measure_theory.integral.integrable_on ⟷ Mathlib.MeasureTheory.Integral.IntegrableOn

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

@@ -447,7 +447,7 @@ theorem IntegrableOn.integrable_of_ae_not_mem_eq_zero (hf : IntegrableOn f s μ)
 #align measure_theory.integrable_on.integrable_of_ae_not_mem_eq_zero MeasureTheory.IntegrableOn.integrable_of_ae_not_mem_eq_zero
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (x «expr ∉ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:642:2: warning: expanding binder collection (x «expr ∉ » s) -/
 #print MeasureTheory.IntegrableOn.integrable_of_forall_not_mem_eq_zero /-
 /-- If a function is integrable on a set `s` and vanishes everywhere on its complement,
 then it is integrable. -/

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

@@ -3,8 +3,8 @@ Copyright (c) 2021 Rémy Degenne. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Zhouhang Zhou, Yury Kudryashov
 -/
-import Mathbin.MeasureTheory.Function.L1Space
-import Mathbin.Analysis.NormedSpace.IndicatorFunction
+import MeasureTheory.Function.L1Space
+import Analysis.NormedSpace.IndicatorFunction
 
 #align_import measure_theory.integral.integrable_on from "leanprover-community/mathlib"@"599fffe78f0e11eb6a034e834ec51882167b9688"
 
@@ -447,7 +447,7 @@ theorem IntegrableOn.integrable_of_ae_not_mem_eq_zero (hf : IntegrableOn f s μ)
 #align measure_theory.integrable_on.integrable_of_ae_not_mem_eq_zero MeasureTheory.IntegrableOn.integrable_of_ae_not_mem_eq_zero
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x «expr ∉ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (x «expr ∉ » s) -/
 #print MeasureTheory.IntegrableOn.integrable_of_forall_not_mem_eq_zero /-
 /-- If a function is integrable on a set `s` and vanishes everywhere on its complement,
 then it is integrable. -/

mathlib commit https://github.com/leanprover-community/mathlib/commit/32a7e535287f9c73f2e4d2aef306a39190f0b504

@@ -558,7 +558,7 @@ theorem IntegrableAtFilter.inf_ae_iff {l : Filter α} :
 #align measure_theory.integrable_at_filter.inf_ae_iff MeasureTheory.IntegrableAtFilter.inf_ae_iff
 -/
 
-alias integrable_at_filter.inf_ae_iff ↔ integrable_at_filter.of_inf_ae _
+alias ⟨integrable_at_filter.of_inf_ae, _⟩ := integrable_at_filter.inf_ae_iff
 #align measure_theory.integrable_at_filter.of_inf_ae MeasureTheory.IntegrableAtFilter.of_inf_ae
 
 #print MeasureTheory.Measure.FiniteAtFilter.integrableAtFilter /-
@@ -588,8 +588,8 @@ theorem Measure.FiniteAtFilter.integrableAtFilter_of_tendsto_ae {l : Filter α}
 #align measure_theory.measure.finite_at_filter.integrable_at_filter_of_tendsto_ae MeasureTheory.Measure.FiniteAtFilter.integrableAtFilter_of_tendsto_ae
 -/
 
-alias measure.finite_at_filter.integrable_at_filter_of_tendsto_ae ←
-  _root_.filter.tendsto.integrable_at_filter_ae
+alias _root_.filter.tendsto.integrable_at_filter_ae :=
+  measure.finite_at_filter.integrable_at_filter_of_tendsto_ae
 #align filter.tendsto.integrable_at_filter_ae Filter.Tendsto.integrableAtFilter_ae
 
 #print MeasureTheory.Measure.FiniteAtFilter.integrableAtFilter_of_tendsto /-
@@ -600,8 +600,8 @@ theorem Measure.FiniteAtFilter.integrableAtFilter_of_tendsto {l : Filter α}
 #align measure_theory.measure.finite_at_filter.integrable_at_filter_of_tendsto MeasureTheory.Measure.FiniteAtFilter.integrableAtFilter_of_tendsto
 -/
 
