ a in s, f a • g a ∂μ := by
+theorem set_integral_withDensity_eq_set_integral_smul {f : X → ℝ≥0} (f_meas : Measurable f)
+    (g : X → E) {s : Set X} (hs : MeasurableSet s) :
+    ∫ x in s, g x ∂μ.withDensity (fun x => f x) = ∫ x in s, f x • g x ∂μ := by
   rw [restrict_withDensity hs, integral_withDensity_eq_integral_smul f_meas]
 #align set_integral_with_density_eq_set_integral_smul set_integral_withDensity_eq_set_integral_smul
 
-theorem set_integral_withDensity_eq_set_integral_smul₀ {f : α → ℝ≥0} {s : Set α}
-    (hf : AEMeasurable f (μ.restrict s)) (g : α → E) (hs : MeasurableSet s) :
-    ∫ a in s, g a ∂μ.withDensity (fun x => f x) = ∫ a in s, f a • g a ∂μ := by
+theorem set_integral_withDensity_eq_set_integral_smul₀ {f : X → ℝ≥0} {s : Set X}
+    (hf : AEMeasurable f (μ.restrict s)) (g : X → E) (hs : MeasurableSet s) :
+    ∫ x in s, g x ∂μ.withDensity (fun x => f x) = ∫ x in s, f x • g x ∂μ := by
   rw [restrict_withDensity hs, integral_withDensity_eq_integral_smul₀ hf]
 #align set_integral_with_density_eq_set_integral_smul₀ set_integral_withDensity_eq_set_integral_smul₀
 
-theorem set_integral_withDensity_eq_set_integral_smul₀' [SFinite μ] {f : α → ℝ≥0} (s : Set α)
-    (hf : AEMeasurable f (μ.restrict s)) (g : α → E)  :
-    ∫ a in s, g a ∂μ.withDensity (fun x => f x) = ∫ a in s, f a • g a ∂μ := by
+theorem set_integral_withDensity_eq_set_integral_smul₀' [SFinite μ] {f : X → ℝ≥0} (s : Set X)
+    (hf : AEMeasurable f (μ.restrict s)) (g : X → E)  :
+    ∫ x in s, g x ∂μ.withDensity (fun x => f x) = ∫ x in s, f x • g x ∂μ := by
   rw [restrict_withDensity' s, integral_withDensity_eq_integral_smul₀ hf]
 
 end
 
 section thickenedIndicator
 
-variable [PseudoEMetricSpace α]
+variable [PseudoEMetricSpace X]
 
-theorem measure_le_lintegral_thickenedIndicatorAux (μ : Measure α) {E : Set α}
-    (E_mble : MeasurableSet E) (δ : ℝ) : μ E ≤ ∫⁻ a, (thickenedIndicatorAux δ E a : ℝ≥0∞) ∂μ := by
+theorem measure_le_lintegral_thickenedIndicatorAux (μ : Measure X) {E : Set X}
+    (E_mble : MeasurableSet E) (δ : ℝ) : μ E ≤ ∫⁻ x, (thickenedIndicatorAux δ E x : ℝ≥0∞) ∂μ := by
   convert_to lintegral μ (E.indicator fun _ => (1 : ℝ≥0∞)) ≤ lintegral μ (thickenedIndicatorAux δ E)
   · rw [lintegral_indicator _ E_mble]
     simp only [lintegral_one, Measure.restrict_apply, MeasurableSet.univ, univ_inter]
@@ -1326,9 +1326,9 @@ theorem measure_le_lintegral_thickenedIndicatorAux (μ : Measure α) {E : Set α
     apply indicator_le_thickenedIndicatorAux
 #align measure_le_lintegral_thickened_indicator_aux measure_le_lintegral_thickenedIndicatorAux
 
-theorem measure_le_lintegral_thickenedIndicator (μ : Measure α) {E : Set α}
+theorem measure_le_lintegral_thickenedIndicator (μ : Measure X) {E : Set X}
     (E_mble : MeasurableSet E) {δ : ℝ} (δ_pos : 0 < δ) :
-    μ E ≤ ∫⁻ a, (thickenedIndicator δ_pos E a : ℝ≥0∞) ∂μ := by
+    μ E ≤ ∫⁻ x, (thickenedIndicator δ_pos E x : ℝ≥0∞) ∂μ := by
   convert measure_le_lintegral_thickenedIndicatorAux μ E_mble δ
   dsimp
   simp only [thickenedIndicatorAux_lt_top.ne, ENNReal.coe_toNNReal, Ne.def, not_false_iff]
@@ -1340,9 +1340,9 @@ section BilinearMap
 
 namespace MeasureTheory
 
-variable {f : β → ℝ} {m m0 : MeasurableSpace β} {μ : Measure β}
+variable {f : X → ℝ} {m m0 : MeasurableSpace X} {μ : Measure X}
 
-theorem Integrable.simpleFunc_mul (g : SimpleFunc β ℝ) (hf : Integrable f μ) :
+theorem Integrable.simpleFunc_mul (g : SimpleFunc X ℝ) (hf : Integrable f μ) :
     Integrable (⇑g * f) μ := by
   refine'
     SimpleFunc.induction (fun c s hs => _)
@@ -1351,7 +1351,7 @@ theorem Integrable.simpleFunc_mul (g : SimpleFunc β ℝ) (hf : Integrable f μ)
       g
   simp only [SimpleFunc.const_zero, SimpleFunc.coe_piecewise, SimpleFunc.coe_const,
     SimpleFunc.coe_zero, Set.piecewise_eq_indicator]
-  have : Set.indicator s (Function.const β c) * f = s.indicator (c • f) := by
+  have : Set.indicator s (Function.const X c) * f = s.indicator (c • f) := by
     ext1 x
     by_cases hx : x ∈ s
     · simp only [hx, Pi.mul_apply, Set.indicator_of_mem, Pi.smul_apply, Algebra.id.smul_eq_mul,
@@ -1361,7 +1361,7 @@ theorem Integrable.simpleFunc_mul (g : SimpleFunc β ℝ) (hf : Integrable f μ)
   exact (hf.smul c).integrableOn
 #align measure_theory.integrable.simple_func_mul MeasureTheory.Integrable.simpleFunc_mul
 
-theorem Integrable.simpleFunc_mul' (hm : m ≤ m0) (g : @SimpleFunc β m ℝ) (hf : Integrable f μ) :
+theorem Integrable.simpleFunc_mul' (hm : m ≤ m0) (g : @SimpleFunc X m ℝ) (hf : Integrable f μ) :
     Integrable (⇑g * f) μ := by
   rw [← SimpleFunc.coe_toLargerSpace_eq hm g]; exact hf.simpleFunc_mul (g.toLargerSpace hm)
 #align measure_theory.integrable.simple_func_mul' MeasureTheory.Integrable.simpleFunc_mul'
@@ -1372,10 +1372,9 @@ end BilinearMap
 
 section ParametricIntegral
 
-variable [NormedAddCommGroup E]
-
-variable {α β F G 𝕜 : Type*} [TopologicalSpace α] [TopologicalSpace β] [MeasurableSpace β]
-  [OpensMeasurableSpace β] {μ : Measure β} [NontriviallyNormedField 𝕜] [NormedSpace ℝ E]
+variable {X Y F G 𝕜 : Type*} [TopologicalSpace X]
+  [TopologicalSpace Y] [MeasurableSpace Y] [OpensMeasurableSpace Y] {μ : Measure Y}
+  [NontriviallyNormedField 𝕜] [NormedAddCommGroup E] [NormedSpace ℝ E]
   [NormedAddCommGroup F] [NormedSpace 𝕜 F] [NormedAddCommGroup G] [NormedSpace 𝕜 G]
 
 open Metric ContinuousLinearMap
@@ -1385,12 +1384,12 @@ open Metric ContinuousLinearMap
 integral depends continuously on `a`. -/
 lemma continuousOn_integral_bilinear_of_locally_integrable_of_compact_support
     [NormedSpace 𝕜 E] (L : F →L[𝕜] G →L[𝕜] E)
-    {f : α → β → G} {s : Set α} {k : Set β} {g : β → F}
+    {f : X → Y → G} {s : Set X} {k : Set Y} {g : Y → F}
     (hk : IsCompact k) (hf : ContinuousOn f.uncurry (s ×ˢ univ))
     (hfs : ∀ p, ∀ x, p ∈ s → x ∉ k → f p x = 0) (hg : IntegrableOn g k μ) :
     ContinuousOn (fun a ↦ ∫ x, L (g x) (f a x) ∂μ) s := by
   have A : ∀ p ∈ s, Continuous (f p) := fun p hp ↦ by
-    refine hf.comp_continuous (continuous_const.prod_mk continuous_id') fun x => ?_
+    refine hf.comp_continuous (continuous_const.prod_mk continuous_id') fun y => ?_
     simpa only [prod_mk_mem_set_prod_eq, mem_univ, and_true] using hp
   intro q hq
   apply Metric.continuousWithinAt_iff'.2 (fun ε εpos ↦ ?_)
@@ -1400,26 +1399,26 @@ lemma continuousOn_integral_bilinear_of_locally_integrable_of_compact_support
     hk.mem_uniformity_of_prod
       (hf.mono (Set.prod_mono_right (subset_univ k))) hq (dist_mem_uniformity δpos)
   simp_rw [dist_eq_norm] at hv ⊢
-  have I : ∀ p ∈ s, IntegrableOn (fun x ↦ L (g x) (f p x)) k μ := by
+  have I : ∀ p ∈ s, IntegrableOn (fun y ↦ L (g y) (f p y)) k μ := by
     intro p hp
-    obtain ⟨C, hC⟩ : ∃ C, ∀ x, ‖f p x‖ ≤ C := by
+    obtain ⟨C, hC⟩ : ∃ C, ∀ y, ‖f p y‖ ≤ C := by
       have : ContinuousOn (f p) k := by
-        have : ContinuousOn (fun x ↦ (p, x)) k := (Continuous.Prod.mk p).continuousOn
+        have : ContinuousOn (fun y ↦ (p, y)) k := (Continuous.Prod.mk p).continuousOn
         exact hf.comp this (by simp [MapsTo, hp])
       rcases IsCompact.exists_bound_of_continuousOn hk this with ⟨C, hC⟩
-      refine ⟨max C 0, fun x ↦ ?_⟩
-      by_cases hx : x ∈ k
-      · exact (hC x hx).trans (le_max_left _ _)
-      · simp [hfs p x hp hx]
-    have : IntegrableOn (fun x ↦ ‖L‖ * ‖g x‖ * C) k μ :=
+      refine ⟨max C 0, fun y ↦ ?_⟩
+      by_cases hx : y ∈ k
+      · exact (hC y hx).trans (le_max_left _ _)
+      · simp [hfs p y hp hx]
+    have : IntegrableOn (fun y ↦ ‖L‖ * ‖g y‖ * C) k μ :=
       (hg.norm.const_mul _).mul_const _
     apply Integrable.mono' this ?_ ?_
     · borelize G
       apply L.aestronglyMeasurable_comp₂ hg.aestronglyMeasurable
       apply StronglyMeasurable.aestronglyMeasurable
       apply Continuous.stronglyMeasurable_of_support_subset_isCompact (A p hp) hk
-      apply support_subset_iff'.2 (fun x hx ↦ hfs p x hp hx)
-    · apply eventually_of_forall (fun x ↦ (le_opNorm₂ L (g x) (f p x)).trans ?_)
+      apply support_subset_iff'.2 (fun y hy ↦ hfs p y hp hy)
+    · apply eventually_of_forall (fun y ↦ (le_opNorm₂ L (g y) (f p y)).trans ?_)
       gcongr
       apply hC
   filter_upwards [v_mem, self_mem_nhdsWithin] with p hp h'p
@@ -1427,32 +1426,32 @@ lemma continuousOn_integral_bilinear_of_locally_integrable_of_compact_support
   ‖∫ x, L (g x) (f p x) ∂μ - ∫ x, L (g x) (f q x) ∂μ‖
     = ‖∫ x in k, L (g x) (f p x) ∂μ - ∫ x in k, L (g x) (f q x) ∂μ‖ := by
       congr 2
-      · refine (set_integral_eq_integral_of_forall_compl_eq_zero (fun x hx ↦ ?_)).symm
-        simp [hfs p x h'p hx]
-      · refine (set_integral_eq_integral_of_forall_compl_eq_zero (fun x hx ↦ ?_)).symm
-        simp [hfs q x hq hx]
+      · refine (set_integral_eq_integral_of_forall_compl_eq_zero (fun y hy ↦ ?_)).symm
+        simp [hfs p y h'p hy]
+      · refine (set_integral_eq_integral_of_forall_compl_eq_zero (fun y hy ↦ ?_)).symm
+        simp [hfs q y hq hy]
   _ = ‖∫ x in k, L (g x) (f p x) - L (g x) (f q x) ∂μ‖ := by rw [integral_sub (I p h'p) (I q hq)]
   _ ≤ ∫ x in k, ‖L (g x) (f p x) - L (g x) (f q x)‖ ∂μ := norm_integral_le_integral_norm _
   _ ≤ ∫ x in k, ‖L‖ * ‖g x‖ * δ ∂μ := by
-      apply integral_mono_of_nonneg (eventually_of_forall (fun x ↦ by positivity))
+      apply integral_mono_of_nonneg (eventually_of_forall (fun y ↦ by positivity))
       · exact (hg.norm.const_mul _).mul_const _
-      · apply eventually_of_forall (fun x ↦ ?_)
-        by_cases hx : x ∈ k
+      · apply eventually_of_forall (fun y ↦ ?_)
+        by_cases hy : y ∈ k
         · dsimp only
-          specialize hv p hp x hx
+          specialize hv p hp y hy
           calc
-          ‖L (g x) (f p x) - L (g x) (f q x)‖
-            = ‖L (g x) (f p x - f q x)‖ := by simp only [map_sub]
-          _ ≤ ‖L‖ * ‖g x‖ * ‖f p x - f q x‖ := le_opNorm₂ _ _ _
-          _ ≤ ‖L‖ * ‖g x‖ * δ := by gcongr
-        · simp only [hfs p x h'p hx, hfs q x hq hx, sub_self, norm_zero, mul_zero]
+          ‖L (g y) (f p y) - L (g y) (f q y)‖
+            = ‖L (g y) (f p y - f q y)‖ := by simp only [map_sub]
+          _ ≤ ‖L‖ * ‖g y‖ * ‖f p y - f q y‖ := le_opNorm₂ _ _ _
+          _ ≤ ‖L‖ * ‖g y‖ * δ := by gcongr
+        · simp only [hfs p y h'p hy, hfs q y hq hy, sub_self, norm_zero, mul_zero]
           positivity
   _ < ε := hδ
 
 /-- Consider a parameterized integral `a ↦ ∫ x, f a x` where `f` is continuous and uniformly
 compactly supported. Then the integral depends continuously on `a`. -/
 lemma continuousOn_integral_of_compact_support
-    {f : α → β → E} {s : Set α} {k : Set β} [IsFiniteMeasureOnCompacts μ]
+    {f : X → Y → E} {s : Set X} {k : Set Y} [IsFiniteMeasureOnCompacts μ]
     (hk : IsCompact k) (hf : ContinuousOn f.uncurry (s ×ˢ univ))
     (hfs : ∀ p, ∀ x, p ∈ s → x ∉ k → f p x = 0) :
     ContinuousOn (fun a ↦ ∫ x, f a x ∂μ) s := by

See the individual commit messages for details.

Extracted from #11108.

@@ -56,7 +56,7 @@ noncomputable section
 
 open Set Filter TopologicalSpace MeasureTheory Function
 
-open scoped Classical Topology Interval BigOperators Filter ENNReal NNReal MeasureTheory
+open scoped Classical Topology BigOperators ENNReal NNReal
 
 variable {α β E F : Type*} [MeasurableSpace α]
 
@@ -64,9 +64,8 @@ namespace MeasureTheory
 
 section NormedAddCommGroup
 
-variable [NormedAddCommGroup E] {f g : α → E} {s t : Set α} {μ ν : Measure α} {l l' : Filter α}
-
-variable [NormedSpace ℝ E]
+variable [NormedAddCommGroup E] [NormedSpace ℝ E]
+  {f g : α → E} {s t : Set α} {μ ν : Measure α} {l l' : Filter α}
 
 theorem set_integral_congr_ae₀ (hs : NullMeasurableSet s μ) (h : ∀ᵐ x ∂μ, x ∈ s → f x = g x) :
     ∫ x in s, f x ∂μ = ∫ x in s, g x ∂μ :=
@@ -866,8 +865,8 @@ We prove that for any set `s`, the function
 
 section ContinuousSetIntegral
 
-variable [NormedAddCommGroup E] {𝕜 : Type*} [NormedField 𝕜] [NormedAddCommGroup F]
-  [NormedSpace 𝕜 F] {p : ℝ≥0∞} {μ : Measure α}
+variable [NormedAddCommGroup E]
+  {𝕜 : Type*} [NormedField 𝕜] [NormedAddCommGroup F] [NormedSpace 𝕜 F] {p : ℝ≥0∞} {μ : Measure α}
 
 /-- For `f : Lp E p μ`, we can define an element of `Lp E p (μ.restrict s)` by
 `(Lp.memℒp f).restrict s).toLp f`. This map is additive. -/
@@ -910,8 +909,7 @@ theorem norm_Lp_toLp_restrict_le (s : Set α) (f : Lp E p μ) :
 set_option linter.uppercaseLean3 false in
 #align measure_theory.norm_Lp_to_Lp_restrict_le MeasureTheory.norm_Lp_toLp_restrict_le
 
-variable (α F 𝕜)
-
+variable (α F 𝕜) in
 /-- Continuous linear map sending a function of `Lp F p μ` to the same function in
 `Lp F p (μ.restrict s)`. -/
 def LpToLpRestrictCLM (μ : Measure α) (p : ℝ≥0∞) [hp : Fact (1 ≤ p)] (s : Set α) :
@@ -923,18 +921,13 @@ def LpToLpRestrictCLM (μ : Measure α) (p : ℝ≥0∞) [hp : Fact (1 ≤ p)] (
 set_option linter.uppercaseLean3 false in
 #align measure_theory.Lp_to_Lp_restrict_clm MeasureTheory.LpToLpRestrictCLM
 
-variable {α F 𝕜}
-
-variable (𝕜)
-
+variable (𝕜) in
 theorem LpToLpRestrictCLM_coeFn [Fact (1 ≤ p)] (s : Set α) (f : Lp F p μ) :
     LpToLpRestrictCLM α F 𝕜 μ p s f =ᵐ[μ.restrict s] f :=
   Memℒp.coeFn_toLp ((Lp.memℒp f).restrict s)
 set_option linter.uppercaseLean3 false in
 #align measure_theory.Lp_to_Lp_restrict_clm_coe_fn MeasureTheory.LpToLpRestrictCLM_coeFn
 
-variable {𝕜}
-
 @[continuity]
 theorem continuous_set_integral [NormedSpace ℝ E] (s : Set α) :
     Continuous fun f : α →₁[μ] E => ∫ x in s, f x ∂μ := by
@@ -952,9 +945,12 @@ end ContinuousSetIntegral
 
 end MeasureTheory
 
+/-! Fundamental theorem of calculus for set integrals -/
+section FTC
+
 open MeasureTheory Asymptotics Metric
 
-variable {ι : Type*} [NormedAddCommGroup E]
+variable {ι : Type*} [NormedAddCommGroup E] [NormedSpace ℝ E] [CompleteSpace E]
 
 /-- Fundamental theorem of calculus for set integrals:
 if `μ` is a measure that is finite at a filter `l` and
@@ -966,7 +962,7 @@ Since `μ (s i)` is an `ℝ≥0∞` number, we use `(μ (s i)).toReal` in the ac
 Often there is a good formula for `(μ (s i)).toReal`, so the formalization can take an optional
 argument `m` with this formula and a proof of `(fun i => (μ (s i)).toReal) =ᶠ[li] m`. Without these
 arguments, `m i = (μ (s i)).toReal` is used in the output. -/
-theorem Filter.Tendsto.integral_sub_linear_isLittleO_ae [NormedSpace ℝ E] [CompleteSpace E]
+theorem Filter.Tendsto.integral_sub_linear_isLittleO_ae
     {μ : Measure α} {l : Filter α} [l.IsMeasurablyGenerated] {f : α → E} {b : E}
     (h : Tendsto f (l ⊓ μ.ae) (𝓝 b)) (hfm : StronglyMeasurableAtFilter f l μ)
     (hμ : μ.FiniteAtFilter l) {s : ι → Set α} {li : Filter ι} (hs : Tendsto s li l.smallSets)
@@ -999,7 +995,7 @@ Often there is a good formula for `(μ (s i)).toReal`, so the formalization can
 argument `m` with this formula and a proof of `(fun i => (μ (s i)).toReal) =ᶠ[li] m`. Without these
 arguments, `m i = (μ (s i)).toReal` is used in the output. -/
 theorem ContinuousWithinAt.integral_sub_linear_isLittleO_ae [TopologicalSpace α]
-    [OpensMeasurableSpace α] [NormedSpace ℝ E] [CompleteSpace E] {μ : Measure α}
+    [OpensMeasurableSpace α] {μ : Measure α}
     [IsLocallyFiniteMeasure μ] {a : α} {t : Set α} {f : α → E} (ha : ContinuousWithinAt f t a)
     (ht : MeasurableSet t) (hfm : StronglyMeasurableAtFilter f (𝓝[t] a) μ) {s : ι → Set α}
     {li : Filter ι} (hs : Tendsto s li (𝓝[t] a).smallSets) (m : ι → ℝ := fun i => (μ (s i)).toReal)
@@ -1020,7 +1016,7 @@ Often there is a good formula for `(μ (s i)).toReal`, so the formalization can
 argument `m` with this formula and a proof of `(fun i => (μ (s i)).toReal) =ᶠ[li] m`. Without these
 arguments, `m i = (μ (s i)).toReal` is used in the output. -/
 theorem ContinuousAt.integral_sub_linear_isLittleO_ae [TopologicalSpace α] [OpensMeasurableSpace α]
-    [NormedSpace ℝ E] [CompleteSpace E] {μ : Measure α} [IsLocallyFiniteMeasure μ] {a : α}
+    {μ : Measure α} [IsLocallyFiniteMeasure μ] {a : α}
     {f : α → E} (ha : ContinuousAt f a) (hfm : StronglyMeasurableAtFilter f (𝓝 a) μ) {s : ι → Set α}
     {li : Filter ι} (hs : Tendsto s li (𝓝 a).smallSets) (m : ι → ℝ := fun i => (μ (s i)).toReal)
     (hsμ : (fun i => (μ (s i)).toReal) =ᶠ[li] m := by rfl) :
@@ -1037,7 +1033,7 @@ Often there is a good formula for `(μ (s i)).toReal`, so the formalization can
 argument `m` with this formula and a proof of `(fun i => (μ (s i)).toReal) =ᶠ[li] m`. Without these
 arguments, `m i = (μ (s i)).toReal` is used in the output. -/
 theorem ContinuousOn.integral_sub_linear_isLittleO_ae [TopologicalSpace α] [OpensMeasurableSpace α]
-    [NormedSpace ℝ E] [CompleteSpace E] [SecondCountableTopologyEither α E] {μ : Measure α}
+    [SecondCountableTopologyEither α E] {μ : Measure α}
     [IsLocallyFiniteMeasure μ] {a : α} {t : Set α} {f : α → E} (hft : ContinuousOn f t) (ha : a ∈ t)
     (ht : MeasurableSet t) {s : ι → Set α} {li : Filter ι} (hs : Tendsto s li (𝓝[t] a).smallSets)
     (m : ι → ℝ := fun i => (μ (s i)).toReal)
@@ -1047,6 +1043,8 @@ theorem ContinuousOn.integral_sub_linear_isLittleO_ae [TopologicalSpace α] [Ope
     ⟨t, self_mem_nhdsWithin, hft.aestronglyMeasurable ht⟩ hs m hsμ
 #align continuous_on.integral_sub_linear_is_o_ae ContinuousOn.integral_sub_linear_isLittleO_ae
 
+end FTC
+
 section
 
 /-! ### Continuous linear maps composed with integration
@@ -1058,11 +1056,10 @@ the composition, as we are dealing with classes of functions, but it has already
 as `ContinuousLinearMap.compLp`. We take advantage of this construction here.
 -/
 
-
 open scoped ComplexConjugate
 
-variable {μ : Measure α} {𝕜 : Type*} [IsROrC 𝕜] [NormedSpace 𝕜 E] [NormedAddCommGroup F]
-  [NormedSpace 𝕜 F] {p : ENNReal}
+variable {μ : Measure α} {𝕜 : Type*} [IsROrC 𝕜] [NormedAddCommGroup E] [NormedSpace 𝕜 E]
+  [NormedAddCommGroup F] [NormedSpace 𝕜 F] {p : ENNReal}
 
 namespace ContinuousLinearMap
 
@@ -1375,11 +1372,13 @@ end BilinearMap
 
 section ParametricIntegral
 
+variable [NormedAddCommGroup E]
+
 variable {α β F G 𝕜 : Type*} [TopologicalSpace α] [TopologicalSpace β] [MeasurableSpace β]
   [OpensMeasurableSpace β] {μ : Measure β} [NontriviallyNormedField 𝕜] [NormedSpace ℝ E]
   [NormedAddCommGroup F] [NormedSpace 𝕜 F] [NormedAddCommGroup G] [NormedSpace 𝕜 G]
 
-open Metric Function ContinuousLinearMap
+open Metric ContinuousLinearMap
 
 /-- Consider a parameterized integral `a ↦ ∫ x, L (g x) (f a x)` where `L` is bilinear,
 `g` is locally integrable and `f` is continuous and uniformly compactly supported. Then the

Suggested by @loefflerd. Only code motion (and cosmetic adaptions, such as minimising import and open statements).

Pre-requisite for #11108 and (morally) #11110.

@@ -6,7 +6,6 @@ Authors: Zhouhang Zhou, Yury Kudryashov
 import Mathlib.MeasureTheory.Integral.IntegrableOn
 import Mathlib.MeasureTheory.Integral.Bochner
 import Mathlib.MeasureTheory.Function.LocallyIntegrable
-import Mathlib.Order.Filter.IndicatorFunction
 import Mathlib.Topology.MetricSpace.ThickenedIndicator
 import Mathlib.Topology.ContinuousFunction.Compact
 
@@ -859,33 +858,6 @@ theorem integrable_of_summable_norm_restrict {f : C(α, E)} {s : β → Compacts
 
 end IntegrableUnion
 
-section TendstoMono
-
-variable {μ : Measure α} [NormedAddCommGroup E] [NormedSpace ℝ E] {s : ℕ → Set α}
-  {f : α → E}
-
-theorem _root_.Antitone.tendsto_set_integral (hsm : ∀ i, MeasurableSet (s i)) (h_anti : Antitone s)
-    (hfi : IntegrableOn f (s 0) μ) :
-    Tendsto (fun i => ∫ a in s i, f a ∂μ) atTop (𝓝 (∫ a in ⋂ n, s n, f a ∂μ)) := by
-  let bound : α → ℝ := indicator (s 0) fun a => ‖f a‖
-  have h_int_eq : (fun i => ∫ a in s i, f a ∂μ) = fun i => ∫ a, (s i).indicator f a ∂μ :=
-    funext fun i => (integral_indicator (hsm i)).symm
-  rw [h_int_eq]
-  rw [← integral_indicator (MeasurableSet.iInter hsm)]
-  refine' tendsto_integral_of_dominated_convergence bound _ _ _ _
-  · intro n
-    rw [aestronglyMeasurable_indicator_iff (hsm n)]
-    exact (IntegrableOn.mono_set hfi (h_anti (zero_le n))).1
-  · rw [integrable_indicator_iff (hsm 0)]
-    exact hfi.norm
-  · simp_rw [norm_indicator_eq_indicator_norm]
-    refine' fun n => eventually_of_forall fun x => _
-    exact indicator_le_indicator_of_subset (h_anti (zero_le n)) (fun a => norm_nonneg _) _
-  · filter_upwards [] with a using le_trans (h_anti.tendsto_indicator _ _ _) (pure_le_nhds _)
-#align antitone.tendsto_set_integral Antitone.tendsto_set_integral
-
-end TendstoMono
-
 /-! ### Continuity of the set integral
 
 We prove that for any set `s`, the function

Co-authored-by: Patrick Massot <patrickmassot@free.fr> Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

@@ -803,11 +803,11 @@ lemma integral_le_measure {f : α → ℝ} {s : Set α}
   · intro x
     apply ENNReal.ofReal_le_of_le_toReal
     by_cases H : x ∈ s
-    · simpa using hs x H
+    · simpa [g] using hs x H
     · apply le_trans _ zero_le_one
-      simpa using h's x H
+      simpa [g] using h's x H
   · intro x hx
-    simpa using h's x hx
+    simpa [g] using h's x hx
 
 end Nonneg
 

After #9949, Pi.smul_apply can be used in simp again. This PR cleans up some workarounds.

@@ -924,7 +924,7 @@ theorem Lp_toLp_restrict_smul (c : 𝕜) (f : Lp F p μ) (s : Set α) :
   refine' (Memℒp.coeFn_toLp ((Lp.memℒp (c • f)).restrict s)).mp _
   refine'
     (Lp.coeFn_smul c (Memℒp.toLp f ((Lp.memℒp f).restrict s))).mono fun x hx1 hx2 hx3 hx4 => _
-  rw [hx2, hx1, Pi.smul_apply, hx3, hx4, Pi.smul_apply]
+  simp only [hx2, hx1, hx3, hx4, Pi.smul_apply]
 set_option linter.uppercaseLean3 false in
 #align measure_theory.Lp_to_Lp_restrict_smul MeasureTheory.Lp_toLp_restrict_smul
 

@@ -45,7 +45,7 @@ We provide the following notations for expressing the integral of a function on
 * `∫ a in s, f a ∂μ` is `MeasureTheory.integral (μ.restrict s) f`
 * `∫ a in s, f a` is `∫ a in s, f a ∂volume`
 
-Note that the set notations are defined in the file `MeasureTheory/Integral/Bochner.lean`,
+Note that the set notations are defined in the file `Mathlib/MeasureTheory/Integral/Bochner.lean`,
 but we reference them here because all theorems about set integrals are in this file.
 
 -/
@@ -95,30 +95,30 @@ theorem set_integral_congr_set_ae (hst : s =ᵐ[μ] t) : ∫ x in s, f x ∂μ =
 
 theorem integral_union_ae (hst : AEDisjoint μ s t) (ht : NullMeasurableSet t μ)
     (hfs : IntegrableOn f s μ) (hft : IntegrableOn f t μ) :
-    ∫ x in s ∪ t, f x ∂μ = (∫ x in s, f x ∂μ) + ∫ x in t, f x ∂μ := by
+    ∫ x in s ∪ t, f x ∂μ = ∫ x in s, f x ∂μ + ∫ x in t, f x ∂μ := by
   simp only [IntegrableOn, Measure.restrict_union₀ hst ht, integral_add_measure hfs hft]
 #align measure_theory.integral_union_ae MeasureTheory.integral_union_ae
 
 theorem integral_union (hst : Disjoint s t) (ht : MeasurableSet t) (hfs : IntegrableOn f s μ)
-    (hft : IntegrableOn f t μ) : ∫ x in s ∪ t, f x ∂μ = (∫ x in s, f x ∂μ) + ∫ x in t, f x ∂μ :=
+    (hft : IntegrableOn f t μ) : ∫ x in s ∪ t, f x ∂μ = ∫ x in s, f x ∂μ + ∫ x in t, f x ∂μ :=
   integral_union_ae hst.aedisjoint ht.nullMeasurableSet hfs hft
 #align measure_theory.integral_union MeasureTheory.integral_union
 
 theorem integral_diff (ht : MeasurableSet t) (hfs : IntegrableOn f s μ) (hts : t ⊆ s) :
-    ∫ x in s \ t, f x ∂μ = (∫ x in s, f x ∂μ) - ∫ x in t, f x ∂μ := by
+    ∫ x in s \ t, f x ∂μ = ∫ x in s, f x ∂μ - ∫ x in t, f x ∂μ := by
   rw [eq_sub_iff_add_eq, ← integral_union, diff_union_of_subset hts]
   exacts [disjoint_sdiff_self_left, ht, hfs.mono_set (diff_subset _ _), hfs.mono_set hts]
 #align measure_theory.integral_diff MeasureTheory.integral_diff
 
 theorem integral_inter_add_diff₀ (ht : NullMeasurableSet t μ) (hfs : IntegrableOn f s μ) :
-    ((∫ x in s ∩ t, f x ∂μ) + ∫ x in s \ t, f x ∂μ) = ∫ x in s, f x ∂μ := by
+    ∫ x in s ∩ t, f x ∂μ + ∫ x in s \ t, f x ∂μ = ∫ x in s, f x ∂μ := by
   rw [← Measure.restrict_inter_add_diff₀ s ht, integral_add_measure]
   · exact Integrable.mono_measure hfs (Measure.restrict_mono (inter_subset_left _ _) le_rfl)
   · exact Integrable.mono_measure hfs (Measure.restrict_mono (diff_subset _ _) le_rfl)
 #align measure_theory.integral_inter_add_diff₀ MeasureTheory.integral_inter_add_diff₀
 
 theorem integral_inter_add_diff (ht : MeasurableSet t) (hfs : IntegrableOn f s μ) :
-    ((∫ x in s ∩ t, f x ∂μ) + ∫ x in s \ t, f x ∂μ) = ∫ x in s, f x ∂μ :=
+    ∫ x in s ∩ t, f x ∂μ + ∫ x in s \ t, f x ∂μ = ∫ x in s, f x ∂μ :=
   integral_inter_add_diff₀ ht.nullMeasurableSet hfs
 #align measure_theory.integral_inter_add_diff MeasureTheory.integral_inter_add_diff
 
@@ -153,14 +153,14 @@ theorem integral_univ : ∫ x in univ, f x ∂μ = ∫ x, f x ∂μ := by rw [Me
 #align measure_theory.integral_univ MeasureTheory.integral_univ
 
 theorem integral_add_compl₀ (hs : NullMeasurableSet s μ) (hfi : Integrable f μ) :
-    ((∫ x in s, f x ∂μ) + ∫ x in sᶜ, f x ∂μ) = ∫ x, f x ∂μ := by
-  rw [← integral_union_ae (@disjoint_compl_right (Set α) _ _).aedisjoint hs.compl hfi.integrableOn
-      hfi.integrableOn,
+    ∫ x in s, f x ∂μ + ∫ x in sᶜ, f x ∂μ = ∫ x, f x ∂μ := by
+  rw [
+    ← integral_union_ae disjoint_compl_right.aedisjoint hs.compl hfi.integrableOn hfi.integrableOn,
     union_compl_self, integral_univ]
 #align measure_theory.integral_add_compl₀ MeasureTheory.integral_add_compl₀
 
 theorem integral_add_compl (hs : MeasurableSet s) (hfi : Integrable f μ) :
-    ((∫ x in s, f x ∂μ) + ∫ x in sᶜ, f x ∂μ) = ∫ x, f x ∂μ :=
+    ∫ x in s, f x ∂μ + ∫ x in sᶜ, f x ∂μ = ∫ x, f x ∂μ :=
   integral_add_compl₀ hs.nullMeasurableSet hfi
 #align measure_theory.integral_add_compl MeasureTheory.integral_add_compl
 
@@ -169,12 +169,12 @@ over the whole space is equal to `∫ x in s, f x ∂μ` defined as `∫ x, f x
 theorem integral_indicator (hs : MeasurableSet s) :
     ∫ x, indicator s f x ∂μ = ∫ x in s, f x ∂μ := by
   by_cases hfi : IntegrableOn f s μ; swap
-  · rwa [integral_undef, integral_undef]
+  · rw [integral_undef hfi, integral_undef]
     rwa [integrable_indicator_iff hs]
   calc
-    ∫ x, indicator s f x ∂μ = (∫ x in s, indicator s f x ∂μ) + ∫ x in sᶜ, indicator s f x ∂μ :=
+    ∫ x, indicator s f x ∂μ = ∫ x in s, indicator s f x ∂μ + ∫ x in sᶜ, indicator s f x ∂μ :=
       (integral_add_compl hs (hfi.integrable_indicator hs)).symm
-    _ = (∫ x in s, f x ∂μ) + ∫ x in sᶜ, 0 ∂μ :=
+    _ = ∫ x in s, f x ∂μ + ∫ x in sᶜ, 0 ∂μ :=
       (congr_arg₂ (· + ·) (integral_congr_ae (indicator_ae_eq_restrict hs))
         (integral_congr_ae (indicator_ae_eq_restrict_compl hs)))
     _ = ∫ x in s, f x ∂μ := by simp
@@ -203,7 +203,7 @@ theorem ofReal_set_integral_one {α : Type*} {_ : MeasurableSpace α} (μ : Meas
 
 theorem integral_piecewise [DecidablePred (· ∈ s)] (hs : MeasurableSet s) (hf : IntegrableOn f s μ)
     (hg : IntegrableOn g sᶜ μ) :
-    ∫ x, s.piecewise f g x ∂μ = (∫ x in s, f x ∂μ) + ∫ x in sᶜ, g x ∂μ := by
+    ∫ x, s.piecewise f g x ∂μ = ∫ x in s, f x ∂μ + ∫ x in sᶜ, g x ∂μ := by
   rw [← Set.indicator_add_compl_eq_piecewise,
     integral_add' (hf.integrable_indicator hs) (hg.integrable_indicator hs.compl),
     integral_indicator hs, integral_indicator hs.compl]
@@ -213,7 +213,7 @@ theorem tendsto_set_integral_of_monotone {ι : Type*} [Countable ι] [Semilattic
     {s : ι → Set α} (hsm : ∀ i, MeasurableSet (s i)) (h_mono : Monotone s)
     (hfi : IntegrableOn f (⋃ n, s n) μ) :
     Tendsto (fun i => ∫ a in s i, f a ∂μ) atTop (𝓝 (∫ a in ⋃ n, s n, f a ∂μ)) := by
-  have hfi' : (∫⁻ x in ⋃ n, s n, ‖f x‖₊ ∂μ) < ∞ := hfi.2
+  have hfi' : ∫⁻ x in ⋃ n, s n, ‖f x‖₊ ∂μ < ∞ := hfi.2
   set S := ⋃ i, s i
   have hSm : MeasurableSet S := MeasurableSet.iUnion hsm
   have hsub : ∀ {i}, s i ⊆ S := @(subset_iUnion s)
@@ -334,7 +334,7 @@ theorem set_integral_eq_of_subset_of_ae_diff_eq_zero_aux (hts : s ⊆ t)
   let k := f ⁻¹' {0}
   have hk : MeasurableSet k := by borelize E; exact haux.measurable (measurableSet_singleton _)
   calc
-    ∫ x in t, f x ∂μ = (∫ x in t ∩ k, f x ∂μ) + ∫ x in t \ k, f x ∂μ := by
+    ∫ x in t, f x ∂μ = ∫ x in t ∩ k, f x ∂μ + ∫ x in t \ k, f x ∂μ := by
       rw [integral_inter_add_diff hk h'aux]
     _ = ∫ x in t \ k, f x ∂μ := by
       rw [set_integral_eq_zero_of_forall_eq_zero fun x hx => ?_, zero_add]; exact hx.2
@@ -349,7 +349,7 @@ theorem set_integral_eq_of_subset_of_ae_diff_eq_zero_aux (hts : s ⊆ t)
       · simp only [xs, iff_false_iff]
         intro xt
         exact h'x (hx ⟨xt, xs⟩)
-    _ = (∫ x in s ∩ k, f x ∂μ) + ∫ x in s \ k, f x ∂μ := by
+    _ = ∫ x in s ∩ k, f x ∂μ + ∫ x in s \ k, f x ∂μ := by
       have : ∀ x ∈ s ∩ k, f x = 0 := fun x hx => hx.2
       rw [set_integral_eq_zero_of_forall_eq_zero this, zero_add]
     _ = ∫ x in s, f x ∂μ := by rw [integral_inter_add_diff hk (h'aux.mono hts le_rfl)]
@@ -375,7 +375,6 @@ theorem set_integral_eq_of_subset_of_ae_diff_eq_zero (ht : NullMeasurableSet t 
       apply integral_congr_ae
       apply ae_restrict_of_ae_restrict_of_subset hts
       exact h.1.ae_eq_mk.symm
-
 #align measure_theory.set_integral_eq_of_subset_of_ae_diff_eq_zero MeasureTheory.set_integral_eq_of_subset_of_ae_diff_eq_zero
 
 /-- If a function vanishes on `t \ s` with `s ⊆ t`, then its integrals on `s`
@@ -407,7 +406,7 @@ theorem set_integral_neg_eq_set_integral_nonpos [LinearOrder E] {f : α → E}
     (hf : AEStronglyMeasurable f μ) :
     ∫ x in {x | f x < 0}, f x ∂μ = ∫ x in {x | f x ≤ 0}, f x ∂μ := by
   have h_union : {x | f x ≤ 0} = {x | f x < 0} ∪ {x | f x = 0} := by
-    ext; simp_rw [Set.mem_union, Set.mem_setOf_eq]; exact le_iff_lt_or_eq
+    simp_rw [le_iff_lt_or_eq, setOf_or]
   rw [h_union]
   have B : NullMeasurableSet {x | f x = 0} μ :=
     hf.nullMeasurableSet_eq_fun aestronglyMeasurable_zero
@@ -417,19 +416,19 @@ theorem set_integral_neg_eq_set_integral_nonpos [LinearOrder E] {f : α → E}
 #align measure_theory.set_integral_neg_eq_set_integral_nonpos MeasureTheory.set_integral_neg_eq_set_integral_nonpos
 
 theorem integral_norm_eq_pos_sub_neg {f : α → ℝ} (hfi : Integrable f μ) :
-    ∫ x, ‖f x‖ ∂μ = (∫ x in {x | 0 ≤ f x}, f x ∂μ) - ∫ x in {x | f x ≤ 0}, f x ∂μ :=
+    ∫ x, ‖f x‖ ∂μ = ∫ x in {x | 0 ≤ f x}, f x ∂μ - ∫ x in {x | f x ≤ 0}, f x ∂μ :=
   have h_meas : NullMeasurableSet {x | 0 ≤ f x} μ :=
     aestronglyMeasurable_const.nullMeasurableSet_le hfi.1
   calc
-    ∫ x, ‖f x‖ ∂μ = (∫ x in {x | 0 ≤ f x}, ‖f x‖ ∂μ) + ∫ x in {x | 0 ≤ f x}ᶜ, ‖f x‖ ∂μ := by
+    ∫ x, ‖f x‖ ∂μ = ∫ x in {x | 0 ≤ f x}, ‖f x‖ ∂μ + ∫ x in {x | 0 ≤ f x}ᶜ, ‖f x‖ ∂μ := by
       rw [← integral_add_compl₀ h_meas hfi.norm]
-    _ = (∫ x in {x | 0 ≤ f x}, f x ∂μ) + ∫ x in {x | 0 ≤ f x}ᶜ, ‖f x‖ ∂μ := by
+    _ = ∫ x in {x | 0 ≤ f x}, f x ∂μ + ∫ x in {x | 0 ≤ f x}ᶜ, ‖f x‖ ∂μ := by
       congr 1
       refine' set_integral_congr₀ h_meas fun x hx => _
       dsimp only
       rw [Real.norm_eq_abs, abs_eq_self.mpr _]
       exact hx
-    _ = (∫ x in {x | 0 ≤ f x}, f x ∂μ) - ∫ x in {x | 0 ≤ f x}ᶜ, f x ∂μ := by
+    _ = ∫ x in {x | 0 ≤ f x}, f x ∂μ - ∫ x in {x | 0 ≤ f x}ᶜ, f x ∂μ := by
       congr 1
       rw [← integral_neg]
       refine' set_integral_congr₀ h_meas.compl fun x hx => _
@@ -437,8 +436,8 @@ theorem integral_norm_eq_pos_sub_neg {f : α → ℝ} (hfi : Integrable f μ) :
       rw [Real.norm_eq_abs, abs_eq_neg_self.mpr _]
       rw [Set.mem_compl_iff, Set.nmem_setOf_iff] at hx
       linarith
-    _ = (∫ x in {x | 0 ≤ f x}, f x ∂μ) - ∫ x in {x | f x ≤ 0}, f x ∂μ := by
-      rw [← set_integral_neg_eq_set_integral_nonpos hfi.1]; congr; ext1 x; simp
+    _ = ∫ x in {x | 0 ≤ f x}, f x ∂μ - ∫ x in {x | f x ≤ 0}, f x ∂μ := by
+      rw [← set_integral_neg_eq_set_integral_nonpos hfi.1, compl_setOf]; simp only [not_le]
 #align measure_theory.integral_norm_eq_pos_sub_neg MeasureTheory.integral_norm_eq_pos_sub_neg
 
 theorem set_integral_const [CompleteSpace E] (c : E) : ∫ _ in s, c ∂μ = (μ s).toReal • c := by
@@ -447,7 +446,7 @@ theorem set_integral_const [CompleteSpace E] (c : E) : ∫ _ in s, c ∂μ = (μ
 