-alias measure.finite_at_filter.integrable_at_filter_of_tendsto ←
-  _root_.filter.tendsto.integrable_at_filter
+alias _root_.filter.tendsto.integrable_at_filter :=
+  measure.finite_at_filter.integrable_at_filter_of_tendsto
 #align filter.tendsto.integrable_at_filter Filter.Tendsto.integrableAtFilter
 
 #print MeasureTheory.integrable_add_of_disjoint /-

mathlib commit https://github.com/leanprover-community/mathlib/commit/63721b2c3eba6c325ecf8ae8cca27155a4f6306f

@@ -55,7 +55,7 @@ theorem stronglyMeasurableAt_bot {f : α → β} : StronglyMeasurableAtFilter f
 #print StronglyMeasurableAtFilter.eventually /-
 protected theorem StronglyMeasurableAtFilter.eventually (h : StronglyMeasurableAtFilter f l μ) :
     ∀ᶠ s in l.smallSets, AEStronglyMeasurable f (μ.restrict s) :=
-  (eventually_small_sets' fun s t => AEStronglyMeasurable.mono_set).2 h
+  (eventually_smallSets' fun s t => AEStronglyMeasurable.mono_set).2 h
 #align strongly_measurable_at_filter.eventually StronglyMeasurableAtFilter.eventually
 -/
 
@@ -517,7 +517,7 @@ theorem Integrable.integrableAtFilter (h : Integrable f μ) (l : Filter α) :
 #print MeasureTheory.IntegrableAtFilter.eventually /-
 protected theorem IntegrableAtFilter.eventually (h : IntegrableAtFilter f l μ) :
     ∀ᶠ s in l.smallSets, IntegrableOn f s μ :=
-  Iff.mpr (eventually_small_sets' fun s t hst ht => ht.mono_set hst) h
+  Iff.mpr (eventually_smallSets' fun s t hst ht => ht.mono_set hst) h
 #align measure_theory.integrable_at_filter.eventually MeasureTheory.IntegrableAtFilter.eventually
 -/
 

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

@@ -2,15 +2,12 @@
 Copyright (c) 2021 Rémy Degenne. 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.integrable_on
-! leanprover-community/mathlib commit 599fffe78f0e11eb6a034e834ec51882167b9688
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.MeasureTheory.Function.L1Space
 import Mathbin.Analysis.NormedSpace.IndicatorFunction
 
+#align_import measure_theory.integral.integrable_on from "leanprover-community/mathlib"@"599fffe78f0e11eb6a034e834ec51882167b9688"
+
 /-! # Functions integrable on a set and at a filter
 
 > THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
@@ -450,7 +447,7 @@ theorem IntegrableOn.integrable_of_ae_not_mem_eq_zero (hf : IntegrableOn f s μ)
 #align measure_theory.integrable_on.integrable_of_ae_not_mem_eq_zero MeasureTheory.IntegrableOn.integrable_of_ae_not_mem_eq_zero
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (x «expr ∉ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x «expr ∉ » s) -/
 #print MeasureTheory.IntegrableOn.integrable_of_forall_not_mem_eq_zero /-
 /-- If a function is integrable on a set `s` and vanishes everywhere on its complement,
 then it is integrable. -/

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

@@ -48,36 +48,48 @@ def StronglyMeasurableAtFilter (f : α → β) (l : Filter α)
 #align strongly_measurable_at_filter StronglyMeasurableAtFilter
 -/
 
+#print stronglyMeasurableAt_bot /-
 @[simp]
 theorem stronglyMeasurableAt_bot {f : α → β} : StronglyMeasurableAtFilter f ⊥ μ :=
   ⟨∅, mem_bot, by simp⟩
 #align strongly_measurable_at_bot stronglyMeasurableAt_bot
+-/
 
+#print StronglyMeasurableAtFilter.eventually /-
 protected theorem StronglyMeasurableAtFilter.eventually (h : StronglyMeasurableAtFilter f l μ) :
     ∀ᶠ s in l.smallSets, AEStronglyMeasurable f (μ.restrict s) :=
   (eventually_small_sets' fun s t => AEStronglyMeasurable.mono_set).2 h
 #align strongly_measurable_at_filter.eventually StronglyMeasurableAtFilter.eventually
+-/
 