 @[simp]
 theorem integral_indicator_const [CompleteSpace E] (e : E) ⦃s : Set α⦄ (s_meas : MeasurableSet s) :
-    (∫ a : α, s.indicator (fun _ : α => e) a ∂μ) = (μ s).toReal • e := by
+    ∫ a : α, s.indicator (fun _ : α => e) a ∂μ = (μ s).toReal • e := by
   rw [integral_indicator s_meas, ← set_integral_const]
 #align measure_theory.integral_indicator_const MeasureTheory.integral_indicator_const
 
@@ -500,7 +499,7 @@ theorem _root_.ClosedEmbedding.set_integral_map [TopologicalSpace α] [BorelSpac
 
 theorem MeasurePreserving.set_integral_preimage_emb {β} {_ : MeasurableSpace β} {f : α → β} {ν}
     (h₁ : MeasurePreserving f μ ν) (h₂ : MeasurableEmbedding f) (g : β → E) (s : Set β) :
-    (∫ x in f ⁻¹' s, g (f x) ∂μ) = ∫ y in s, g y ∂ν :=
+    ∫ x in f ⁻¹' s, g (f x) ∂μ = ∫ y in s, g y ∂ν :=
   (h₁.restrict_preimage_emb h₂ s).integral_comp h₂ _
 #align measure_theory.measure_preserving.set_integral_preimage_emb MeasureTheory.MeasurePreserving.set_integral_preimage_emb
 
@@ -518,7 +517,7 @@ theorem set_integral_map_equiv {β} [MeasurableSpace β] (e : α ≃ᵐ β) (f :
 theorem norm_set_integral_le_of_norm_le_const_ae {C : ℝ} (hs : μ s < ∞)
     (hC : ∀ᵐ x ∂μ.restrict s, ‖f x‖ ≤ C) : ‖∫ x in s, f x ∂μ‖ ≤ C * (μ s).toReal := by
   rw [← Measure.restrict_apply_univ] at *
-  haveI : IsFiniteMeasure (μ.restrict s) := ⟨‹_›⟩
+  haveI : IsFiniteMeasure (μ.restrict s) := ⟨hs⟩
   exact norm_integral_le_of_norm_le_const hC
 #align measure_theory.norm_set_integral_le_of_norm_le_const_ae MeasureTheory.norm_set_integral_le_of_norm_le_const_ae
 
@@ -530,7 +529,7 @@ theorem norm_set_integral_le_of_norm_le_const_ae' {C : ℝ} (hs : μ s < ∞)
     filter_upwards [hC, hfm.ae_mem_imp_eq_mk] with _ h1 h2 h3
     rw [← h2 h3]
     exact h1 h3
-  have B : MeasurableSet {x | ‖(hfm.mk f) x‖ ≤ C} :=
+  have B : MeasurableSet {x | ‖hfm.mk f x‖ ≤ C} :=
     hfm.stronglyMeasurable_mk.norm.measurable measurableSet_Iic
   filter_upwards [hfm.ae_eq_mk, (ae_restrict_iff B).2 A] with _ h1 _
   rwa [h1]
@@ -581,8 +580,7 @@ theorem set_integral_gt_gt {R : ℝ} {f : α → ℝ} (hR : 0 ≤ R) (hfm : Meas
   · rw [← zero_lt_iff] at hμ
     rwa [Set.inter_eq_self_of_subset_right]
     exact fun x hx => Ne.symm (ne_of_lt <| sub_pos.2 hx)
-  · change ∀ᵐ x ∂μ.restrict _, _
-    rw [ae_restrict_iff]
+  · rw [Pi.zero_def, EventuallyLE, ae_restrict_iff]
     · exact eventually_of_forall fun x hx => sub_nonneg.2 <| le_of_lt hx
     · exact measurableSet_le measurable_zero (hfm.sub measurable_const)
   · exact Integrable.sub hfint this
@@ -680,36 +678,36 @@ variable {μ : Measure α} {f g : α → ℝ} {s t : Set α} (hf : IntegrableOn
   (hg : IntegrableOn g s μ)
 
 theorem set_integral_mono_ae_restrict (h : f ≤ᵐ[μ.restrict s] g) :
-    (∫ a in s, f a ∂μ) ≤ ∫ a in s, g a ∂μ :=
+    ∫ a in s, f a ∂μ ≤ ∫ a in s, g a ∂μ :=
   integral_mono_ae hf hg h
 #align measure_theory.set_integral_mono_ae_restrict MeasureTheory.set_integral_mono_ae_restrict
 
-theorem set_integral_mono_ae (h : f ≤ᵐ[μ] g) : (∫ a in s, f a ∂μ) ≤ ∫ a in s, g a ∂μ :=
+theorem set_integral_mono_ae (h : f ≤ᵐ[μ] g) : ∫ a in s, f a ∂μ ≤ ∫ a in s, g a ∂μ :=
   set_integral_mono_ae_restrict hf hg (ae_restrict_of_ae h)
 #align measure_theory.set_integral_mono_ae MeasureTheory.set_integral_mono_ae
 
 theorem set_integral_mono_on (hs : MeasurableSet s) (h : ∀ x ∈ s, f x ≤ g x) :
-    (∫ a in s, f a ∂μ) ≤ ∫ a in s, g a ∂μ :=
+    ∫ a in s, f a ∂μ ≤ ∫ a in s, g a ∂μ :=
   set_integral_mono_ae_restrict hf hg
     (by simp [hs, EventuallyLE, eventually_inf_principal, ae_of_all _ h])
 #align measure_theory.set_integral_mono_on MeasureTheory.set_integral_mono_on
 
 theorem set_integral_mono_on_ae (hs : MeasurableSet s) (h : ∀ᵐ x ∂μ, x ∈ s → f x ≤ g x) :
-    (∫ a in s, f a ∂μ) ≤ ∫ a in s, g a ∂μ := by
+    ∫ a in s, f a ∂μ ≤ ∫ a in s, g a ∂μ := by
   refine' set_integral_mono_ae_restrict hf hg _; rwa [EventuallyLE, ae_restrict_iff' hs]
 #align measure_theory.set_integral_mono_on_ae MeasureTheory.set_integral_mono_on_ae
 
-theorem set_integral_mono (h : f ≤ g) : (∫ a in s, f a ∂μ) ≤ ∫ a in s, g a ∂μ :=
+theorem set_integral_mono (h : f ≤ g) : ∫ a in s, f a ∂μ ≤ ∫ a in s, g a ∂μ :=
   integral_mono hf hg h
 #align measure_theory.set_integral_mono MeasureTheory.set_integral_mono
 
 theorem set_integral_mono_set (hfi : IntegrableOn f t μ) (hf : 0 ≤ᵐ[μ.restrict t] f)
-    (hst : s ≤ᵐ[μ] t) : (∫ x in s, f x ∂μ) ≤ ∫ x in t, f x ∂μ :=
+    (hst : s ≤ᵐ[μ] t) : ∫ x in s, f x ∂μ ≤ ∫ x in t, f x ∂μ :=
   integral_mono_measure (Measure.restrict_mono_ae hst) hf hfi
 #align measure_theory.set_integral_mono_set MeasureTheory.set_integral_mono_set
 
 theorem set_integral_le_integral (hfi : Integrable f μ) (hf : 0 ≤ᵐ[μ] f) :
-    (∫ x in s, f x ∂μ) ≤ ∫ x, f x ∂μ :=
+    ∫ x in s, f x ∂μ ≤ ∫ x, f x ∂μ :=
   integral_mono_measure (Measure.restrict_le_self) hf hfi
 
 theorem set_integral_ge_of_const_le {c : ℝ} (hs : MeasurableSet s) (hμs : μ s ≠ ∞)
@@ -744,7 +742,7 @@ theorem set_integral_nonneg_ae (hs : MeasurableSet s) (hf : ∀ᵐ a ∂μ, a 
 #align measure_theory.set_integral_nonneg_ae MeasureTheory.set_integral_nonneg_ae
 
 theorem set_integral_le_nonneg {s : Set α} (hs : MeasurableSet s) (hf : StronglyMeasurable f)
-    (hfi : Integrable f μ) : (∫ x in s, f x ∂μ) ≤ ∫ x in {y | 0 ≤ f y}, f x ∂μ := by
+    (hfi : Integrable f μ) : ∫ x in s, f x ∂μ ≤ ∫ x in {y | 0 ≤ f y}, f x ∂μ := by
   rw [← integral_indicator hs, ←
     integral_indicator (stronglyMeasurable_const.measurableSet_le hf)]
   exact
@@ -753,26 +751,26 @@ theorem set_integral_le_nonneg {s : Set α} (hs : MeasurableSet s) (hf : Strongl
       (indicator_le_indicator_nonneg s f)
 #align measure_theory.set_integral_le_nonneg MeasureTheory.set_integral_le_nonneg
 
-theorem set_integral_nonpos_of_ae_restrict (hf : f ≤ᵐ[μ.restrict s] 0) : (∫ a in s, f a ∂μ) ≤ 0 :=
+theorem set_integral_nonpos_of_ae_restrict (hf : f ≤ᵐ[μ.restrict s] 0) : ∫ a in s, f a ∂μ ≤ 0 :=
   integral_nonpos_of_ae hf
 #align measure_theory.set_integral_nonpos_of_ae_restrict MeasureTheory.set_integral_nonpos_of_ae_restrict
 
-theorem set_integral_nonpos_of_ae (hf : f ≤ᵐ[μ] 0) : (∫ a in s, f a ∂μ) ≤ 0 :=
+theorem set_integral_nonpos_of_ae (hf : f ≤ᵐ[μ] 0) : ∫ a in s, f a ∂μ ≤ 0 :=
   set_integral_nonpos_of_ae_restrict (ae_restrict_of_ae hf)
 #align measure_theory.set_integral_nonpos_of_ae MeasureTheory.set_integral_nonpos_of_ae
 
-theorem set_integral_nonpos (hs : MeasurableSet s) (hf : ∀ a, a ∈ s → f a ≤ 0) :
-    (∫ a in s, f a ∂μ) ≤ 0 :=
-  set_integral_nonpos_of_ae_restrict ((ae_restrict_iff' hs).mpr (ae_of_all μ hf))
-#align measure_theory.set_integral_nonpos MeasureTheory.set_integral_nonpos
-
 theorem set_integral_nonpos_ae (hs : MeasurableSet s) (hf : ∀ᵐ a ∂μ, a ∈ s → f a ≤ 0) :
-    (∫ a in s, f a ∂μ) ≤ 0 :=
+    ∫ a in s, f a ∂μ ≤ 0 :=
   set_integral_nonpos_of_ae_restrict <| by rwa [EventuallyLE, ae_restrict_iff' hs]
 #align measure_theory.set_integral_nonpos_ae MeasureTheory.set_integral_nonpos_ae
 
+theorem set_integral_nonpos (hs : MeasurableSet s) (hf : ∀ a, a ∈ s → f a ≤ 0) :
+    ∫ a in s, f a ∂μ ≤ 0 :=
+  set_integral_nonpos_ae hs <| ae_of_all μ hf
+#align measure_theory.set_integral_nonpos MeasureTheory.set_integral_nonpos
+
 theorem set_integral_nonpos_le {s : Set α} (hs : MeasurableSet s) (hf : StronglyMeasurable f)
-    (hfi : Integrable f μ) : (∫ x in {y | f y ≤ 0}, f x ∂μ) ≤ ∫ x in s, f x ∂μ := by
+    (hfi : Integrable f μ) : ∫ x in {y | f y ≤ 0}, f x ∂μ ≤ ∫ x in s, f x ∂μ := by
   rw [← integral_indicator hs, ←
     integral_indicator (hf.measurableSet_le stronglyMeasurable_const)]
   exact
@@ -1099,13 +1097,13 @@ namespace ContinuousLinearMap
 variable [NormedSpace ℝ F]
 
 theorem integral_compLp (L : E →L[𝕜] F) (φ : Lp E p μ) :
-    (∫ a, (L.compLp φ) a ∂μ) = ∫ a, L (φ a) ∂μ :=
+    ∫ a, (L.compLp φ) a ∂μ = ∫ a, L (φ a) ∂μ :=
   integral_congr_ae <| coeFn_compLp _ _
 set_option linter.uppercaseLean3 false in
 #align continuous_linear_map.integral_comp_Lp ContinuousLinearMap.integral_compLp
 
 theorem set_integral_compLp (L : E →L[𝕜] F) (φ : Lp E p μ) {s : Set α} (hs : MeasurableSet s) :
-    (∫ a in s, (L.compLp φ) a ∂μ) = ∫ a in s, L (φ a) ∂μ :=
+    ∫ a in s, (L.compLp φ) a ∂μ = ∫ a in s, L (φ a) ∂μ :=
   set_integral_congr_ae hs ((L.coeFn_compLp φ).mono fun _x hx _ => hx)
 set_option linter.uppercaseLean3 false in
 #align continuous_linear_map.set_integral_comp_Lp ContinuousLinearMap.set_integral_compLp
@@ -1119,15 +1117,14 @@ set_option linter.uppercaseLean3 false in
 variable [CompleteSpace E] [CompleteSpace F] [NormedSpace ℝ E]
 
 theorem integral_comp_comm (L : E →L[𝕜] F) {φ : α → E} (φ_int : Integrable φ μ) :
-    (∫ a, L (φ a) ∂μ) = L (∫ a, φ a ∂μ) := by
-  apply Integrable.induction (P := fun φ => (∫ a, L (φ a) ∂μ) = L (∫ a, φ a ∂μ))
+    ∫ a, L (φ a) ∂μ = L (∫ a, φ a ∂μ) := by
+  apply φ_int.induction (P := fun φ => ∫ a, L (φ a) ∂μ = L (∫ a, φ a ∂μ))
   · intro e s s_meas _
     rw [integral_indicator_const e s_meas, ← @smul_one_smul E ℝ 𝕜 _ _ _ _ _ (μ s).toReal e,
       ContinuousLinearMap.map_smul, @smul_one_smul F ℝ 𝕜 _ _ _ _ _ (μ s).toReal (L e), ←
       integral_indicator_const (L e) s_meas]
     congr 1 with a
-    erw [Set.indicator_comp_of_zero L.map_zero]
-    rfl
+    rw [← Function.comp_def L, Set.indicator_comp_of_zero L.map_zero, Function.comp_apply]
   · intro f g _ f_int g_int hf hg
     simp [L.map_add, integral_add (μ := μ) f_int g_int,
       integral_add (μ := μ) (L.integrable_comp f_int) (L.integrable_comp g_int), hf, hg]
@@ -1136,7 +1133,6 @@ theorem integral_comp_comm (L : E →L[𝕜] F) {φ : α → E} (φ_int : Integr
     convert hf using 1 <;> clear hf
     · exact integral_congr_ae (hfg.fun_comp L).symm
     · rw [integral_congr_ae hfg.symm]
-  all_goals assumption
 #align continuous_linear_map.integral_comp_comm ContinuousLinearMap.integral_comp_comm
 
 theorem integral_apply {H : Type*} [NormedAddCommGroup H] [NormedSpace 𝕜 H] {φ : α → H →L[𝕜] E}
@@ -1145,7 +1141,7 @@ theorem integral_apply {H : Type*} [NormedAddCommGroup H] [NormedSpace 𝕜 H] {
 #align continuous_linear_map.integral_apply ContinuousLinearMap.integral_apply
 
 theorem integral_comp_comm' (L : E →L[𝕜] F) {K} (hL : AntilipschitzWith K L) (φ : α → E) :
-    (∫ a, L (φ a) ∂μ) = L (∫ a, φ a ∂μ) := by
+    ∫ a, L (φ a) ∂μ = L (∫ a, φ a ∂μ) := by
   by_cases h : Integrable φ μ
   · exact integral_comp_comm L h
   have : ¬Integrable (fun a => L (φ a)) μ := by
@@ -1155,7 +1151,7 @@ theorem integral_comp_comm' (L : E →L[𝕜] F) {K} (hL : AntilipschitzWith K L
 #align continuous_linear_map.integral_comp_comm' ContinuousLinearMap.integral_comp_comm'
 
 theorem integral_comp_L1_comm (L : E →L[𝕜] F) (φ : α →₁[μ] E) :
-    (∫ a, L (φ a) ∂μ) = L (∫ a, φ a ∂μ) :=
+    ∫ a, L (φ a) ∂μ = L (∫ a, φ a ∂μ) :=
   L.integral_comp_comm (L1.integrable_coeFn φ)
 set_option linter.uppercaseLean3 false in
 #align continuous_linear_map.integral_comp_L1_comm ContinuousLinearMap.integral_comp_L1_comm
@@ -1166,7 +1162,7 @@ namespace LinearIsometry
 
 variable [CompleteSpace F] [NormedSpace ℝ F] [CompleteSpace E] [NormedSpace ℝ E]
 
-theorem integral_comp_comm (L : E →ₗᵢ[𝕜] F) (φ : α → E) : (∫ a, L (φ a) ∂μ) = L (∫ a, φ a ∂μ) :=
+theorem integral_comp_comm (L : E →ₗᵢ[𝕜] F) (φ : α → E) : ∫ a, L (φ a) ∂μ = L (∫ a, φ a ∂μ) :=
   L.toContinuousLinearMap.integral_comp_comm' L.antilipschitz _
 #align linear_isometry.integral_comp_comm LinearIsometry.integral_comp_comm
 
@@ -1176,39 +1172,37 @@ namespace ContinuousLinearEquiv
 
 variable [NormedSpace ℝ F] [NormedSpace ℝ E]
 
-theorem integral_comp_comm (L : E ≃L[𝕜] F) (φ : α → E) : (∫ a, L (φ a) ∂μ) = L (∫ a, φ a ∂μ) := by
+theorem integral_comp_comm (L : E ≃L[𝕜] F) (φ : α → E) : ∫ a, L (φ a) ∂μ = L (∫ a, φ a ∂μ) := by
   have : CompleteSpace E ↔ CompleteSpace F :=
     completeSpace_congr (e := L.toEquiv) L.uniformEmbedding
-  by_cases hE : CompleteSpace E
-  · have : CompleteSpace F := this.1 hE
-    exact L.toContinuousLinearMap.integral_comp_comm' L.antilipschitz _
-  · have := this.not.1 hE
-    simp [integral, *]
+  obtain ⟨_, _⟩|⟨_, _⟩ := iff_iff_and_or_not_and_not.mp this
+  · exact L.toContinuousLinearMap.integral_comp_comm' L.antilipschitz _
+  · simp [integral, *]
 #align continuous_linear_equiv.integral_comp_comm ContinuousLinearEquiv.integral_comp_comm
 
 end ContinuousLinearEquiv
 
 @[norm_cast]
-theorem integral_ofReal {f : α → ℝ} : (∫ a, (f a : 𝕜) ∂μ) = ↑(∫ a, f a ∂μ) :=
+theorem integral_ofReal {f : α → ℝ} : ∫ a, (f a : 𝕜) ∂μ = ↑(∫ a, f a ∂μ) :=
   (@IsROrC.ofRealLI 𝕜 _).integral_comp_comm f
 #align integral_of_real integral_ofReal
 
 theorem integral_re {f : α → 𝕜} (hf : Integrable f μ) :
-    (∫ a, IsROrC.re (f a) ∂μ) = IsROrC.re (∫ a, f a ∂μ) :=
+    ∫ a, IsROrC.re (f a) ∂μ = IsROrC.re (∫ a, f a ∂μ) :=
   (@IsROrC.reCLM 𝕜 _).integral_comp_comm hf
 #align integral_re integral_re
 
 theorem integral_im {f : α → 𝕜} (hf : Integrable f μ) :
-    (∫ a, IsROrC.im (f a) ∂μ) = IsROrC.im (∫ a, f a ∂μ) :=
+    ∫ a, IsROrC.im (f a) ∂μ = IsROrC.im (∫ a, f a ∂μ) :=
   (@IsROrC.imCLM 𝕜 _).integral_comp_comm hf
 #align integral_im integral_im
 
-theorem integral_conj {f : α → 𝕜} : (∫ a, conj (f a) ∂μ) = conj (∫ a, f a ∂μ) :=
+theorem integral_conj {f : α → 𝕜} : ∫ a, conj (f a) ∂μ = conj (∫ a, f a ∂μ) :=
   (@IsROrC.conjLIE 𝕜 _).toLinearIsometry.integral_comp_comm f
 #align integral_conj integral_conj
 
 theorem integral_coe_re_add_coe_im {f : α → 𝕜} (hf : Integrable f μ) :
-    (∫ x, (IsROrC.re (f x) : 𝕜) ∂μ) + (∫ x, (IsROrC.im (f x) : 𝕜) ∂μ) * IsROrC.I = ∫ x, f x ∂μ := by
+    ∫ x, (IsROrC.re (f x) : 𝕜) ∂μ + (∫ x, (IsROrC.im (f x) : 𝕜) ∂μ) * IsROrC.I = ∫ x, f x ∂μ := by
   rw [mul_comm, ← smul_eq_mul, ← integral_smul, ← integral_add]
   · congr
     ext1 x
@@ -1250,7 +1244,7 @@ theorem snd_integral [CompleteSpace E] {f : α → E × F} (hf : Integrable f μ
 
 theorem integral_pair [CompleteSpace E] [CompleteSpace F] {f : α → E} {g : α → F}
     (hf : Integrable f μ) (hg : Integrable g μ) :
-    (∫ x, (f x, g x) ∂μ) = (∫ x, f x ∂μ, ∫ x, g x ∂μ) :=
+    ∫ x, (f x, g x) ∂μ = (∫ x, f x ∂μ, ∫ x, g x ∂μ) :=
   have := hf.prod_mk hg
   Prod.ext (fst_integral this) (snd_integral this)
 #align integral_pair integral_pair

Co-authored-by: adomani <adomani@gmail.com>

@@ -1454,7 +1454,7 @@ lemma continuousOn_integral_bilinear_of_locally_integrable_of_compact_support
       apply StronglyMeasurable.aestronglyMeasurable
       apply Continuous.stronglyMeasurable_of_support_subset_isCompact (A p hp) hk
       apply support_subset_iff'.2 (fun x hx ↦ hfs p x hp hx)
-    · apply eventually_of_forall (fun x ↦ (le_op_norm₂ L (g x) (f p x)).trans ?_)
+    · apply eventually_of_forall (fun x ↦ (le_opNorm₂ L (g x) (f p x)).trans ?_)
       gcongr
       apply hC
   filter_upwards [v_mem, self_mem_nhdsWithin] with p hp h'p
@@ -1478,7 +1478,7 @@ lemma continuousOn_integral_bilinear_of_locally_integrable_of_compact_support
           calc
           ‖L (g x) (f p x) - L (g x) (f q x)‖
             = ‖L (g x) (f p x - f q x)‖ := by simp only [map_sub]
-          _ ≤ ‖L‖ * ‖g x‖ * ‖f p x - f q x‖ := le_op_norm₂ _ _ _
+          _ ≤ ‖L‖ * ‖g x‖ * ‖f p x - f q x‖ := le_opNorm₂ _ _ _
           _ ≤ ‖L‖ * ‖g x‖ * δ := by gcongr
         · simp only [hfs p x h'p hx, hfs q x hq hx, sub_self, norm_zero, mul_zero]
           positivity

Fixes a typo: the RHS of integral_Icc_eq_integral_Ioo was an Ico not an Ioo.

@@ -658,7 +658,7 @@ theorem integral_Ico_eq_integral_Ioo : ∫ t in Ico a b, f t ∂μ = ∫ t in Io
   integral_Ico_eq_integral_Ioo' <| measure_singleton a
 #align measure_theory.integral_Ico_eq_integral_Ioo MeasureTheory.integral_Ico_eq_integral_Ioo
 
-theorem integral_Icc_eq_integral_Ioo : ∫ t in Icc a b, f t ∂μ = ∫ t in Ico a b, f t ∂μ := by
+theorem integral_Icc_eq_integral_Ioo : ∫ t in Icc a b, f t ∂μ = ∫ t in Ioo a b, f t ∂μ := by
   rw [integral_Icc_eq_integral_Ico, integral_Ico_eq_integral_Ioo]
 #align measure_theory.integral_Icc_eq_integral_Ioo MeasureTheory.integral_Icc_eq_integral_Ioo
 

Rename

• Complex.equivRealProdClm → Complex.equivRealProdCLM;
  • TODO: should this one use CLE?
• Complex.reClm → Complex.reCLM;
• Complex.imClm → Complex.imCLM;
• Complex.conjLie → Complex.conjLIE;
• Complex.conjCle → Complex.conjCLE;
• Complex.ofRealLi → Complex.ofRealLI;
• Complex.ofRealClm → Complex.ofRealCLM;
• fderivInnerClm → fderivInnerCLM;
• LinearPMap.adjointDomainMkClm → LinearPMap.adjointDomainMkCLM;
• LinearPMap.adjointDomainMkClmExtend → LinearPMap.adjointDomainMkCLMExtend;
• IsROrC.reClm → IsROrC.reCLM;
• IsROrC.imClm → IsROrC.imCLM;
• IsROrC.conjLie → IsROrC.conjLIE;
• IsROrC.conjCle → IsROrC.conjCLE;
• IsROrC.ofRealLi → IsROrC.ofRealLI;
• IsROrC.ofRealClm → IsROrC.ofRealCLM;
• MeasureTheory.condexpL1Clm → MeasureTheory.condexpL1CLM;
• algebraMapClm → algebraMapCLM;
• WeakDual.CharacterSpace.toClm → WeakDual.CharacterSpace.toCLM;
• BoundedContinuousFunction.evalClm → BoundedContinuousFunction.evalCLM;
• ContinuousMap.evalClm → ContinuousMap.evalCLM;
• TrivSqZeroExt.fstClm → TrivSqZeroExt.fstClm;
• TrivSqZeroExt.sndClm → TrivSqZeroExt.sndCLM;
• TrivSqZeroExt.inlClm → TrivSqZeroExt.inlCLM;
• TrivSqZeroExt.inrClm → TrivSqZeroExt.inrCLM

and related theorems.

@@ -1190,21 +1190,21 @@ end ContinuousLinearEquiv
 
 @[norm_cast]
 theorem integral_ofReal {f : α → ℝ} : (∫ a, (f a : 𝕜) ∂μ) = ↑(∫ a, f a ∂μ) :=
-  (@IsROrC.ofRealLi 𝕜 _).integral_comp_comm f
+  (@IsROrC.ofRealLI 𝕜 _).integral_comp_comm f
 #align integral_of_real integral_ofReal
 
 theorem integral_re {f : α → 𝕜} (hf : Integrable f μ) :
     (∫ a, IsROrC.re (f a) ∂μ) = IsROrC.re (∫ a, f a ∂μ) :=
-  (@IsROrC.reClm 𝕜 _).integral_comp_comm hf
+  (@IsROrC.reCLM 𝕜 _).integral_comp_comm hf
 #align integral_re integral_re
 
 theorem integral_im {f : α → 𝕜} (hf : Integrable f μ) :
     (∫ a, IsROrC.im (f a) ∂μ) = IsROrC.im (∫ a, f a ∂μ) :=
-  (@IsROrC.imClm 𝕜 _).integral_comp_comm hf
+  (@IsROrC.imCLM 𝕜 _).integral_comp_comm hf
 #align integral_im integral_im
 
 theorem integral_conj {f : α → 𝕜} : (∫ a, conj (f a) ∂μ) = conj (∫ a, f a ∂μ) :=
-  (@IsROrC.conjLie 𝕜 _).toLinearIsometry.integral_comp_comm f
+  (@IsROrC.conjLIE 𝕜 _).toLinearIsometry.integral_comp_comm f
 #align integral_conj integral_conj
 
 theorem integral_coe_re_add_coe_im {f : α → 𝕜} (hf : Integrable f μ) :

Reorder/golf lemmas, add ae_restrict_iff₀.

Also remove 3 lemmas that are no longer needed and can be proved in 1 line each.

@@ -403,36 +403,6 @@ theorem set_integral_eq_integral_of_forall_compl_eq_zero (h : ∀ x, x ∉ s →
   set_integral_eq_integral_of_ae_compl_eq_zero (eventually_of_forall h)
 #align measure_theory.set_integral_eq_integral_of_forall_compl_eq_zero MeasureTheory.set_integral_eq_integral_of_forall_compl_eq_zero
 
-lemma ae_restrict_eq_const_iff_ae_eq_const_of_mem {E : Type*} [MeasurableSpace E]
-    [MeasurableSingletonClass E] {f : α → E} (c : E) {s : Set α}
-    (f_mble : NullMeasurable f (μ.restrict s)) :
-    f =ᵐ[Measure.restrict μ s] (fun _ ↦ c) ↔ ∀ᵐ x ∂μ, x ∈ s → f x = c := by
-  simp only [Measure.ae, MeasurableSet.compl_iff, EventuallyEq, Filter.Eventually,
-             Pi.zero_apply, Filter.mem_mk, mem_setOf_eq]
-  rw [Measure.restrict_apply₀]
-  · constructor <;> intro h <;> rw [← h] <;> congr <;> ext x <;> aesop
-  · apply NullMeasurableSet.compl
-    convert f_mble (MeasurableSet.singleton c)
-
-lemma ae_restrict_eq_const_iff_ae_eq_const_of_mem' {E : Type*} (c : E) (f : α → E) {s : Set α}
-    (s_mble : MeasurableSet s) :
-    f =ᵐ[Measure.restrict μ s] (fun _ ↦ c) ↔ ∀ᵐ x ∂μ, x ∈ s → f x = c := by
-  simp only [Measure.ae, MeasurableSet.compl_iff, EventuallyEq, Filter.Eventually,
-             Pi.zero_apply, Filter.mem_mk, mem_setOf_eq]
-  rw [Measure.restrict_apply_eq_zero']
-  · constructor <;> intro h <;> rw [← h] <;> congr <;> ext x <;> aesop
-  · exact s_mble
-
-/-- If a function equals zero almost everywhere w.r.t. restriction of the measure to `sᶜ`, then its
-integral on `s` coincides with its integral on the whole space. -/
-lemma set_integral_eq_integral_of_ae_restrict_eq_zero (hs : f =ᵐ[μ.restrict sᶜ] 0) :
-    ∫ ω in s, f ω ∂μ = ∫ ω, f ω ∂μ := by
-  borelize E
-  refine set_integral_eq_integral_of_ae_compl_eq_zero ?_
-  have f_mble : NullMeasurable f (μ.restrict sᶜ) :=
-    NullMeasurable.congr measurable_const.nullMeasurable hs.symm
-  simpa only [mem_compl_iff] using (ae_restrict_eq_const_iff_ae_eq_const_of_mem 0 f_mble).mp hs
-
 theorem set_integral_neg_eq_set_integral_nonpos [LinearOrder E] {f : α → E}
     (hf : AEStronglyMeasurable f μ) :
     ∫ x in {x | f x < 0}, f x ∂μ = ∫ x in {x | f x ≤ 0}, f x ∂μ := by

Define exponentially tilted measures. The exponential tilting of a measure μ on α by a function f : α → ℝ is the measure with density x ↦ exp (f x) / ∫ y, exp (f y) ∂μ with respect to μ.

Co-authored-by: Rémy Degenne <remydegenne@gmail.com> Co-authored-by: RemyDegenne <remydegenne@gmail.com>

@@ -1373,6 +1373,11 @@ theorem set_integral_withDensity_eq_set_integral_smul₀ {f : α → ℝ≥0} {s
   rw [restrict_withDensity hs, integral_withDensity_eq_integral_smul₀ hf]
 #align set_integral_with_density_eq_set_integral_smul₀ set_integral_withDensity_eq_set_integral_smul₀
 
+theorem set_integral_withDensity_eq_set_integral_smul₀' [SFinite μ] {f : α → ℝ≥0} (s : Set α)
+    (hf : AEMeasurable f (μ.restrict s)) (g : α → E)  :
+    ∫ a in s, g a ∂μ.withDensity (fun x => f x) = ∫ a in s, f a • g a ∂μ := by
+  rw [restrict_withDensity' s, integral_withDensity_eq_integral_smul₀ hf]
+
 end
 
 section thickenedIndicator

@@ -1179,8 +1179,8 @@ theorem integral_comp_comm' (L : E →L[𝕜] F) {K} (hL : AntilipschitzWith K L
   by_cases h : Integrable φ μ
   · exact integral_comp_comm L h
   have : ¬Integrable (fun a => L (φ a)) μ := by
-    erw [LipschitzWith.integrable_comp_iff_of_antilipschitz L.lipschitz hL L.map_zero]
-    assumption
+    rwa [← Function.comp_def,
+      LipschitzWith.integrable_comp_iff_of_antilipschitz L.lipschitz hL L.map_zero]
   simp [integral_undef, h, this]
 #align continuous_linear_map.integral_comp_comm' ContinuousLinearMap.integral_comp_comm'
 

PR contents

This is the supremum of

• #8284
• #8056
• #8023
• #8332
• #8226 (already approved)
• #7834 (already approved)

along with some minor fixes from failures on nightly-testing as Mathlib master is merged into it.

Note that some PRs for changes that are already compatible with the current toolchain and will be necessary have already been split out: #8380.

I am hopeful that in future we will be able to progressively merge adaptation PRs into a bump/v4.X.0 branch, so we never end up with a "big merge" like this. However one of these adaptation PRs (#8056) predates my new scheme for combined CI, and it wasn't possible to keep that PR viable in the meantime.

Lean PRs involved in this bump

In particular this includes adjustments for the Lean PRs

• leanprover/lean4#2778
• leanprover/lean4#2790
• leanprover/lean4#2783
• leanprover/lean4#2825
• leanprover/lean4#2722

leanprover/lean4#2778

We can get rid of all the

local macro_rules | `($x ^ $y) => `(HPow.hPow $x $y) -- Porting note: See issue [lean4#2220](https://github.com/leanprover/lean4/pull/2220)

macros across Mathlib (and in any projects that want to write natural number powers of reals).

leanprover/lean4#2722

Changes the default behaviour of simp to (config := {decide := false}). This makes simp (and consequentially norm_num) less powerful, but also more consistent, and less likely to blow up in long failures. This requires a variety of changes: changing some previously by simp or norm_num to decide or rfl, or adding (config := {decide := true}).

leanprover/lean4#2783

This changed the behaviour of simp so that simp [f] will only unfold "fully applied" occurrences of f. The old behaviour can be recovered with simp (config := { unfoldPartialApp := true }). We may in future add a syntax for this, e.g. simp [!f]; please provide feedback! In the meantime, we have made the following changes:

• switching to using explicit lemmas that have the intended level of application
• (config := { unfoldPartialApp := true }) in some places, to recover the old behaviour
• Using @[eqns] to manually adjust the equation lemmas for a particular definition, recovering the old behaviour just for that definition. See #8371, where we do this for Function.comp and Function.flip.

This change in Lean may require further changes down the line (e.g. adding the !f syntax, and/or upstreaming the special treatment for Function.comp and Function.flip, and/or removing this special treatment). Please keep an open and skeptical mind about these changes!

Co-authored-by: leanprover-community-mathlib4-bot <leanprover-community-mathlib4-bot@users.noreply.github.com> Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: Mauricio Collares <mauricio@collares.org>

@@ -1291,10 +1291,10 @@ theorem integral_smul_const {𝕜 : Type*} [IsROrC 𝕜] [NormedSpace 𝕜 E] [C
   by_cases hf : Integrable f μ
   · exact ((1 : 𝕜 →L[𝕜] 𝕜).smulRight c).integral_comp_comm hf
   · by_cases hc : c = 0
-    · simp only [hc, integral_zero, smul_zero]
+    · simp [hc, integral_zero, smul_zero]
     rw [integral_undef hf, integral_undef, zero_smul]
     rw [integrable_smul_const hc]
-    simp_rw [hf]
+    simp_rw [hf, not_false_eq_true]
 #align integral_smul_const integral_smul_const
 
 theorem integral_withDensity_eq_integral_smul {f : α → ℝ≥0} (f_meas : Measurable f) (g : α → E) :

Rename

• summable_of_norm_bounded -> Summable.of_norm_bounded;
• summable_of_norm_bounded_eventually -> Summable.of_norm_bounded_eventually;
• summable_of_nnnorm_bounded -> Summable.of_nnnorm_bounded;
• summable_of_summable_norm -> Summable.of_norm;
• summable_of_summable_nnnorm -> Summable.of_nnnorm;

New lemmas

• Summable.of_norm_bounded_eventually_nat
• Summable.norm

Misc changes

• Golf a few proofs.

@@ -873,7 +873,7 @@ theorem integrableOn_iUnion_of_summable_norm_restrict {f : C(α, E)} {s : β →
   refine'
     integrableOn_iUnion_of_summable_integral_norm (fun i => (s i).isCompact.isClosed.measurableSet)
       (fun i => (map_continuous f).continuousOn.integrableOn_compact (s i).isCompact)
-      (summable_of_nonneg_of_le (fun ι => integral_nonneg fun x => norm_nonneg _) (fun i => _) hf)
+      (.of_nonneg_of_le (fun ι => integral_nonneg fun x => norm_nonneg _) (fun i => _) hf)
   rw [← (Real.norm_of_nonneg (integral_nonneg fun a => norm_nonneg _) : ‖_‖ = ∫ x in s i, ‖f x‖ ∂μ)]
   exact
     norm_set_integral_le_of_norm_le_const' (s i).isCompact.measure_lt_top

The current version of continuity of parametric integrals assume a first countable topology, to apply the dominated convergence theorem. When one deals with continuous compactly supported functions, this is not necessary, and a direct elementary approach makes it possible to remove the first countable assumption.

@@ -1431,3 +1431,92 @@ theorem Integrable.simpleFunc_mul' (hm : m ≤ m0) (g : @SimpleFunc β m ℝ) (h
 end MeasureTheory
 
 end BilinearMap
+
+section ParametricIntegral
+
+variable {α β F G 𝕜 : Type*} [TopologicalSpace α] [TopologicalSpace β] [MeasurableSpace β]
+  [OpensMeasurableSpace β] {μ : Measure β} [NontriviallyNormedField 𝕜] [NormedSpace ℝ E]
+  [NormedAddCommGroup F] [NormedSpace 𝕜 F] [NormedAddCommGroup G] [NormedSpace 𝕜 G]
+
+open Metric Function ContinuousLinearMap
+
+/-- Consider a parameterized integral `a ↦ ∫ x, L (g x) (f a x)` where `L` is bilinear,
+`g` is locally integrable and `f` is continuous and uniformly compactly supported. Then the
+integral depends continuously on `a`. -/
+lemma continuousOn_integral_bilinear_of_locally_integrable_of_compact_support
+    [NormedSpace 𝕜 E] (L : F →L[𝕜] G →L[𝕜] E)
+    {f : α → β → G} {s : Set α} {k : Set β} {g : β → F}
+    (hk : IsCompact k) (hf : ContinuousOn f.uncurry (s ×ˢ univ))
+    (hfs : ∀ p, ∀ x, p ∈ s → x ∉ k → f p x = 0) (hg : IntegrableOn g k μ) :
+    ContinuousOn (fun a ↦ ∫ x, L (g x) (f a x) ∂μ) s := by
+  have A : ∀ p ∈ s, Continuous (f p) := fun p hp ↦ by
+    refine hf.comp_continuous (continuous_const.prod_mk continuous_id') fun x => ?_
+    simpa only [prod_mk_mem_set_prod_eq, mem_univ, and_true] using hp
+  intro q hq
+  apply Metric.continuousWithinAt_iff'.2 (fun ε εpos ↦ ?_)
+  obtain ⟨δ, δpos, hδ⟩ : ∃ (δ : ℝ), 0 < δ ∧ ∫ x in k, ‖L‖ * ‖g x‖ * δ ∂μ < ε := by
+    simpa [integral_mul_right] using exists_pos_mul_lt εpos _
+  obtain ⟨v, v_mem, hv⟩ : ∃ v ∈ 𝓝[s] q, ∀ p ∈ v, ∀ x ∈ k, dist (f p x) (f q x) < δ :=
+    hk.mem_uniformity_of_prod
+      (hf.mono (Set.prod_mono_right (subset_univ k))) hq (dist_mem_uniformity δpos)
+  simp_rw [dist_eq_norm] at hv ⊢
+  have I : ∀ p ∈ s, IntegrableOn (fun x ↦ L (g x) (f p x)) k μ := by
+    intro p hp
+    obtain ⟨C, hC⟩ : ∃ C, ∀ x, ‖f p x‖ ≤ C := by
+      have : ContinuousOn (f p) k := by
+        have : ContinuousOn (fun x ↦ (p, x)) k := (Continuous.Prod.mk p).continuousOn
+        exact hf.comp this (by simp [MapsTo, hp])
+      rcases IsCompact.exists_bound_of_continuousOn hk this with ⟨C, hC⟩
+      refine ⟨max C 0, fun x ↦ ?_⟩
+      by_cases hx : x ∈ k
+      · exact (hC x hx).trans (le_max_left _ _)
+      · simp [hfs p x hp hx]
+    have : IntegrableOn (fun x ↦ ‖L‖ * ‖g x‖ * C) k μ :=
+      (hg.norm.const_mul _).mul_const _
+    apply Integrable.mono' this ?_ ?_
+    · borelize G
+      apply L.aestronglyMeasurable_comp₂ hg.aestronglyMeasurable
+      apply StronglyMeasurable.aestronglyMeasurable
+      apply Continuous.stronglyMeasurable_of_support_subset_isCompact (A p hp) hk
+      apply support_subset_iff'.2 (fun x hx ↦ hfs p x hp hx)
+    · apply eventually_of_forall (fun x ↦ (le_op_norm₂ L (g x) (f p x)).trans ?_)
+      gcongr
+      apply hC
+  filter_upwards [v_mem, self_mem_nhdsWithin] with p hp h'p
+  calc
+  ‖∫ x, L (g x) (f p x) ∂μ - ∫ x, L (g x) (f q x) ∂μ‖
+    = ‖∫ x in k, L (g x) (f p x) ∂μ - ∫ x in k, L (g x) (f q x) ∂μ‖ := by
+      congr 2
+      · refine (set_integral_eq_integral_of_forall_compl_eq_zero (fun x hx ↦ ?_)).symm
+        simp [hfs p x h'p hx]
+      · refine (set_integral_eq_integral_of_forall_compl_eq_zero (fun x hx ↦ ?_)).symm
+        simp [hfs q x hq hx]
+  _ = ‖∫ x in k, L (g x) (f p x) - L (g x) (f q x) ∂μ‖ := by rw [integral_sub (I p h'p) (I q hq)]
+  _ ≤ ∫ x in k, ‖L (g x) (f p x) - L (g x) (f q x)‖ ∂μ := norm_integral_le_integral_norm _
+  _ ≤ ∫ x in k, ‖L‖ * ‖g x‖ * δ ∂μ := by
+      apply integral_mono_of_nonneg (eventually_of_forall (fun x ↦ by positivity))
+      · exact (hg.norm.const_mul _).mul_const _
+      · apply eventually_of_forall (fun x ↦ ?_)
+        by_cases hx : x ∈ k
+        · dsimp only
+          specialize hv p hp x hx
+          calc
+          ‖L (g x) (f p x) - L (g x) (f q x)‖
+            = ‖L (g x) (f p x - f q x)‖ := by simp only [map_sub]
+          _ ≤ ‖L‖ * ‖g x‖ * ‖f p x - f q x‖ := le_op_norm₂ _ _ _
+          _ ≤ ‖L‖ * ‖g x‖ * δ := by gcongr
+        · simp only [hfs p x h'p hx, hfs q x hq hx, sub_self, norm_zero, mul_zero]
+          positivity
+  _ < ε := hδ
+
+/-- Consider a parameterized integral `a ↦ ∫ x, f a x` where `f` is continuous and uniformly
+compactly supported. Then the integral depends continuously on `a`. -/
+lemma continuousOn_integral_of_compact_support
+    {f : α → β → E} {s : Set α} {k : Set β} [IsFiniteMeasureOnCompacts μ]
+    (hk : IsCompact k) (hf : ContinuousOn f.uncurry (s ×ˢ univ))
+    (hfs : ∀ p, ∀ x, p ∈ s → x ∉ k → f p x = 0) :
+    ContinuousOn (fun a ↦ ∫ x, f a x ∂μ) s := by
+  simpa using continuousOn_integral_bilinear_of_locally_integrable_of_compact_support (lsmul ℝ ℝ)
+    hk hf hfs (integrableOn_const.2 (Or.inr hk.measure_lt_top)) (μ := μ) (g := fun _ ↦ 1)
+
+end ParametricIntegral

Also weaken some T2 space assumptions in some integration lemmas.