+#print StronglyMeasurableAtFilter.filter_mono /-
 protected theorem StronglyMeasurableAtFilter.filter_mono (h : StronglyMeasurableAtFilter f l μ)
     (h' : l' ≤ l) : StronglyMeasurableAtFilter f l' μ :=
   let ⟨s, hsl, hs⟩ := h
   ⟨s, h' hsl, hs⟩
 #align strongly_measurable_at_filter.filter_mono StronglyMeasurableAtFilter.filter_mono
+-/
 
+#print MeasureTheory.AEStronglyMeasurable.stronglyMeasurableAtFilter /-
 protected theorem MeasureTheory.AEStronglyMeasurable.stronglyMeasurableAtFilter
     (h : AEStronglyMeasurable f μ) : StronglyMeasurableAtFilter f l μ :=
   ⟨univ, univ_mem, by rwa [measure.restrict_univ]⟩
 #align measure_theory.ae_strongly_measurable.strongly_measurable_at_filter MeasureTheory.AEStronglyMeasurable.stronglyMeasurableAtFilter
+-/
 
+#print AeStronglyMeasurable.stronglyMeasurableAtFilter_of_mem /-
 theorem AeStronglyMeasurable.stronglyMeasurableAtFilter_of_mem {s}
     (h : AEStronglyMeasurable f (μ.restrict s)) (hl : s ∈ l) : StronglyMeasurableAtFilter f l μ :=
   ⟨s, hl, h⟩
 #align ae_strongly_measurable.strongly_measurable_at_filter_of_mem AeStronglyMeasurable.stronglyMeasurableAtFilter_of_mem
+-/
 
+#print MeasureTheory.StronglyMeasurable.stronglyMeasurableAtFilter /-
 protected theorem MeasureTheory.StronglyMeasurable.stronglyMeasurableAtFilter
     (h : StronglyMeasurable f) : StronglyMeasurableAtFilter f l μ :=
   h.AEStronglyMeasurable.StronglyMeasurableAtFilter
 #align measure_theory.strongly_measurable.strongly_measurable_at_filter MeasureTheory.StronglyMeasurable.stronglyMeasurableAtFilter
+-/
 
 end
 
@@ -85,12 +97,14 @@ namespace MeasureTheory
 
 section NormedAddCommGroup
 
+#print MeasureTheory.hasFiniteIntegral_restrict_of_bounded /-
 theorem hasFiniteIntegral_restrict_of_bounded [NormedAddCommGroup E] {f : α → E} {s : Set α}
     {μ : Measure α} {C} (hs : μ s < ∞) (hf : ∀ᵐ x ∂μ.restrict s, ‖f x‖ ≤ C) :
     HasFiniteIntegral f (μ.restrict s) :=
   haveI : is_finite_measure (μ.restrict s) := ⟨by rwa [measure.restrict_apply_univ]⟩
   has_finite_integral_of_bounded hf
 #align measure_theory.has_finite_integral_restrict_of_bounded MeasureTheory.hasFiniteIntegral_restrict_of_bounded
+-/
 
 variable [NormedAddCommGroup E] {f g : α → E} {s t : Set α} {μ ν : Measure α}
 
@@ -103,67 +117,95 @@ def IntegrableOn (f : α → E) (s : Set α)
 #align measure_theory.integrable_on MeasureTheory.IntegrableOn
 -/
 
+#print MeasureTheory.IntegrableOn.integrable /-
 theorem IntegrableOn.integrable (h : IntegrableOn f s μ) : Integrable f (μ.restrict s) :=
   h
 #align measure_theory.integrable_on.integrable MeasureTheory.IntegrableOn.integrable
+-/
 
+#print MeasureTheory.integrableOn_empty /-
 @[simp]
 theorem integrableOn_empty : IntegrableOn f ∅ μ := by simp [integrable_on, integrable_zero_measure]
 #align measure_theory.integrable_on_empty MeasureTheory.integrableOn_empty
+-/
 
+#print MeasureTheory.integrableOn_univ /-
 @[simp]
 theorem integrableOn_univ : IntegrableOn f univ μ ↔ Integrable f μ := by
   rw [integrable_on, measure.restrict_univ]
 #align measure_theory.integrable_on_univ MeasureTheory.integrableOn_univ
+-/
 