Co-authored-by: Heather Macbeth <25316162+hrmacbeth@users.noreply.github.com>

@@ -810,6 +810,37 @@ theorem set_integral_nonpos_le {s : Set α} (hs : MeasurableSet s) (hf : Strongl
       (hfi.indicator hs) (indicator_nonpos_le_indicator s f)
 #align measure_theory.set_integral_nonpos_le MeasureTheory.set_integral_nonpos_le
 
+lemma Integrable.measure_le_integral {f : α → ℝ} (f_int : Integrable f μ) (f_nonneg : 0 ≤ᵐ[μ] f)
+    {s : Set α} (hs : ∀ x ∈ s, 1 ≤ f x) :
+    μ s ≤ ENNReal.ofReal (∫ x, f x ∂μ) := by
+  rw [ofReal_integral_eq_lintegral_ofReal f_int f_nonneg]
+  apply meas_le_lintegral₀
+  · exact ENNReal.continuous_ofReal.measurable.comp_aemeasurable f_int.1.aemeasurable
+  · intro x hx
+    simpa using ENNReal.ofReal_le_ofReal (hs x hx)
+
+lemma integral_le_measure {f : α → ℝ} {s : Set α}
+    (hs : ∀ x ∈ s, f x ≤ 1) (h's : ∀ x ∈ sᶜ, f x ≤ 0) :
+    ENNReal.ofReal (∫ x, f x ∂μ) ≤ μ s := by
+  by_cases H : Integrable f μ; swap
+  · simp [integral_undef H]
+  let g x := max (f x) 0
+  have g_int : Integrable g μ := H.pos_part
+  have : ENNReal.ofReal (∫ x, f x ∂μ) ≤ ENNReal.ofReal (∫ x, g x ∂μ) := by
+    apply ENNReal.ofReal_le_ofReal
+    exact integral_mono H g_int (fun x ↦ le_max_left _ _)
+  apply this.trans
+  rw [ofReal_integral_eq_lintegral_ofReal g_int (eventually_of_forall (fun x ↦ le_max_right _ _))]
+  apply lintegral_le_meas
+  · intro x
+    apply ENNReal.ofReal_le_of_le_toReal
+    by_cases H : x ∈ s
+    · simpa using hs x H
+    · apply le_trans _ zero_le_one
+      simpa using h's x H
+  · intro x hx
+    simpa using h's x hx
+
 end Nonneg
 
 section IntegrableUnion

Also add completeSpace_prod, integrable_prod.

@@ -862,7 +862,7 @@ end IntegrableUnion
 
 section TendstoMono
 
-variable {μ : Measure α} [NormedAddCommGroup E] [CompleteSpace E] [NormedSpace ℝ E] {s : ℕ → Set α}
+variable {μ : Measure α} [NormedAddCommGroup E] [NormedSpace ℝ E] {s : ℕ → Set α}
   {f : α → E}
 
 theorem _root_.Antitone.tendsto_set_integral (hsm : ∀ i, MeasurableSet (s i)) (h_anti : Antitone s)
@@ -1095,7 +1095,7 @@ variable {μ : Measure α} {𝕜 : Type*} [IsROrC 𝕜] [NormedSpace 𝕜 E] [No
 
 namespace ContinuousLinearMap
 
-variable [CompleteSpace F] [NormedSpace ℝ F]
+variable [NormedSpace ℝ F]
 
 theorem integral_compLp (L : E →L[𝕜] F) (φ : Lp E p μ) :
     (∫ a, (L.compLp φ) a ∂μ) = ∫ a, L (φ a) ∂μ :=
@@ -1115,7 +1115,7 @@ theorem continuous_integral_comp_L1 (L : E →L[𝕜] F) :
 set_option linter.uppercaseLean3 false in
 #align continuous_linear_map.continuous_integral_comp_L1 ContinuousLinearMap.continuous_integral_comp_L1
 
-variable [CompleteSpace E] [NormedSpace ℝ E]
+variable [CompleteSpace E] [CompleteSpace F] [NormedSpace ℝ E]
 
 theorem integral_comp_comm (L : E →L[𝕜] F) {φ : α → E} (φ_int : Integrable φ μ) :
     (∫ a, L (φ a) ∂μ) = L (∫ a, φ a ∂μ) := by
@@ -1173,16 +1173,20 @@ end LinearIsometry
 
 namespace ContinuousLinearEquiv
 
-variable [CompleteSpace F] [NormedSpace ℝ F] [CompleteSpace E] [NormedSpace ℝ E]
+variable [NormedSpace ℝ F] [NormedSpace ℝ E]
 
-theorem integral_comp_comm (L : E ≃L[𝕜] F) (φ : α → E) : (∫ a, L (φ a) ∂μ) = L (∫ a, φ a ∂μ) :=
-  L.toContinuousLinearMap.integral_comp_comm' L.antilipschitz _
+theorem integral_comp_comm (L : E ≃L[𝕜] F) (φ : α → E) : (∫ a, L (φ a) ∂μ) = L (∫ a, φ a ∂μ) := by
+  have : CompleteSpace E ↔ CompleteSpace F :=
+    completeSpace_congr (e := L.toEquiv) L.uniformEmbedding
+  by_cases hE : CompleteSpace E
+  · have : CompleteSpace F := this.1 hE
+    exact L.toContinuousLinearMap.integral_comp_comm' L.antilipschitz _
+  · have := this.not.1 hE
+    simp [integral, *]
 #align continuous_linear_equiv.integral_comp_comm ContinuousLinearEquiv.integral_comp_comm
 
 end ContinuousLinearEquiv
 
-variable [CompleteSpace E] [NormedSpace ℝ E] [CompleteSpace F] [NormedSpace ℝ F]
-
 @[norm_cast]
 theorem integral_ofReal {f : α → ℝ} : (∫ a, (f a : 𝕜) ∂μ) = ↑(∫ a, f a ∂μ) :=
   (@IsROrC.ofRealLi 𝕜 _).integral_comp_comm f
@@ -1224,21 +1228,34 @@ theorem set_integral_re_add_im {f : α → 𝕜} {i : Set α} (hf : IntegrableOn
   integral_re_add_im hf
 #align set_integral_re_add_im set_integral_re_add_im
 
-theorem fst_integral {f : α → E × F} (hf : Integrable f μ) : (∫ x, f x ∂μ).1 = ∫ x, (f x).1 ∂μ :=
-  ((ContinuousLinearMap.fst ℝ E F).integral_comp_comm hf).symm
+variable [NormedSpace ℝ E] [NormedSpace ℝ F]
+
+lemma swap_integral (f : α → E × F) : (∫ x, f x ∂μ).swap = ∫ x, (f x).swap ∂μ :=
+  .symm <| (ContinuousLinearEquiv.prodComm ℝ E F).integral_comp_comm f
+
+theorem fst_integral [CompleteSpace F] {f : α → E × F} (hf : Integrable f μ) :
+    (∫ x, f x ∂μ).1 = ∫ x, (f x).1 ∂μ := by
+  by_cases hE : CompleteSpace E
+  · exact ((ContinuousLinearMap.fst ℝ E F).integral_comp_comm hf).symm
+  · have : ¬(CompleteSpace (E × F)) := fun h ↦ hE <| .fst_of_prod (β := F)
+    simp [integral, *]
 #align fst_integral fst_integral
 
-theorem snd_integral {f : α → E × F} (hf : Integrable f μ) : (∫ x, f x ∂μ).2 = ∫ x, (f x).2 ∂μ :=
-  ((ContinuousLinearMap.snd ℝ E F).integral_comp_comm hf).symm
+theorem snd_integral [CompleteSpace E] {f : α → E × F} (hf : Integrable f μ) :
+    (∫ x, f x ∂μ).2 = ∫ x, (f x).2 ∂μ := by
+  rw [← Prod.fst_swap, swap_integral]
+  exact fst_integral <| hf.snd.prod_mk hf.fst
 #align snd_integral snd_integral
 
-theorem integral_pair {f : α → E} {g : α → F} (hf : Integrable f μ) (hg : Integrable g μ) :
+theorem integral_pair [CompleteSpace E] [CompleteSpace F] {f : α → E} {g : α → F}
+    (hf : Integrable f μ) (hg : Integrable g μ) :
     (∫ x, (f x, g x) ∂μ) = (∫ x, f x ∂μ, ∫ x, g x ∂μ) :=
   have := hf.prod_mk hg
   Prod.ext (fst_integral this) (snd_integral this)
 #align integral_pair integral_pair
 
-theorem integral_smul_const {𝕜 : Type*} [IsROrC 𝕜] [NormedSpace 𝕜 E] (f : α → 𝕜) (c : E) :
+theorem integral_smul_const {𝕜 : Type*} [IsROrC 𝕜] [NormedSpace 𝕜 E] [CompleteSpace E]
+    (f : α → 𝕜) (c : E) :
     ∫ x, f x • c ∂μ = (∫ x, f x ∂μ) • c := by
   by_cases hf : Integrable f μ
   · exact ((1 : 𝕜 →L[𝕜] 𝕜).smulRight c).integral_comp_comm hf
@@ -1251,6 +1268,7 @@ theorem integral_smul_const {𝕜 : Type*} [IsROrC 𝕜] [NormedSpace 𝕜 E] (f
 
 theorem integral_withDensity_eq_integral_smul {f : α → ℝ≥0} (f_meas : Measurable f) (g : α → E) :
     ∫ a, g a ∂μ.withDensity (fun x => f x) = ∫ a, f a • g a ∂μ := by
+  by_cases hE : CompleteSpace E; swap; · simp [integral, hE]
   by_cases hg : Integrable g (μ.withDensity fun x => f x); swap
   · rw [integral_undef hg, integral_undef]
     rwa [← integrable_withDensity_iff_integrable_smul f_meas]

Layer cake formulas currently exist for ENNReal-valued functions and Lebesgue integrals. This PR adds the most common version of the layer cake formula for integrable a.e.-nonnegative real-valued functions and Bochner integrals.

Co-authored-by: kkytola <“kalle.kytola@aalto.fi”> Co-authored-by: kkytola <39528102+kkytola@users.noreply.github.com>

@@ -403,6 +403,36 @@ theorem set_integral_eq_integral_of_forall_compl_eq_zero (h : ∀ x, x ∉ s →
   set_integral_eq_integral_of_ae_compl_eq_zero (eventually_of_forall h)
 #align measure_theory.set_integral_eq_integral_of_forall_compl_eq_zero MeasureTheory.set_integral_eq_integral_of_forall_compl_eq_zero
 
+lemma ae_restrict_eq_const_iff_ae_eq_const_of_mem {E : Type*} [MeasurableSpace E]
+    [MeasurableSingletonClass E] {f : α → E} (c : E) {s : Set α}
+    (f_mble : NullMeasurable f (μ.restrict s)) :
+    f =ᵐ[Measure.restrict μ s] (fun _ ↦ c) ↔ ∀ᵐ x ∂μ, x ∈ s → f x = c := by
+  simp only [Measure.ae, MeasurableSet.compl_iff, EventuallyEq, Filter.Eventually,
+             Pi.zero_apply, Filter.mem_mk, mem_setOf_eq]
+  rw [Measure.restrict_apply₀]
+  · constructor <;> intro h <;> rw [← h] <;> congr <;> ext x <;> aesop
+  · apply NullMeasurableSet.compl
+    convert f_mble (MeasurableSet.singleton c)
+
+lemma ae_restrict_eq_const_iff_ae_eq_const_of_mem' {E : Type*} (c : E) (f : α → E) {s : Set α}
+    (s_mble : MeasurableSet s) :
+    f =ᵐ[Measure.restrict μ s] (fun _ ↦ c) ↔ ∀ᵐ x ∂μ, x ∈ s → f x = c := by
+  simp only [Measure.ae, MeasurableSet.compl_iff, EventuallyEq, Filter.Eventually,
+             Pi.zero_apply, Filter.mem_mk, mem_setOf_eq]
+  rw [Measure.restrict_apply_eq_zero']
+  · constructor <;> intro h <;> rw [← h] <;> congr <;> ext x <;> aesop
+  · exact s_mble
+
+/-- If a function equals zero almost everywhere w.r.t. restriction of the measure to `sᶜ`, then its
+integral on `s` coincides with its integral on the whole space. -/
+lemma set_integral_eq_integral_of_ae_restrict_eq_zero (hs : f =ᵐ[μ.restrict sᶜ] 0) :
+    ∫ ω in s, f ω ∂μ = ∫ ω, f ω ∂μ := by
+  borelize E
+  refine set_integral_eq_integral_of_ae_compl_eq_zero ?_
+  have f_mble : NullMeasurable f (μ.restrict sᶜ) :=
+    NullMeasurable.congr measurable_const.nullMeasurable hs.symm
+  simpa only [mem_compl_iff] using (ae_restrict_eq_const_iff_ae_eq_const_of_mem 0 f_mble).mp hs
+
 theorem set_integral_neg_eq_set_integral_nonpos [LinearOrder E] {f : α → E}
     (hf : AEStronglyMeasurable f μ) :
     ∫ x in {x | f x < 0}, f x ∂μ = ∫ x in {x | f x ≤ 0}, f x ∂μ := by

@@ -45,7 +45,7 @@ We provide the following notations for expressing the integral of a function on
 * `∫ a in s, f a ∂μ` is `MeasureTheory.integral (μ.restrict s) f`
 * `∫ a in s, f a` is `∫ a in s, f a ∂volume`
 
-Note that the set notations are defined in the file `MeasureTheory/Integral/Bochner`,
+Note that the set notations are defined in the file `MeasureTheory/Integral/Bochner.lean`,
 but we reference them here because all theorems about set integrals are in this file.
 
 -/
@@ -955,10 +955,12 @@ open MeasureTheory Asymptotics Metric
 
 variable {ι : Type*} [NormedAddCommGroup E]
 
-/-- Fundamental theorem of calculus for set integrals: if `μ` is a measure that is finite at a
-filter `l` and `f` is a measurable function that has a finite limit `b` at `l ⊓ μ.ae`, then `∫ x in
-s i, f x ∂μ = μ (s i) • b + o(μ (s i))` at a filter `li` provided that `s i` tends to `l.small_sets`
-along `li`. Since `μ (s i)` is an `ℝ≥0∞` number, we use `(μ (s i)).toReal` in the actual statement.
+/-- Fundamental theorem of calculus for set integrals:
+if `μ` is a measure that is finite at a filter `l` and
+`f` is a measurable function that has a finite limit `b` at `l ⊓ μ.ae`, then
+`∫ x in s i, f x ∂μ = μ (s i) • b + o(μ (s i))` at a filter `li` provided that
+`s i` tends to `l.smallSets` along `li`.
+Since `μ (s i)` is an `ℝ≥0∞` number, we use `(μ (s i)).toReal` in the actual statement.
 
 Often there is a good formula for `(μ (s i)).toReal`, so the formalization can take an optional
 argument `m` with this formula and a proof of `(fun i => (μ (s i)).toReal) =ᶠ[li] m`. Without these
@@ -970,9 +972,10 @@ theorem Filter.Tendsto.integral_sub_linear_isLittleO_ae [NormedSpace ℝ E] [Com
     (m : ι → ℝ := fun i => (μ (s i)).toReal)
     (hsμ : (fun i => (μ (s i)).toReal) =ᶠ[li] m := by rfl) :
     (fun i => (∫ x in s i, f x ∂μ) - m i • b) =o[li] m := by
-  suffices : (fun s => (∫ x in s, f x ∂μ) - (μ s).toReal • b) =o[l.smallSets] fun s => (μ s).toReal
-  exact (this.comp_tendsto hs).congr'
-    (hsμ.mono fun a ha => by dsimp only [Function.comp_apply] at ha ⊢; rw [ha]) hsμ
+  suffices
+      (fun s => (∫ x in s, f x ∂μ) - (μ s).toReal • b) =o[l.smallSets] fun s => (μ s).toReal from
+    (this.comp_tendsto hs).congr'
+      (hsμ.mono fun a ha => by dsimp only [Function.comp_apply] at ha ⊢; rw [ha]) hsμ
   refine' isLittleO_iff.2 fun ε ε₀ => _
   have : ∀ᶠ s in l.smallSets, ∀ᶠ x in μ.ae, x ∈ s → f x ∈ closedBall b ε :=
     eventually_smallSets_eventually.2 (h.eventually <| closedBall_mem_nhds _ ε₀)

Search&replace MulZeroClass.mul_zero -> mul_zero, MulZeroClass.zero_mul -> zero_mul.

These were introduced by Mathport, as the full name of mul_zero is actually MulZeroClass.mul_zero (it's exported with the short name).

@@ -1336,7 +1336,7 @@ theorem Integrable.simpleFunc_mul (g : SimpleFunc β ℝ) (hf : Integrable f μ)
     by_cases hx : x ∈ s
     · simp only [hx, Pi.mul_apply, Set.indicator_of_mem, Pi.smul_apply, Algebra.id.smul_eq_mul,
         ← Function.const_def]
-    · simp only [hx, Pi.mul_apply, Set.indicator_of_not_mem, not_false_iff, MulZeroClass.zero_mul]
+    · simp only [hx, Pi.mul_apply, Set.indicator_of_not_mem, not_false_iff, zero_mul]
   rw [this, integrable_indicator_iff hs]
   exact (hf.smul c).integrableOn
 #align measure_theory.integrable.simple_func_mul MeasureTheory.Integrable.simpleFunc_mul

We remove all possible occurences of Type _ and Sort _ in favor of Type* and Sort*.

This has nice performance benefits.

@@ -59,7 +59,7 @@ open Set Filter TopologicalSpace MeasureTheory Function
 
 open scoped Classical Topology Interval BigOperators Filter ENNReal NNReal MeasureTheory
 
-variable {α β E F : Type _} [MeasurableSpace α]
+variable {α β E F : Type*} [MeasurableSpace α]
 
 namespace MeasureTheory
 
@@ -122,7 +122,7 @@ theorem integral_inter_add_diff (ht : MeasurableSet t) (hfs : IntegrableOn f s 
   integral_inter_add_diff₀ ht.nullMeasurableSet hfs
 #align measure_theory.integral_inter_add_diff MeasureTheory.integral_inter_add_diff
 
-theorem integral_finset_biUnion {ι : Type _} (t : Finset ι) {s : ι → Set α}
+theorem integral_finset_biUnion {ι : Type*} (t : Finset ι) {s : ι → Set α}
     (hs : ∀ i ∈ t, MeasurableSet (s i)) (h's : Set.Pairwise (↑t) (Disjoint on s))
     (hf : ∀ i ∈ t, IntegrableOn f (s i) μ) :
     ∫ x in ⋃ i ∈ t, s i, f x ∂μ = ∑ i in t, ∫ x in s i, f x ∂μ := by
@@ -137,7 +137,7 @@ theorem integral_finset_biUnion {ι : Type _} (t : Finset ι) {s : ι → Set α
     · exact Finset.measurableSet_biUnion _ hs.2
 #align measure_theory.integral_finset_bUnion MeasureTheory.integral_finset_biUnion
 
-theorem integral_fintype_iUnion {ι : Type _} [Fintype ι] {s : ι → Set α}
+theorem integral_fintype_iUnion {ι : Type*} [Fintype ι] {s : ι → Set α}
     (hs : ∀ i, MeasurableSet (s i)) (h's : Pairwise (Disjoint on s))
     (hf : ∀ i, IntegrableOn f (s i) μ) : ∫ x in ⋃ i, s i, f x ∂μ = ∑ i, ∫ x in s i, f x ∂μ := by
   convert integral_finset_biUnion Finset.univ (fun i _ => hs i) _ fun i _ => hf i
@@ -185,7 +185,7 @@ theorem set_integral_indicator (ht : MeasurableSet t) :
   rw [integral_indicator ht, Measure.restrict_restrict ht, Set.inter_comm]
 #align measure_theory.set_integral_indicator MeasureTheory.set_integral_indicator
 
-theorem ofReal_set_integral_one_of_measure_ne_top {α : Type _} {m : MeasurableSpace α}
+theorem ofReal_set_integral_one_of_measure_ne_top {α : Type*} {m : MeasurableSpace α}
     {μ : Measure α} {s : Set α} (hs : μ s ≠ ∞) : ENNReal.ofReal (∫ _ in s, (1 : ℝ) ∂μ) = μ s :=
   calc
     ENNReal.ofReal (∫ _ in s, (1 : ℝ) ∂μ) = ENNReal.ofReal (∫ _ in s, ‖(1 : ℝ)‖ ∂μ) := by
@@ -196,7 +196,7 @@ theorem ofReal_set_integral_one_of_measure_ne_top {α : Type _} {m : MeasurableS
     _ = μ s := set_lintegral_one _
 #align measure_theory.of_real_set_integral_one_of_measure_ne_top MeasureTheory.ofReal_set_integral_one_of_measure_ne_top
 
-theorem ofReal_set_integral_one {α : Type _} {_ : MeasurableSpace α} (μ : Measure α)
+theorem ofReal_set_integral_one {α : Type*} {_ : MeasurableSpace α} (μ : Measure α)
     [IsFiniteMeasure μ] (s : Set α) : ENNReal.ofReal (∫ _ in s, (1 : ℝ) ∂μ) = μ s :=
   ofReal_set_integral_one_of_measure_ne_top (measure_ne_top μ s)
 #align measure_theory.of_real_set_integral_one MeasureTheory.ofReal_set_integral_one
@@ -209,7 +209,7 @@ theorem integral_piecewise [DecidablePred (· ∈ s)] (hs : MeasurableSet s) (hf
     integral_indicator hs, integral_indicator hs.compl]
 #align measure_theory.integral_piecewise MeasureTheory.integral_piecewise
 
-theorem tendsto_set_integral_of_monotone {ι : Type _} [Countable ι] [SemilatticeSup ι]
+theorem tendsto_set_integral_of_monotone {ι : Type*} [Countable ι] [SemilatticeSup ι]
     {s : ι → Set α} (hsm : ∀ i, MeasurableSet (s i)) (h_mono : Monotone s)
     (hfi : IntegrableOn f (⋃ n, s n) μ) :
     Tendsto (fun i => ∫ a in s i, f a ∂μ) atTop (𝓝 (∫ a in ⋃ n, s n, f a ∂μ)) := by
@@ -232,7 +232,7 @@ theorem tendsto_set_integral_of_monotone {ι : Type _} [Countable ι] [Semilatti
     (hi.2.trans_lt <| ENNReal.add_lt_top.2 ⟨hfi', ENNReal.coe_lt_top⟩).ne]
 #align measure_theory.tendsto_set_integral_of_monotone MeasureTheory.tendsto_set_integral_of_monotone
 
-theorem hasSum_integral_iUnion_ae {ι : Type _} [Countable ι] {s : ι → Set α}
+theorem hasSum_integral_iUnion_ae {ι : Type*} [Countable ι] {s : ι → Set α}
     (hm : ∀ i, NullMeasurableSet (s i) μ) (hd : Pairwise (AEDisjoint μ on s))
     (hfi : IntegrableOn f (⋃ i, s i) μ) :
     HasSum (fun n => ∫ a in s n, f a ∂μ) (∫ a in ⋃ n, s n, f a ∂μ) := by
@@ -240,7 +240,7 @@ theorem hasSum_integral_iUnion_ae {ι : Type _} [Countable ι] {s : ι → Set 
   exact hasSum_integral_measure hfi
 #align measure_theory.has_sum_integral_Union_ae MeasureTheory.hasSum_integral_iUnion_ae
 
-theorem hasSum_integral_iUnion {ι : Type _} [Countable ι] {s : ι → Set α}
+theorem hasSum_integral_iUnion {ι : Type*} [Countable ι] {s : ι → Set α}
     (hm : ∀ i, MeasurableSet (s i)) (hd : Pairwise (Disjoint on s))
     (hfi : IntegrableOn f (⋃ i, s i) μ) :
     HasSum (fun n => ∫ a in s n, f a ∂μ) (∫ a in ⋃ n, s n, f a ∂μ) :=
@@ -248,13 +248,13 @@ theorem hasSum_integral_iUnion {ι : Type _} [Countable ι] {s : ι → Set α}
     hfi
 #align measure_theory.has_sum_integral_Union MeasureTheory.hasSum_integral_iUnion
 
-theorem integral_iUnion {ι : Type _} [Countable ι] {s : ι → Set α} (hm : ∀ i, MeasurableSet (s i))
+theorem integral_iUnion {ι : Type*} [Countable ι] {s : ι → Set α} (hm : ∀ i, MeasurableSet (s i))
     (hd : Pairwise (Disjoint on s)) (hfi : IntegrableOn f (⋃ i, s i) μ) :
     ∫ a in ⋃ n, s n, f a ∂μ = ∑' n, ∫ a in s n, f a ∂μ :=
   (HasSum.tsum_eq (hasSum_integral_iUnion hm hd hfi)).symm
 #align measure_theory.integral_Union MeasureTheory.integral_iUnion
 
-theorem integral_iUnion_ae {ι : Type _} [Countable ι] {s : ι → Set α}
+theorem integral_iUnion_ae {ι : Type*} [Countable ι] {s : ι → Set α}
     (hm : ∀ i, NullMeasurableSet (s i) μ) (hd : Pairwise (AEDisjoint μ on s))
     (hfi : IntegrableOn f (⋃ i, s i) μ) : ∫ a in ⋃ n, s n, f a ∂μ = ∑' n, ∫ a in s n, f a ∂μ :=
   (HasSum.tsum_eq (hasSum_integral_iUnion_ae hm hd hfi)).symm
@@ -865,7 +865,7 @@ We prove that for any set `s`, the function
 
 section ContinuousSetIntegral
 
-variable [NormedAddCommGroup E] {𝕜 : Type _} [NormedField 𝕜] [NormedAddCommGroup F]
+variable [NormedAddCommGroup E] {𝕜 : Type*} [NormedField 𝕜] [NormedAddCommGroup F]
   [NormedSpace 𝕜 F] {p : ℝ≥0∞} {μ : Measure α}
 
 /-- For `f : Lp E p μ`, we can define an element of `Lp E p (μ.restrict s)` by
@@ -953,7 +953,7 @@ end MeasureTheory
 
 open MeasureTheory Asymptotics Metric
 
-variable {ι : Type _} [NormedAddCommGroup E]
+variable {ι : Type*} [NormedAddCommGroup E]
 
 /-- Fundamental theorem of calculus for set integrals: if `μ` is a measure that is finite at a
 filter `l` and `f` is a measurable function that has a finite limit `b` at `l ⊓ μ.ae`, then `∫ x in
@@ -1057,7 +1057,7 @@ as `ContinuousLinearMap.compLp`. We take advantage of this construction here.
 
 open scoped ComplexConjugate
 
-variable {μ : Measure α} {𝕜 : Type _} [IsROrC 𝕜] [NormedSpace 𝕜 E] [NormedAddCommGroup F]
+variable {μ : Measure α} {𝕜 : Type*} [IsROrC 𝕜] [NormedSpace 𝕜 E] [NormedAddCommGroup F]
   [NormedSpace 𝕜 F] {p : ENNReal}
 
 namespace ContinuousLinearMap
@@ -1105,7 +1105,7 @@ theorem integral_comp_comm (L : E →L[𝕜] F) {φ : α → E} (φ_int : Integr
   all_goals assumption
 #align continuous_linear_map.integral_comp_comm ContinuousLinearMap.integral_comp_comm
 
-theorem integral_apply {H : Type _} [NormedAddCommGroup H] [NormedSpace 𝕜 H] {φ : α → H →L[𝕜] E}
+theorem integral_apply {H : Type*} [NormedAddCommGroup H] [NormedSpace 𝕜 H] {φ : α → H →L[𝕜] E}
     (φ_int : Integrable φ μ) (v : H) : (∫ a, φ a ∂μ) v = ∫ a, φ a v ∂μ :=
   ((ContinuousLinearMap.apply 𝕜 E v).integral_comp_comm φ_int).symm
 #align continuous_linear_map.integral_apply ContinuousLinearMap.integral_apply
@@ -1205,7 +1205,7 @@ theorem integral_pair {f : α → E} {g : α → F} (hf : Integrable f μ) (hg :
   Prod.ext (fst_integral this) (snd_integral this)
 #align integral_pair integral_pair
 
-theorem integral_smul_const {𝕜 : Type _} [IsROrC 𝕜] [NormedSpace 𝕜 E] (f : α → 𝕜) (c : E) :
+theorem integral_smul_const {𝕜 : Type*} [IsROrC 𝕜] [NormedSpace 𝕜 E] (f : α → 𝕜) (c : E) :
     ∫ x, f x • c ∂μ = (∫ x, f x ∂μ) • c := by
   by_cases hf : Integrable f μ
   · exact ((1 : 𝕜 →L[𝕜] 𝕜).smulRight c).integral_comp_comm hf

@@ -708,6 +708,10 @@ theorem set_integral_mono_set (hfi : IntegrableOn f t μ) (hf : 0 ≤ᵐ[μ.rest
   integral_mono_measure (Measure.restrict_mono_ae hst) hf hfi
 #align measure_theory.set_integral_mono_set MeasureTheory.set_integral_mono_set
 
+theorem set_integral_le_integral (hfi : Integrable f μ) (hf : 0 ≤ᵐ[μ] f) :
+    (∫ x in s, f x ∂μ) ≤ ∫ x, f x ∂μ :=
+  integral_mono_measure (Measure.restrict_le_self) hf hfi
+
 theorem set_integral_ge_of_const_le {c : ℝ} (hs : MeasurableSet s) (hμs : μ s ≠ ∞)
     (hf : ∀ x ∈ s, c ≤ f x) (hfint : IntegrableOn (fun x : α => f x) s μ) :
     c * (μ s).toReal ≤ ∫ x in s, f x ∂μ := by

• depends on: #5966

Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

@@ -2,11 +2,6 @@
 Copyright (c) 2020 Zhouhang Zhou. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Zhouhang Zhou, Yury Kudryashov
-
-! This file was ported from Lean 3 source module measure_theory.integral.set_integral
-! leanprover-community/mathlib commit 24e0c85412ff6adbeca08022c25ba4876eedf37a
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.MeasureTheory.Integral.IntegrableOn
 import Mathlib.MeasureTheory.Integral.Bochner
@@ -15,6 +10,8 @@ import Mathlib.Order.Filter.IndicatorFunction
 import Mathlib.Topology.MetricSpace.ThickenedIndicator
 import Mathlib.Topology.ContinuousFunction.Compact
 
+#align_import measure_theory.integral.set_integral from "leanprover-community/mathlib"@"24e0c85412ff6adbeca08022c25ba4876eedf37a"
+
 /-!
 # Set integral
 

The notion of Bochner integral of a function taking values in a normed space E requires that E is complete. This means that whenever we write down an integral, the term contains the assertion that E is complete.

In this PR, we remove the completeness requirement from the definition, using the junk value 0 when the space is not complete. Mathematically this does not make any difference, as all reasonable applications will be with a complete E. But it means that terms involving integrals become a little bit simpler and that completeness will not have to be checked by the system when applying a bunch of basic lemmas on integrals.

@@ -70,7 +70,7 @@ section NormedAddCommGroup
 
 variable [NormedAddCommGroup E] {f g : α → E} {s t : Set α} {μ ν : Measure α} {l l' : Filter α}
 
-variable [CompleteSpace E] [NormedSpace ℝ E]
+variable [NormedSpace ℝ E]
 
 theorem set_integral_congr_ae₀ (hs : NullMeasurableSet s μ) (h : ∀ᵐ x ∂μ, x ∈ s → f x = g x) :
     ∫ x in s, f x ∂μ = ∫ x in s, g x ∂μ :=
@@ -444,12 +444,12 @@ theorem integral_norm_eq_pos_sub_neg {f : α → ℝ} (hfi : Integrable f μ) :
       rw [← set_integral_neg_eq_set_integral_nonpos hfi.1]; congr; ext1 x; simp
 #align measure_theory.integral_norm_eq_pos_sub_neg MeasureTheory.integral_norm_eq_pos_sub_neg
 
-theorem set_integral_const (c : E) : ∫ _ in s, c ∂μ = (μ s).toReal • c := by
+theorem set_integral_const [CompleteSpace E] (c : E) : ∫ _ in s, c ∂μ = (μ s).toReal • c := by
   rw [integral_const, Measure.restrict_apply_univ]
 #align measure_theory.set_integral_const MeasureTheory.set_integral_const
 
 @[simp]
-theorem integral_indicator_const (e : E) ⦃s : Set α⦄ (s_meas : MeasurableSet s) :
+theorem integral_indicator_const [CompleteSpace E] (e : E) ⦃s : Set α⦄ (s_meas : MeasurableSet s) :
     (∫ a : α, s.indicator (fun _ : α => e) a ∂μ) = (μ s).toReal • e := by
   rw [integral_indicator s_meas, ← set_integral_const]
 #align measure_theory.integral_indicator_const MeasureTheory.integral_indicator_const
@@ -460,8 +460,8 @@ theorem integral_indicator_one ⦃s : Set α⦄ (hs : MeasurableSet s) :
   (integral_indicator_const 1 hs).trans ((smul_eq_mul _).trans (mul_one _))
 #align measure_theory.integral_indicator_one MeasureTheory.integral_indicator_one
 
-theorem set_integral_indicatorConstLp {p : ℝ≥0∞} (hs : MeasurableSet s) (ht : MeasurableSet t)
-    (hμt : μ t ≠ ∞) (x : E) :
+theorem set_integral_indicatorConstLp [CompleteSpace E]
+    {p : ℝ≥0∞} (hs : MeasurableSet s) (ht : MeasurableSet t) (hμt : μ t ≠ ∞) (x : E) :
     ∫ a in s, indicatorConstLp p ht hμt x a ∂μ = (μ (t ∩ s)).toReal • x :=
   calc
     ∫ a in s, indicatorConstLp p ht hμt x a ∂μ = ∫ a in s, t.indicator (fun _ => x) a ∂μ := by
@@ -470,7 +470,8 @@ theorem set_integral_indicatorConstLp {p : ℝ≥0∞} (hs : MeasurableSet s) (h
 set_option linter.uppercaseLean3 false in
 #align measure_theory.set_integral_indicator_const_Lp MeasureTheory.set_integral_indicatorConstLp
 
-theorem integral_indicatorConstLp {p : ℝ≥0∞} (ht : MeasurableSet t) (hμt : μ t ≠ ∞) (x : E) :
+theorem integral_indicatorConstLp [CompleteSpace E]
+    {p : ℝ≥0∞} (ht : MeasurableSet t) (hμt : μ t ≠ ∞) (x : E) :
     ∫ a, indicatorConstLp p ht hμt x a ∂μ = (μ t).toReal • x :=
   calc
     ∫ a, indicatorConstLp p ht hμt x a ∂μ = ∫ a in univ, indicatorConstLp p ht hμt x a ∂μ := by
@@ -933,7 +934,7 @@ set_option linter.uppercaseLean3 false in
 variable {𝕜}
 
 @[continuity]
-theorem continuous_set_integral [NormedSpace ℝ E] [CompleteSpace E] (s : Set α) :
+theorem continuous_set_integral [NormedSpace ℝ E] (s : Set α) :
     Continuous fun f : α →₁[μ] E => ∫ x in s, f x ∂μ := by
   haveI : Fact ((1 : ℝ≥0∞) ≤ 1) := ⟨le_rfl⟩
   have h_comp :

@@ -822,7 +822,7 @@ theorem integrableOn_iUnion_of_summable_norm_restrict {f : C(α, E)} {s : β →
 the sequence `‖f.restrict (s i)‖ * μ (s i)` is summable, then `f` is integrable. -/
 theorem integrable_of_summable_norm_restrict {f : C(α, E)} {s : β → Compacts α}
     (hf : Summable fun i : β => ‖f.restrict (s i)‖ * ENNReal.toReal (μ <| s i))
-    (hs : (⋃ i : β, ↑(s i)) = (univ : Set α)) : Integrable f μ := by
+    (hs : ⋃ i : β, ↑(s i) = (univ : Set α)) : Integrable f μ := by
   simpa only [hs, integrableOn_univ] using integrableOn_iUnion_of_summable_norm_restrict hf
 #align measure_theory.integrable_of_summable_norm_restrict MeasureTheory.integrable_of_summable_norm_restrict
 

Co-authored-by: Yury G. Kudryashov <urkud@urkud.name>

@@ -205,7 +205,7 @@ theorem ofReal_set_integral_one {α : Type _} {_ : MeasurableSpace α} (μ : Mea
 #align measure_theory.of_real_set_integral_one MeasureTheory.ofReal_set_integral_one
 
 theorem integral_piecewise [DecidablePred (· ∈ s)] (hs : MeasurableSet s) (hf : IntegrableOn f s μ)
-    (hg : IntegrableOn g (sᶜ) μ) :
+    (hg : IntegrableOn g sᶜ μ) :
     ∫ x, s.piecewise f g x ∂μ = (∫ x in s, f x ∂μ) + ∫ x in sᶜ, g x ∂μ := by
   rw [← Set.indicator_add_compl_eq_piecewise,
     integral_add' (hf.integrable_indicator hs) (hg.integrable_indicator hs.compl),

@@ -73,42 +73,42 @@ variable [NormedAddCommGroup E] {f g : α → E} {s t : Set α} {μ ν : Measure
 variable [CompleteSpace E] [NormedSpace ℝ E]
 
 theorem set_integral_congr_ae₀ (hs : NullMeasurableSet s μ) (h : ∀ᵐ x ∂μ, x ∈ s → f x = g x) :
-    (∫ x in s, f x ∂μ) = ∫ x in s, g x ∂μ :=
+    ∫ x in s, f x ∂μ = ∫ x in s, g x ∂μ :=
   integral_congr_ae ((ae_restrict_iff'₀ hs).2 h)
 #align measure_theory.set_integral_congr_ae₀ MeasureTheory.set_integral_congr_ae₀
 
 theorem set_integral_congr_ae (hs : MeasurableSet s) (h : ∀ᵐ x ∂μ, x ∈ s → f x = g x) :
-    (∫ x in s, f x ∂μ) = ∫ x in s, g x ∂μ :=
+    ∫ x in s, f x ∂μ = ∫ x in s, g x ∂μ :=
   integral_congr_ae ((ae_restrict_iff' hs).2 h)
 #align measure_theory.set_integral_congr_ae MeasureTheory.set_integral_congr_ae
 
 theorem set_integral_congr₀ (hs : NullMeasurableSet s μ) (h : EqOn f g s) :
-    (∫ x in s, f x ∂μ) = ∫ x in s, g x ∂μ :=
+    ∫ x in s, f x ∂μ = ∫ x in s, g x ∂μ :=
   set_integral_congr_ae₀ hs <| eventually_of_forall h
 #align measure_theory.set_integral_congr₀ MeasureTheory.set_integral_congr₀
 
 theorem set_integral_congr (hs : MeasurableSet s) (h : EqOn f g s) :
-    (∫ x in s, f x ∂μ) = ∫ x in s, g x ∂μ :=
+    ∫ x in s, f x ∂μ = ∫ x in s, g x ∂μ :=
   set_integral_congr_ae hs <| eventually_of_forall h
 #align measure_theory.set_integral_congr MeasureTheory.set_integral_congr
 
-theorem set_integral_congr_set_ae (hst : s =ᵐ[μ] t) : (∫ x in s, f x ∂μ) = ∫ x in t, f x ∂μ := by
+theorem set_integral_congr_set_ae (hst : s =ᵐ[μ] t) : ∫ x in s, f x ∂μ = ∫ x in t, f x ∂μ := by
   rw [Measure.restrict_congr_set hst]
 #align measure_theory.set_integral_congr_set_ae MeasureTheory.set_integral_congr_set_ae
 
 theorem integral_union_ae (hst : AEDisjoint μ s t) (ht : NullMeasurableSet t μ)
     (hfs : IntegrableOn f s μ) (hft : IntegrableOn f t μ) :
-    (∫ x in s ∪ t, f x ∂μ) = (∫ x in s, f x ∂μ) + ∫ x in t, f x ∂μ := by
+    ∫ x in s ∪ t, f x ∂μ = (∫ x in s, f x ∂μ) + ∫ x in t, f x ∂μ := by
   simp only [IntegrableOn, Measure.restrict_union₀ hst ht, integral_add_measure hfs hft]
 #align measure_theory.integral_union_ae MeasureTheory.integral_union_ae
 
 theorem integral_union (hst : Disjoint s t) (ht : MeasurableSet t) (hfs : IntegrableOn f s μ)
-    (hft : IntegrableOn f t μ) : (∫ x in s ∪ t, f x ∂μ) = (∫ x in s, f x ∂μ) + ∫ x in t, f x ∂μ :=
+    (hft : IntegrableOn f t μ) : ∫ x in s ∪ t, f x ∂μ = (∫ x in s, f x ∂μ) + ∫ x in t, f x ∂μ :=
   integral_union_ae hst.aedisjoint ht.nullMeasurableSet hfs hft
 #align measure_theory.integral_union MeasureTheory.integral_union
 
 theorem integral_diff (ht : MeasurableSet t) (hfs : IntegrableOn f s μ) (hts : t ⊆ s) :
-    (∫ x in s \ t, f x ∂μ) = (∫ x in s, f x ∂μ) - ∫ x in t, f x ∂μ := by
+    ∫ x in s \ t, f x ∂μ = (∫ x in s, f x ∂μ) - ∫ x in t, f x ∂μ := by
   rw [eq_sub_iff_add_eq, ← integral_union, diff_union_of_subset hts]
   exacts [disjoint_sdiff_self_left, ht, hfs.mono_set (diff_subset _ _), hfs.mono_set hts]
 #align measure_theory.integral_diff MeasureTheory.integral_diff
@@ -128,7 +128,7 @@ theorem integral_inter_add_diff (ht : MeasurableSet t) (hfs : IntegrableOn f s 
 theorem integral_finset_biUnion {ι : Type _} (t : Finset ι) {s : ι → Set α}
     (hs : ∀ i ∈ t, MeasurableSet (s i)) (h's : Set.Pairwise (↑t) (Disjoint on s))
     (hf : ∀ i ∈ t, IntegrableOn f (s i) μ) :
-    (∫ x in ⋃ i ∈ t, s i, f x ∂μ) = ∑ i in t, ∫ x in s i, f x ∂μ := by
+    ∫ x in ⋃ i ∈ t, s i, f x ∂μ = ∑ i in t, ∫ x in s i, f x ∂μ := by
   induction' t using Finset.induction_on with a t hat IH hs h's
   · simp
   · simp only [Finset.coe_insert, Finset.forall_mem_insert, Set.pairwise_insert,
@@ -142,17 +142,17 @@ theorem integral_finset_biUnion {ι : Type _} (t : Finset ι) {s : ι → Set α
 
 theorem integral_fintype_iUnion {ι : Type _} [Fintype ι] {s : ι → Set α}
     (hs : ∀ i, MeasurableSet (s i)) (h's : Pairwise (Disjoint on s))
-    (hf : ∀ i, IntegrableOn f (s i) μ) : (∫ x in ⋃ i, s i, f x ∂μ) = ∑ i, ∫ x in s i, f x ∂μ := by
+    (hf : ∀ i, IntegrableOn f (s i) μ) : ∫ x in ⋃ i, s i, f x ∂μ = ∑ i, ∫ x in s i, f x ∂μ := by
   convert integral_finset_biUnion Finset.univ (fun i _ => hs i) _ fun i _ => hf i
   · simp
   · simp [pairwise_univ, h's]
 #align measure_theory.integral_fintype_Union MeasureTheory.integral_fintype_iUnion
 
-theorem integral_empty : (∫ x in ∅, f x ∂μ) = 0 := by
+theorem integral_empty : ∫ x in ∅, f x ∂μ = 0 := by
   rw [Measure.restrict_empty, integral_zero_measure]
 #align measure_theory.integral_empty MeasureTheory.integral_empty
 
-theorem integral_univ : (∫ x in univ, f x ∂μ) = ∫ x, f x ∂μ := by rw [Measure.restrict_univ]
+theorem integral_univ : ∫ x in univ, f x ∂μ = ∫ x, f x ∂μ := by rw [Measure.restrict_univ]
 #align measure_theory.integral_univ MeasureTheory.integral_univ
 
 theorem integral_add_compl₀ (hs : NullMeasurableSet s μ) (hfi : Integrable f μ) :
@@ -170,12 +170,12 @@ theorem integral_add_compl (hs : MeasurableSet s) (hfi : Integrable f μ) :
 /-- For a function `f` and a measurable set `s`, the integral of `indicator s f`
 over the whole space is equal to `∫ x in s, f x ∂μ` defined as `∫ x, f x ∂(μ.restrict s)`. -/
 theorem integral_indicator (hs : MeasurableSet s) :
-    (∫ x, indicator s f x ∂μ) = ∫ x in s, f x ∂μ := by
+    ∫ x, indicator s f x ∂μ = ∫ x in s, f x ∂μ := by
   by_cases hfi : IntegrableOn f s μ; swap
   · rwa [integral_undef, integral_undef]
     rwa [integrable_indicator_iff hs]
   calc
-    (∫ x, indicator s f x ∂μ) = (∫ x in s, indicator s f x ∂μ) + ∫ x in sᶜ, indicator s f x ∂μ :=
+    ∫ x, indicator s f x ∂μ = (∫ x in s, indicator s f x ∂μ) + ∫ x in sᶜ, indicator s f x ∂μ :=
       (integral_add_compl hs (hfi.integrable_indicator hs)).symm
     _ = (∫ x in s, f x ∂μ) + ∫ x in sᶜ, 0 ∂μ :=
       (congr_arg₂ (· + ·) (integral_congr_ae (indicator_ae_eq_restrict hs))
@@ -184,7 +184,7 @@ theorem integral_indicator (hs : MeasurableSet s) :
 #align measure_theory.integral_indicator MeasureTheory.integral_indicator
 
 theorem set_integral_indicator (ht : MeasurableSet t) :
-    (∫ x in s, t.indicator f x ∂μ) = ∫ x in s ∩ t, f x ∂μ := by
+    ∫ x in s, t.indicator f x ∂μ = ∫ x in s ∩ t, f x ∂μ := by
   rw [integral_indicator ht, Measure.restrict_restrict ht, Set.inter_comm]
 #align measure_theory.set_integral_indicator MeasureTheory.set_integral_indicator
 
@@ -206,7 +206,7 @@ theorem ofReal_set_integral_one {α : Type _} {_ : MeasurableSpace α} (μ : Mea
 
 theorem integral_piecewise [DecidablePred (· ∈ s)] (hs : MeasurableSet s) (hf : IntegrableOn f s μ)
     (hg : IntegrableOn g (sᶜ) μ) :
-    (∫ x, s.piecewise f g x ∂μ) = (∫ x in s, f x ∂μ) + ∫ x in sᶜ, g x ∂μ := by
+    ∫ x, s.piecewise f g x ∂μ = (∫ x in s, f x ∂μ) + ∫ x in sᶜ, g x ∂μ := by
   rw [← Set.indicator_add_compl_eq_piecewise,
     integral_add' (hf.integrable_indicator hs) (hg.integrable_indicator hs.compl),
     integral_indicator hs, integral_indicator hs.compl]
@@ -253,23 +253,23 @@ theorem hasSum_integral_iUnion {ι : Type _} [Countable ι] {s : ι → Set α}
 
 theorem integral_iUnion {ι : Type _} [Countable ι] {s : ι → Set α} (hm : ∀ i, MeasurableSet (s i))
     (hd : Pairwise (Disjoint on s)) (hfi : IntegrableOn f (⋃ i, s i) μ) :
-    (∫ a in ⋃ n, s n, f a ∂μ) = ∑' n, ∫ a in s n, f a ∂μ :=
+    ∫ a in ⋃ n, s n, f a ∂μ = ∑' n, ∫ a in s n, f a ∂μ :=
   (HasSum.tsum_eq (hasSum_integral_iUnion hm hd hfi)).symm
 #align measure_theory.integral_Union MeasureTheory.integral_iUnion
 
 theorem integral_iUnion_ae {ι : Type _} [Countable ι] {s : ι → Set α}
     (hm : ∀ i, NullMeasurableSet (s i) μ) (hd : Pairwise (AEDisjoint μ on s))
-    (hfi : IntegrableOn f (⋃ i, s i) μ) : (∫ a in ⋃ n, s n, f a ∂μ) = ∑' n, ∫ a in s n, f a ∂μ :=
+    (hfi : IntegrableOn f (⋃ i, s i) μ) : ∫ a in ⋃ n, s n, f a ∂μ = ∑' n, ∫ a in s n, f a ∂μ :=
   (HasSum.tsum_eq (hasSum_integral_iUnion_ae hm hd hfi)).symm
 #align measure_theory.integral_Union_ae MeasureTheory.integral_iUnion_ae
 
 theorem set_integral_eq_zero_of_ae_eq_zero (ht_eq : ∀ᵐ x ∂μ, x ∈ t → f x = 0) :
-    (∫ x in t, f x ∂μ) = 0 := by
+    ∫ x in t, f x ∂μ = 0 := by
   by_cases hf : AEStronglyMeasurable f (μ.restrict t); swap
   · rw [integral_undef]
     contrapose! hf
     exact hf.1
-  have : (∫ x in t, hf.mk f x ∂μ) = 0 := by
+  have : ∫ x in t, hf.mk f x ∂μ = 0 := by
     refine' integral_eq_zero_of_ae _
     rw [EventuallyEq,
       ae_restrict_iff (hf.stronglyMeasurable_mk.measurableSet_eq_fun stronglyMeasurable_zero)]
@@ -281,17 +281,17 @@ theorem set_integral_eq_zero_of_ae_eq_zero (ht_eq : ∀ᵐ x ∂μ, x ∈ t →
 #align measure_theory.set_integral_eq_zero_of_ae_eq_zero MeasureTheory.set_integral_eq_zero_of_ae_eq_zero
 
 theorem set_integral_eq_zero_of_forall_eq_zero (ht_eq : ∀ x ∈ t, f x = 0) :
-    (∫ x in t, f x ∂μ) = 0 :=
+    ∫ x in t, f x ∂μ = 0 :=
   set_integral_eq_zero_of_ae_eq_zero (eventually_of_forall ht_eq)
 #align measure_theory.set_integral_eq_zero_of_forall_eq_zero MeasureTheory.set_integral_eq_zero_of_forall_eq_zero
 
 theorem integral_union_eq_left_of_ae_aux (ht_eq : ∀ᵐ x ∂μ.restrict t, f x = 0)
     (haux : StronglyMeasurable f) (H : IntegrableOn f (s ∪ t) μ) :
-    (∫ x in s ∪ t, f x ∂μ) = ∫ x in s, f x ∂μ := by
+    ∫ x in s ∪ t, f x ∂μ = ∫ x in s, f x ∂μ := by
   let k := f ⁻¹' {0}
   have hk : MeasurableSet k := by borelize E; exact haux.measurable (measurableSet_singleton _)
   have h's : IntegrableOn f s μ := H.mono (subset_union_left _ _) le_rfl
-  have A : ∀ u : Set α, (∫ x in u ∩ k, f x ∂μ) = 0 := fun u =>
+  have A : ∀ u : Set α, ∫ x in u ∩ k, f x ∂μ = 0 := fun u =>
     set_integral_eq_zero_of_forall_eq_zero fun x hx => hx.2
   rw [← integral_inter_add_diff hk h's, ← integral_inter_add_diff hk H, A, A, zero_add, zero_add,
     union_diff_distrib, union_comm]
@@ -303,13 +303,13 @@ theorem integral_union_eq_left_of_ae_aux (ht_eq : ∀ᵐ x ∂μ.restrict t, f x
 #align measure_theory.integral_union_eq_left_of_ae_aux MeasureTheory.integral_union_eq_left_of_ae_aux
 
 theorem integral_union_eq_left_of_ae (ht_eq : ∀ᵐ x ∂μ.restrict t, f x = 0) :
-    (∫ x in s ∪ t, f x ∂μ) = ∫ x in s, f x ∂μ := by
+    ∫ x in s ∪ t, f x ∂μ = ∫ x in s, f x ∂μ := by
   have ht : IntegrableOn f t μ := by apply integrableOn_zero.congr_fun_ae; symm; exact ht_eq
   by_cases H : IntegrableOn f (s ∪ t) μ; swap
   · rw [integral_undef H, integral_undef]; simpa [integrableOn_union, ht] using H
   let f' := H.1.mk f
   calc
-    (∫ x : α in s ∪ t, f x ∂μ) = ∫ x : α in s ∪ t, f' x ∂μ := integral_congr_ae H.1.ae_eq_mk
+    ∫ x : α in s ∪ t, f x ∂μ = ∫ x : α in s ∪ t, f' x ∂μ := integral_congr_ae H.1.ae_eq_mk
     _ = ∫ x in s, f' x ∂μ := by
       apply
         integral_union_eq_left_of_ae_aux _ H.1.stronglyMeasurable_mk (H.congr_fun_ae H.1.ae_eq_mk)
@@ -322,22 +322,22 @@ theorem integral_union_eq_left_of_ae (ht_eq : ∀ᵐ x ∂μ.restrict t, f x = 0
 #align measure_theory.integral_union_eq_left_of_ae MeasureTheory.integral_union_eq_left_of_ae
 
 theorem integral_union_eq_left_of_forall₀ {f : α → E} (ht : NullMeasurableSet t μ)
-    (ht_eq : ∀ x ∈ t, f x = 0) : (∫ x in s ∪ t, f x ∂μ) = ∫ x in s, f x ∂μ :=
+    (ht_eq : ∀ x ∈ t, f x = 0) : ∫ x in s ∪ t, f x ∂μ = ∫ x in s, f x ∂μ :=
   integral_union_eq_left_of_ae ((ae_restrict_iff'₀ ht).2 (eventually_of_forall ht_eq))
 #align measure_theory.integral_union_eq_left_of_forall₀ MeasureTheory.integral_union_eq_left_of_forall₀
 
 theorem integral_union_eq_left_of_forall {f : α → E} (ht : MeasurableSet t)
-    (ht_eq : ∀ x ∈ t, f x = 0) : (∫ x in s ∪ t, f x ∂μ) = ∫ x in s, f x ∂μ :=
+    (ht_eq : ∀ x ∈ t, f x = 0) : ∫ x in s ∪ t, f x ∂μ = ∫ x in s, f x ∂μ :=
   integral_union_eq_left_of_forall₀ ht.nullMeasurableSet ht_eq
 #align measure_theory.integral_union_eq_left_of_forall MeasureTheory.integral_union_eq_left_of_forall
 
 theorem set_integral_eq_of_subset_of_ae_diff_eq_zero_aux (hts : s ⊆ t)
     (h't : ∀ᵐ x ∂μ, x ∈ t \ s → f x = 0) (haux : StronglyMeasurable f)
-    (h'aux : IntegrableOn f t μ) : (∫ x in t, f x ∂μ) = ∫ x in s, f x ∂μ := by
+    (h'aux : IntegrableOn f t μ) : ∫ x in t, f x ∂μ = ∫ x in s, f x ∂μ := by
   let k := f ⁻¹' {0}
   have hk : MeasurableSet k := by borelize E; exact haux.measurable (measurableSet_singleton _)
   calc
-    (∫ x in t, f x ∂μ) = (∫ x in t ∩ k, f x ∂μ) + ∫ x in t \ k, f x ∂μ := by
+    ∫ x in t, f x ∂μ = (∫ x in t ∩ k, f x ∂μ) + ∫ x in t \ k, f x ∂μ := by
       rw [integral_inter_add_diff hk h'aux]
     _ = ∫ x in t \ k, f x ∂μ := by
       rw [set_integral_eq_zero_of_forall_eq_zero fun x hx => ?_, zero_add]; exact hx.2
@@ -361,13 +361,13 @@ theorem set_integral_eq_of_subset_of_ae_diff_eq_zero_aux (hts : s ⊆ t)
 /-- If a function vanishes almost everywhere on `t \ s` with `s ⊆ t`, then its integrals on `s`
 and `t` coincide if `t` is null-measurable. -/
 theorem set_integral_eq_of_subset_of_ae_diff_eq_zero (ht : NullMeasurableSet t μ) (hts : s ⊆ t)
-    (h't : ∀ᵐ x ∂μ, x ∈ t \ s → f x = 0) : (∫ x in t, f x ∂μ) = ∫ x in s, f x ∂μ := by
+    (h't : ∀ᵐ x ∂μ, x ∈ t \ s → f x = 0) : ∫ x in t, f x ∂μ = ∫ x in s, f x ∂μ := by
   by_cases h : IntegrableOn f t μ; swap
   · have : ¬IntegrableOn f s μ := fun H => h (H.of_ae_diff_eq_zero ht h't)
     rw [integral_undef h, integral_undef this]
   let f' := h.1.mk f
   calc
-    (∫ x in t, f x ∂μ) = ∫ x in t, f' x ∂μ := integral_congr_ae h.1.ae_eq_mk
+    ∫ x in t, f x ∂μ = ∫ x in t, f' x ∂μ := integral_congr_ae h.1.ae_eq_mk
     _ = ∫ x in s, f' x ∂μ := by
       apply
         set_integral_eq_of_subset_of_ae_diff_eq_zero_aux hts _ h.1.stronglyMeasurable_mk
@@ -384,7 +384,7 @@ theorem set_integral_eq_of_subset_of_ae_diff_eq_zero (ht : NullMeasurableSet t 
 /-- If a function vanishes on `t \ s` with `s ⊆ t`, then its integrals on `s`
 and `t` coincide if `t` is measurable. -/
 theorem set_integral_eq_of_subset_of_forall_diff_eq_zero (ht : MeasurableSet t) (hts : s ⊆ t)
-    (h't : ∀ x ∈ t \ s, f x = 0) : (∫ x in t, f x ∂μ) = ∫ x in s, f x ∂μ :=
+    (h't : ∀ x ∈ t \ s, f x = 0) : ∫ x in t, f x ∂μ = ∫ x in s, f x ∂μ :=
   set_integral_eq_of_subset_of_ae_diff_eq_zero ht.nullMeasurableSet hts
     (eventually_of_forall fun x hx => h't x hx)
 #align measure_theory.set_integral_eq_of_subset_of_forall_diff_eq_zero MeasureTheory.set_integral_eq_of_subset_of_forall_diff_eq_zero
@@ -392,7 +392,7 @@ theorem set_integral_eq_of_subset_of_forall_diff_eq_zero (ht : MeasurableSet t)
 /-- If a function vanishes almost everywhere on `sᶜ`, then its integral on `s`
 coincides with its integral on the whole space. -/
 theorem set_integral_eq_integral_of_ae_compl_eq_zero (h : ∀ᵐ x ∂μ, x ∉ s → f x = 0) :
-    (∫ x in s, f x ∂μ) = ∫ x, f x ∂μ := by
+    ∫ x in s, f x ∂μ = ∫ x, f x ∂μ := by
   symm
   nth_rw 1 [← integral_univ]
   apply set_integral_eq_of_subset_of_ae_diff_eq_zero nullMeasurableSet_univ (subset_univ _)
@@ -402,13 +402,13 @@ theorem set_integral_eq_integral_of_ae_compl_eq_zero (h : ∀ᵐ x ∂μ, x ∉
 /-- If a function vanishes on `sᶜ`, then its integral on `s` coincides with its integral on the
 whole space. -/
 theorem set_integral_eq_integral_of_forall_compl_eq_zero (h : ∀ x, x ∉ s → f x = 0) :
-    (∫ x in s, f x ∂μ) = ∫ x, f x ∂μ :=
+    ∫ x in s, f x ∂μ = ∫ x, f x ∂μ :=
   set_integral_eq_integral_of_ae_compl_eq_zero (eventually_of_forall h)
 #align measure_theory.set_integral_eq_integral_of_forall_compl_eq_zero MeasureTheory.set_integral_eq_integral_of_forall_compl_eq_zero
 
 theorem set_integral_neg_eq_set_integral_nonpos [LinearOrder E] {f : α → E}
     (hf : AEStronglyMeasurable f μ) :
-    (∫ x in {x | f x < 0}, f x ∂μ) = ∫ x in {x | f x ≤ 0}, f x ∂μ := by
+    ∫ x in {x | f x < 0}, f x ∂μ = ∫ x in {x | f x ≤ 0}, f x ∂μ := by
   have h_union : {x | f x ≤ 0} = {x | f x < 0} ∪ {x | f x = 0} := by
     ext; simp_rw [Set.mem_union, Set.mem_setOf_eq]; exact le_iff_lt_or_eq
   rw [h_union]
@@ -420,11 +420,11 @@ theorem set_integral_neg_eq_set_integral_nonpos [LinearOrder E] {f : α → E}
 #align measure_theory.set_integral_neg_eq_set_integral_nonpos MeasureTheory.set_integral_neg_eq_set_integral_nonpos
 
 theorem integral_norm_eq_pos_sub_neg {f : α → ℝ} (hfi : Integrable f μ) :
-    (∫ x, ‖f x‖ ∂μ) = (∫ x in {x | 0 ≤ f x}, f x ∂μ) - ∫ x in {x | f x ≤ 0}, f x ∂μ :=
+    ∫ x, ‖f x‖ ∂μ = (∫ x in {x | 0 ≤ f x}, f x ∂μ) - ∫ x in {x | f x ≤ 0}, f x ∂μ :=
   have h_meas : NullMeasurableSet {x | 0 ≤ f x} μ :=
     aestronglyMeasurable_const.nullMeasurableSet_le hfi.1
   calc
-    (∫ x, ‖f x‖ ∂μ) = (∫ x in {x | 0 ≤ f x}, ‖f x‖ ∂μ) + ∫ x in {x | 0 ≤ f x}ᶜ, ‖f x‖ ∂μ := by
+    ∫ x, ‖f x‖ ∂μ = (∫ x in {x | 0 ≤ f x}, ‖f x‖ ∂μ) + ∫ x in {x | 0 ≤ f x}ᶜ, ‖f x‖ ∂μ := by
       rw [← integral_add_compl₀ h_meas hfi.norm]
     _ = (∫ x in {x | 0 ≤ f x}, f x ∂μ) + ∫ x in {x | 0 ≤ f x}ᶜ, ‖f x‖ ∂μ := by
       congr 1
@@ -444,7 +444,7 @@ theorem integral_norm_eq_pos_sub_neg {f : α → ℝ} (hfi : Integrable f μ) :
       rw [← set_integral_neg_eq_set_integral_nonpos hfi.1]; congr; ext1 x; simp
 #align measure_theory.integral_norm_eq_pos_sub_neg MeasureTheory.integral_norm_eq_pos_sub_neg
 
-theorem set_integral_const (c : E) : (∫ _ in s, c ∂μ) = (μ s).toReal • c := by
+theorem set_integral_const (c : E) : ∫ _ in s, c ∂μ = (μ s).toReal • c := by
   rw [integral_const, Measure.restrict_apply_univ]
 #align measure_theory.set_integral_const MeasureTheory.set_integral_const
 
@@ -456,24 +456,24 @@ theorem integral_indicator_const (e : E) ⦃s : Set α⦄ (s_meas : MeasurableSe
 
 @[simp]
 theorem integral_indicator_one ⦃s : Set α⦄ (hs : MeasurableSet s) :
-    (∫ a, s.indicator 1 a ∂μ) = (μ s).toReal :=
+    ∫ a, s.indicator 1 a ∂μ = (μ s).toReal :=
   (integral_indicator_const 1 hs).trans ((smul_eq_mul _).trans (mul_one _))
 #align measure_theory.integral_indicator_one MeasureTheory.integral_indicator_one
 
 theorem set_integral_indicatorConstLp {p : ℝ≥0∞} (hs : MeasurableSet s) (ht : MeasurableSet t)
     (hμt : μ t ≠ ∞) (x : E) :
-    (∫ a in s, indicatorConstLp p ht hμt x a ∂μ) = (μ (t ∩ s)).toReal • x :=
+    ∫ a in s, indicatorConstLp p ht hμt x a ∂μ = (μ (t ∩ s)).toReal • x :=
   calc
-    (∫ a in s, indicatorConstLp p ht hμt x a ∂μ) = ∫ a in s, t.indicator (fun _ => x) a ∂μ := by
+    ∫ a in s, indicatorConstLp p ht hμt x a ∂μ = ∫ a in s, t.indicator (fun _ => x) a ∂μ := by
       rw [set_integral_congr_ae hs (indicatorConstLp_coeFn.mono fun x hx _ => hx)]
     _ = (μ (t ∩ s)).toReal • x := by rw [integral_indicator_const _ ht, Measure.restrict_apply ht]
 set_option linter.uppercaseLean3 false in
 #align measure_theory.set_integral_indicator_const_Lp MeasureTheory.set_integral_indicatorConstLp
 
 theorem integral_indicatorConstLp {p : ℝ≥0∞} (ht : MeasurableSet t) (hμt : μ t ≠ ∞) (x : E) :
-    (∫ a, indicatorConstLp p ht hμt x a ∂μ) = (μ t).toReal • x :=
+    ∫ a, indicatorConstLp p ht hμt x a ∂μ = (μ t).toReal • x :=
   calc
-    (∫ a, indicatorConstLp p ht hμt x a ∂μ) = ∫ a in univ, indicatorConstLp p ht hμt x a ∂μ := by
+    ∫ a, indicatorConstLp p ht hμt x a ∂μ = ∫ a in univ, indicatorConstLp p ht hμt x a ∂μ := by
       rw [integral_univ]
     _ = (μ (t ∩ univ)).toReal • x := (set_integral_indicatorConstLp MeasurableSet.univ ht hμt x)
     _ = (μ t).toReal • x := by rw [inter_univ]
@@ -482,7 +482,7 @@ set_option linter.uppercaseLean3 false in
 
 theorem set_integral_map {β} [MeasurableSpace β] {g : α → β} {f : β → E} {s : Set β}
     (hs : MeasurableSet s) (hf : AEStronglyMeasurable f (Measure.map g μ)) (hg : AEMeasurable g μ) :
-    (∫ y in s, f y ∂Measure.map g μ) = ∫ x in g ⁻¹' s, f (g x) ∂μ := by
+    ∫ y in s, f y ∂Measure.map g μ = ∫ x in g ⁻¹' s, f (g x) ∂μ := by
   rw [Measure.restrict_map_of_aemeasurable hg hs,
     integral_map (hg.mono_measure Measure.restrict_le_self) (hf.mono_measure _)]
   exact Measure.map_mono_of_aemeasurable Measure.restrict_le_self hg
@@ -490,13 +490,13 @@ theorem set_integral_map {β} [MeasurableSpace β] {g : α → β} {f : β → E
 
 theorem _root_.MeasurableEmbedding.set_integral_map {β} {_ : MeasurableSpace β} {f : α → β}
     (hf : MeasurableEmbedding f) (g : β → E) (s : Set β) :
-    (∫ y in s, g y ∂Measure.map f μ) = ∫ x in f ⁻¹' s, g (f x) ∂μ := by
+    ∫ y in s, g y ∂Measure.map f μ = ∫ x in f ⁻¹' s, g (f x) ∂μ := by
   rw [hf.restrict_map, hf.integral_map]
 #align measurable_embedding.set_integral_map MeasurableEmbedding.set_integral_map
 
 theorem _root_.ClosedEmbedding.set_integral_map [TopologicalSpace α] [BorelSpace α] {β}
     [MeasurableSpace β] [TopologicalSpace β] [BorelSpace β] {g : α → β} {f : β → E} (s : Set β)
-    (hg : ClosedEmbedding g) : (∫ y in s, f y ∂Measure.map g μ) = ∫ x in g ⁻¹' s, f (g x) ∂μ :=
+    (hg : ClosedEmbedding g) : ∫ y in s, f y ∂Measure.map g μ = ∫ x in g ⁻¹' s, f (g x) ∂μ :=
   hg.measurableEmbedding.set_integral_map _ _
 #align closed_embedding.set_integral_map ClosedEmbedding.set_integral_map
 
@@ -508,12 +508,12 @@ theorem MeasurePreserving.set_integral_preimage_emb {β} {_ : MeasurableSpace β
 
 theorem MeasurePreserving.set_integral_image_emb {β} {_ : MeasurableSpace β} {f : α → β} {ν}
     (h₁ : MeasurePreserving f μ ν) (h₂ : MeasurableEmbedding f) (g : β → E) (s : Set α) :
-    (∫ y in f '' s, g y ∂ν) = ∫ x in s, g (f x) ∂μ :=
+    ∫ y in f '' s, g y ∂ν = ∫ x in s, g (f x) ∂μ :=
   Eq.symm <| (h₁.restrict_image_emb h₂ s).integral_comp h₂ _
 #align measure_theory.measure_preserving.set_integral_image_emb MeasureTheory.MeasurePreserving.set_integral_image_emb
 
 theorem set_integral_map_equiv {β} [MeasurableSpace β] (e : α ≃ᵐ β) (f : β → E) (s : Set β) :
-    (∫ y in s, f y ∂Measure.map e μ) = ∫ x in e ⁻¹' s, f (e x) ∂μ :=
+    ∫ y in s, f y ∂Measure.map e μ = ∫ x in e ⁻¹' s, f (e x) ∂μ :=
   e.measurableEmbedding.set_integral_map f s
 #align measure_theory.set_integral_map_equiv MeasureTheory.set_integral_map_equiv
 
@@ -555,7 +555,7 @@ theorem norm_set_integral_le_of_norm_le_const' {C : ℝ} (hs : μ s < ∞) (hsm
 #align measure_theory.norm_set_integral_le_of_norm_le_const' MeasureTheory.norm_set_integral_le_of_norm_le_const'
 
 theorem set_integral_eq_zero_iff_of_nonneg_ae {f : α → ℝ} (hf : 0 ≤ᵐ[μ.restrict s] f)
-    (hfi : IntegrableOn f s μ) : (∫ x in s, f x ∂μ) = 0 ↔ f =ᵐ[μ.restrict s] 0 :=
+    (hfi : IntegrableOn f s μ) : ∫ x in s, f x ∂μ = 0 ↔ f =ᵐ[μ.restrict s] 0 :=
   integral_eq_zero_iff_of_nonneg_ae hf hfi
 #align measure_theory.set_integral_eq_zero_iff_of_nonneg_ae MeasureTheory.set_integral_eq_zero_iff_of_nonneg_ae
 
@@ -592,7 +592,7 @@ theorem set_integral_gt_gt {R : ℝ} {f : α → ℝ} (hR : 0 ≤ R) (hfm : Meas
 
 theorem set_integral_trim {α} {m m0 : MeasurableSpace α} {μ : Measure α} (hm : m ≤ m0) {f : α → E}
     (hf_meas : StronglyMeasurable[m] f) {s : Set α} (hs : MeasurableSet[m] s) :
-    (∫ x in s, f x ∂μ) = ∫ x in s, f x ∂μ.trim hm := by
+    ∫ x in s, f x ∂μ = ∫ x in s, f x ∂μ.trim hm := by
   rwa [integral_trim hm hf_meas, restrict_trim hm μ]
 #align measure_theory.set_integral_trim MeasureTheory.set_integral_trim
 
@@ -608,67 +608,67 @@ section PartialOrder
 variable [PartialOrder α] {a b : α}
 
 theorem integral_Icc_eq_integral_Ioc' (ha : μ {a} = 0) :
-    (∫ t in Icc a b, f t ∂μ) = ∫ t in Ioc a b, f t ∂μ :=
+    ∫ t in Icc a b, f t ∂μ = ∫ t in Ioc a b, f t ∂μ :=
   set_integral_congr_set_ae (Ioc_ae_eq_Icc' ha).symm
 #align measure_theory.integral_Icc_eq_integral_Ioc' MeasureTheory.integral_Icc_eq_integral_Ioc'
 
 theorem integral_Icc_eq_integral_Ico' (hb : μ {b} = 0) :
-    (∫ t in Icc a b, f t ∂μ) = ∫ t in Ico a b, f t ∂μ :=
+    ∫ t in Icc a b, f t ∂μ = ∫ t in Ico a b, f t ∂μ :=
   set_integral_congr_set_ae (Ico_ae_eq_Icc' hb).symm
 #align measure_theory.integral_Icc_eq_integral_Ico' MeasureTheory.integral_Icc_eq_integral_Ico'
 
 theorem integral_Ioc_eq_integral_Ioo' (hb : μ {b} = 0) :
-    (∫ t in Ioc a b, f t ∂μ) = ∫ t in Ioo a b, f t ∂μ :=
+    ∫ t in Ioc a b, f t ∂μ = ∫ t in Ioo a b, f t ∂μ :=
   set_integral_congr_set_ae (Ioo_ae_eq_Ioc' hb).symm
 #align measure_theory.integral_Ioc_eq_integral_Ioo' MeasureTheory.integral_Ioc_eq_integral_Ioo'
 
 theorem integral_Ico_eq_integral_Ioo' (ha : μ {a} = 0) :
-    (∫ t in Ico a b, f t ∂μ) = ∫ t in Ioo a b, f t ∂μ :=
+    ∫ t in Ico a b, f t ∂μ = ∫ t in Ioo a b, f t ∂μ :=
   set_integral_congr_set_ae (Ioo_ae_eq_Ico' ha).symm
 #align measure_theory.integral_Ico_eq_integral_Ioo' MeasureTheory.integral_Ico_eq_integral_Ioo'
 
 theorem integral_Icc_eq_integral_Ioo' (ha : μ {a} = 0) (hb : μ {b} = 0) :
-    (∫ t in Icc a b, f t ∂μ) = ∫ t in Ioo a b, f t ∂μ :=
+    ∫ t in Icc a b, f t ∂μ = ∫ t in Ioo a b, f t ∂μ :=
   set_integral_congr_set_ae (Ioo_ae_eq_Icc' ha hb).symm
 #align measure_theory.integral_Icc_eq_integral_Ioo' MeasureTheory.integral_Icc_eq_integral_Ioo'
 
 theorem integral_Iic_eq_integral_Iio' (ha : μ {a} = 0) :
-    (∫ t in Iic a, f t ∂μ) = ∫ t in Iio a, f t ∂μ :=
+    ∫ t in Iic a, f t ∂μ = ∫ t in Iio a, f t ∂μ :=
   set_integral_congr_set_ae (Iio_ae_eq_Iic' ha).symm
 #align measure_theory.integral_Iic_eq_integral_Iio' MeasureTheory.integral_Iic_eq_integral_Iio'
 
 theorem integral_Ici_eq_integral_Ioi' (ha : μ {a} = 0) :
-    (∫ t in Ici a, f t ∂μ) = ∫ t in Ioi a, f t ∂μ :=
+    ∫ t in Ici a, f t ∂μ = ∫ t in Ioi a, f t ∂μ :=
   set_integral_congr_set_ae (Ioi_ae_eq_Ici' ha).symm
 #align measure_theory.integral_Ici_eq_integral_Ioi' MeasureTheory.integral_Ici_eq_integral_Ioi'
 
 variable [NoAtoms μ]
 
-theorem integral_Icc_eq_integral_Ioc : (∫ t in Icc a b, f t ∂μ) = ∫ t in Ioc a b, f t ∂μ :=
+theorem integral_Icc_eq_integral_Ioc : ∫ t in Icc a b, f t ∂μ = ∫ t in Ioc a b, f t ∂μ :=
   integral_Icc_eq_integral_Ioc' <| measure_singleton a
 #align measure_theory.integral_Icc_eq_integral_Ioc MeasureTheory.integral_Icc_eq_integral_Ioc
 
-theorem integral_Icc_eq_integral_Ico : (∫ t in Icc a b, f t ∂μ) = ∫ t in Ico a b, f t ∂μ :=
+theorem integral_Icc_eq_integral_Ico : ∫ t in Icc a b, f t ∂μ = ∫ t in Ico a b, f t ∂μ :=
   integral_Icc_eq_integral_Ico' <| measure_singleton b
 #align measure_theory.integral_Icc_eq_integral_Ico MeasureTheory.integral_Icc_eq_integral_Ico
 
-theorem integral_Ioc_eq_integral_Ioo : (∫ t in Ioc a b, f t ∂μ) = ∫ t in Ioo a b, f t ∂μ :=
+theorem integral_Ioc_eq_integral_Ioo : ∫ t in Ioc a b, f t ∂μ = ∫ t in Ioo a b, f t ∂μ :=
   integral_Ioc_eq_integral_Ioo' <| measure_singleton b
 #align measure_theory.integral_Ioc_eq_integral_Ioo MeasureTheory.integral_Ioc_eq_integral_Ioo
 
-theorem integral_Ico_eq_integral_Ioo : (∫ t in Ico a b, f t ∂μ) = ∫ t in Ioo a b, f t ∂μ :=
+theorem integral_Ico_eq_integral_Ioo : ∫ t in Ico a b, f t ∂μ = ∫ t in Ioo a b, f t ∂μ :=
   integral_Ico_eq_integral_Ioo' <| measure_singleton a
 #align measure_theory.integral_Ico_eq_integral_Ioo MeasureTheory.integral_Ico_eq_integral_Ioo
 
-theorem integral_Icc_eq_integral_Ioo : (∫ t in Icc a b, f t ∂μ) = ∫ t in Ico a b, f t ∂μ := by
+theorem integral_Icc_eq_integral_Ioo : ∫ t in Icc a b, f t ∂μ = ∫ t in Ico a b, f t ∂μ := by
   rw [integral_Icc_eq_integral_Ico, integral_Ico_eq_integral_Ioo]
 #align measure_theory.integral_Icc_eq_integral_Ioo MeasureTheory.integral_Icc_eq_integral_Ioo
 
-theorem integral_Iic_eq_integral_Iio : (∫ t in Iic a, f t ∂μ) = ∫ t in Iio a, f t ∂μ :=
+theorem integral_Iic_eq_integral_Iio : ∫ t in Iic a, f t ∂μ = ∫ t in Iio a, f t ∂μ :=
   integral_Iic_eq_integral_Iio' <| measure_singleton a
 #align measure_theory.integral_Iic_eq_integral_Iio MeasureTheory.integral_Iic_eq_integral_Iio
 
-theorem integral_Ici_eq_integral_Ioi : (∫ t in Ici a, f t ∂μ) = ∫ t in Ioi a, f t ∂μ :=
+theorem integral_Ici_eq_integral_Ioi : ∫ t in Ici a, f t ∂μ = ∫ t in Ioi a, f t ∂μ :=
   integral_Ici_eq_integral_Ioi' <| measure_singleton a
 #align measure_theory.integral_Ici_eq_integral_Ioi MeasureTheory.integral_Ici_eq_integral_Ioi
 
@@ -1204,7 +1204,7 @@ theorem integral_pair {f : α → E} {g : α → F} (hf : Integrable f μ) (hg :
 #align integral_pair integral_pair
 
 theorem integral_smul_const {𝕜 : Type _} [IsROrC 𝕜] [NormedSpace 𝕜 E] (f : α → 𝕜) (c : E) :
-    (∫ x, f x • c ∂μ) = (∫ x, f x ∂μ) • c := by
+    ∫ x, f x • c ∂μ = (∫ x, f x ∂μ) • c := by
   by_cases hf : Integrable f μ
   · exact ((1 : 𝕜 →L[𝕜] 𝕜).smulRight c).integral_comp_comm hf
   · by_cases hc : c = 0
@@ -1215,12 +1215,12 @@ theorem integral_smul_const {𝕜 : Type _} [IsROrC 𝕜] [NormedSpace 𝕜 E] (
 #align integral_smul_const integral_smul_const
 
 theorem integral_withDensity_eq_integral_smul {f : α → ℝ≥0} (f_meas : Measurable f) (g : α → E) :
-    (∫ a, g a ∂μ.withDensity fun x => f x) = ∫ a, f a • g a ∂μ := by
+    ∫ a, g a ∂μ.withDensity (fun x => f x) = ∫ a, f a • g a ∂μ := by
   by_cases hg : Integrable g (μ.withDensity fun x => f x); swap
   · rw [integral_undef hg, integral_undef]
     rwa [← integrable_withDensity_iff_integrable_smul f_meas]
   refine' Integrable.induction
-    (P := fun g => (∫ a, g a ∂μ.withDensity fun x => f x) = ∫ a, f a • g a ∂μ) _ _ _ _ hg
+    (P := fun g => ∫ a, g a ∂μ.withDensity (fun x => f x) = ∫ a, f a • g a ∂μ) _ _ _ _ hg
   · intro c s s_meas hs
     rw [integral_indicator s_meas]
     simp_rw [← indicator_smul_apply, integral_indicator s_meas]
@@ -1262,10 +1262,10 @@ theorem integral_withDensity_eq_integral_smul {f : α → ℝ≥0} (f_meas : Mea
 #align integral_with_density_eq_integral_smul integral_withDensity_eq_integral_smul
 
 theorem integral_withDensity_eq_integral_smul₀ {f : α → ℝ≥0} (hf : AEMeasurable f μ) (g : α → E) :
-    (∫ a, g a ∂μ.withDensity fun x => f x) = ∫ a, f a • g a ∂μ := by
+    ∫ a, g a ∂μ.withDensity (fun x => f x) = ∫ a, f a • g a ∂μ := by
   let f' := hf.mk _
   calc
-    (∫ a, g a ∂μ.withDensity fun x => f x) = ∫ a, g a ∂μ.withDensity fun x => f' x := by
+    ∫ a, g a ∂μ.withDensity (fun x => f x) = ∫ a, g a ∂μ.withDensity fun x => f' x := by
       congr 1
       apply withDensity_congr_ae
       filter_upwards [hf.ae_eq_mk] with x hx
@@ -1279,13 +1279,13 @@ theorem integral_withDensity_eq_integral_smul₀ {f : α → ℝ≥0} (hf : AEMe
 
 theorem set_integral_withDensity_eq_set_integral_smul {f : α → ℝ≥0} (f_meas : Measurable f)
     (g : α → E) {s : Set α} (hs : MeasurableSet s) :
-    (∫ a in s, g a ∂μ.withDensity fun x => f x) = ∫ a in s, f a • g a ∂μ := by
+    ∫ a in s, g a ∂μ.withDensity (fun x => f x) = ∫ a in s, f a • g a ∂μ := by
   rw [restrict_withDensity hs, integral_withDensity_eq_integral_smul f_meas]
 #align set_integral_with_density_eq_set_integral_smul set_integral_withDensity_eq_set_integral_smul
 
 theorem set_integral_withDensity_eq_set_integral_smul₀ {f : α → ℝ≥0} {s : Set α}
     (hf : AEMeasurable f (μ.restrict s)) (g : α → E) (hs : MeasurableSet s) :
-    (∫ a in s, g a ∂μ.withDensity fun x => f x) = ∫ a in s, f a • g a ∂μ := by
+    ∫ a in s, g a ∂μ.withDensity (fun x => f x) = ∫ a in s, f a • g a ∂μ := by
   rw [restrict_withDensity hs, integral_withDensity_eq_integral_smul₀ hf]
 #align set_integral_with_density_eq_set_integral_smul₀ set_integral_withDensity_eq_set_integral_smul₀
 

I wrote a script to find lines that contain an odd number of backticks

@@ -959,7 +959,7 @@ s i, f x ∂μ = μ (s i) • b + o(μ (s i))` at a filter `li` provided that `s
 along `li`. Since `μ (s i)` is an `ℝ≥0∞` number, we use `(μ (s i)).toReal` in the actual statement.
 
 Often there is a good formula for `(μ (s i)).toReal`, so the formalization can take an optional
-argument `m` with this formula and a proof `of `(fun i => (μ (s i)).toReal) =ᶠ[li] m`. Without these
+argument `m` with this formula and a proof of `(fun i => (μ (s i)).toReal) =ᶠ[li] m`. Without these
 arguments, `m i = (μ (s i)).toReal` is used in the output. -/
 theorem Filter.Tendsto.integral_sub_linear_isLittleO_ae [NormedSpace ℝ E] [CompleteSpace E]
     {μ : Measure α} {l : Filter α} [l.IsMeasurablyGenerated] {f : α → E} {b : E}
@@ -990,7 +990,7 @@ provided that `s i` tends to `(𝓝[t] a).smallSets` along `li`.  Since `μ (s i
 number, we use `(μ (s i)).toReal` in the actual statement.
 
 Often there is a good formula for `(μ (s i)).toReal`, so the formalization can take an optional
-argument `m` with this formula and a proof `of `(fun i => (μ (s i)).toReal) =ᶠ[li] m`. Without these
+argument `m` with this formula and a proof of `(fun i => (μ (s i)).toReal) =ᶠ[li] m`. Without these
 arguments, `m i = (μ (s i)).toReal` is used in the output. -/
 theorem ContinuousWithinAt.integral_sub_linear_isLittleO_ae [TopologicalSpace α]
     [OpensMeasurableSpace α] [NormedSpace ℝ E] [CompleteSpace E] {μ : Measure α}
@@ -1007,11 +1007,11 @@ theorem ContinuousWithinAt.integral_sub_linear_isLittleO_ae [TopologicalSpace α
 /-- Fundamental theorem of calculus for set integrals, `nhds` version: if `μ` is a locally finite
 measure and `f` is an almost everywhere measurable function that is continuous at a point `a`, then
 `∫ x in s i, f x ∂μ = μ (s i) • f a + o(μ (s i))` at `li` provided that `s` tends to
-`(𝓝 a).smallSets` along `li.  Since `μ (s i)` is an `ℝ≥0∞` number, we use `(μ (s i)).toReal` in
+`(𝓝 a).smallSets` along `li`. Since `μ (s i)` is an `ℝ≥0∞` number, we use `(μ (s i)).toReal` in
 the actual statement.
 
 Often there is a good formula for `(μ (s i)).toReal`, so the formalization can take an optional
-argument `m` with this formula and a proof `of `(fun i => (μ (s i)).toReal) =ᶠ[li] m`. Without these
+argument `m` with this formula and a proof of `(fun i => (μ (s i)).toReal) =ᶠ[li] m`. Without these
 arguments, `m i = (μ (s i)).toReal` is used in the output. -/
 theorem ContinuousAt.integral_sub_linear_isLittleO_ae [TopologicalSpace α] [OpensMeasurableSpace α]
     [NormedSpace ℝ E] [CompleteSpace E] {μ : Measure α} [IsLocallyFiniteMeasure μ] {a : α}
@@ -1028,7 +1028,7 @@ finite measure, `f` is continuous on a measurable set `t`, and `a ∈ t`, then `
 Since `μ (s i)` is an `ℝ≥0∞` number, we use `(μ (s i)).toReal` in the actual statement.
 
 Often there is a good formula for `(μ (s i)).toReal`, so the formalization can take an optional
-argument `m` with this formula and a proof `of `(fun i => (μ (s i)).toReal) =ᶠ[li] m`. Without these
+argument `m` with this formula and a proof of `(fun i => (μ (s i)).toReal) =ᶠ[li] m`. Without these
 arguments, `m i = (μ (s i)).toReal` is used in the output. -/
 theorem ContinuousOn.integral_sub_linear_isLittleO_ae [TopologicalSpace α] [OpensMeasurableSpace α]
     [NormedSpace ℝ E] [CompleteSpace E] [SecondCountableTopologyEither α E] {μ : Measure α}

Co-authored-by: Johan Commelin <johan@commelin.net>

@@ -1149,9 +1149,9 @@ end ContinuousLinearEquiv
 variable [CompleteSpace E] [NormedSpace ℝ E] [CompleteSpace F] [NormedSpace ℝ F]
 
 @[norm_cast]
-theorem integral_of_real {f : α → ℝ} : (∫ a, (f a : 𝕜) ∂μ) = ↑(∫ a, f a ∂μ) :=
+theorem integral_ofReal {f : α → ℝ} : (∫ a, (f a : 𝕜) ∂μ) = ↑(∫ a, f a ∂μ) :=
   (@IsROrC.ofRealLi 𝕜 _).integral_comp_comm f
-#align integral_of_real integral_of_real
+#align integral_of_real integral_ofReal
 
 theorem integral_re {f : α → 𝕜} (hf : Integrable f μ) :
     (∫ a, IsROrC.re (f a) ∂μ) = IsROrC.re (∫ a, f a ∂μ) :=
@@ -1180,7 +1180,7 @@ theorem integral_coe_re_add_coe_im {f : α → 𝕜} (hf : Integrable f μ) :
 theorem integral_re_add_im {f : α → 𝕜} (hf : Integrable f μ) :
     ((∫ x, IsROrC.re (f x) ∂μ : ℝ) : 𝕜) + (∫ x, IsROrC.im (f x) ∂μ : ℝ) * IsROrC.I =
       ∫ x, f x ∂μ := by
-  rw [← integral_of_real, ← integral_of_real, integral_coe_re_add_coe_im hf]
+  rw [← integral_ofReal, ← integral_ofReal, integral_coe_re_add_coe_im hf]
 #align integral_re_add_im integral_re_add_im
 
 theorem set_integral_re_add_im {f : α → 𝕜} {i : Set α} (hf : IntegrableOn f i μ) :

Co-authored-by: Moritz Firsching <firsching@google.com>