+#print MeasureTheory.integrableOn_zero /-
 theorem integrableOn_zero : IntegrableOn (fun _ => (0 : E)) s μ :=
   integrable_zero _ _ _
 #align measure_theory.integrable_on_zero MeasureTheory.integrableOn_zero
+-/
 
+#print MeasureTheory.integrableOn_const /-
 @[simp]
 theorem integrableOn_const {C : E} : IntegrableOn (fun _ => C) s μ ↔ C = 0 ∨ μ s < ∞ :=
   integrable_const_iff.trans <| by rw [measure.restrict_apply_univ]
 #align measure_theory.integrable_on_const MeasureTheory.integrableOn_const
+-/
 
+#print MeasureTheory.IntegrableOn.mono /-
 theorem IntegrableOn.mono (h : IntegrableOn f t ν) (hs : s ⊆ t) (hμ : μ ≤ ν) : IntegrableOn f s μ :=
   h.mono_measure <| Measure.restrict_mono hs hμ
 #align measure_theory.integrable_on.mono MeasureTheory.IntegrableOn.mono
+-/
 
+#print MeasureTheory.IntegrableOn.mono_set /-
 theorem IntegrableOn.mono_set (h : IntegrableOn f t μ) (hst : s ⊆ t) : IntegrableOn f s μ :=
   h.mono hst le_rfl
 #align measure_theory.integrable_on.mono_set MeasureTheory.IntegrableOn.mono_set
+-/
 
+#print MeasureTheory.IntegrableOn.mono_measure /-
 theorem IntegrableOn.mono_measure (h : IntegrableOn f s ν) (hμ : μ ≤ ν) : IntegrableOn f s μ :=
   h.mono (Subset.refl _) hμ
 #align measure_theory.integrable_on.mono_measure MeasureTheory.IntegrableOn.mono_measure
+-/
 
+#print MeasureTheory.IntegrableOn.mono_set_ae /-
 theorem IntegrableOn.mono_set_ae (h : IntegrableOn f t μ) (hst : s ≤ᵐ[μ] t) : IntegrableOn f s μ :=
   h.Integrable.mono_measure <| Measure.restrict_mono_ae hst
 #align measure_theory.integrable_on.mono_set_ae MeasureTheory.IntegrableOn.mono_set_ae
+-/
 
+#print MeasureTheory.IntegrableOn.congr_set_ae /-
 theorem IntegrableOn.congr_set_ae (h : IntegrableOn f t μ) (hst : s =ᵐ[μ] t) : IntegrableOn f s μ :=
   h.mono_set_ae hst.le
 #align measure_theory.integrable_on.congr_set_ae MeasureTheory.IntegrableOn.congr_set_ae
+-/
 
+#print MeasureTheory.IntegrableOn.congr_fun_ae /-
 theorem IntegrableOn.congr_fun_ae (h : IntegrableOn f s μ) (hst : f =ᵐ[μ.restrict s] g) :
     IntegrableOn g s μ :=
   Integrable.congr h hst
 #align measure_theory.integrable_on.congr_fun_ae MeasureTheory.IntegrableOn.congr_fun_ae
+-/
 
+#print MeasureTheory.integrableOn_congr_fun_ae /-
 theorem integrableOn_congr_fun_ae (hst : f =ᵐ[μ.restrict s] g) :
     IntegrableOn f s μ ↔ IntegrableOn g s μ :=
   ⟨fun h => h.congr_fun_ae hst, fun h => h.congr_fun_ae hst.symm⟩
 #align measure_theory.integrable_on_congr_fun_ae MeasureTheory.integrableOn_congr_fun_ae
+-/
 
+#print MeasureTheory.IntegrableOn.congr_fun /-
 theorem IntegrableOn.congr_fun (h : IntegrableOn f s μ) (hst : EqOn f g s) (hs : MeasurableSet s) :
     IntegrableOn g s μ :=
   h.congr_fun_ae ((ae_restrict_iff' hs).2 (eventually_of_forall hst))
 #align measure_theory.integrable_on.congr_fun MeasureTheory.IntegrableOn.congr_fun
+-/
 
+#print MeasureTheory.integrableOn_congr_fun /-
 theorem integrableOn_congr_fun (hst : EqOn f g s) (hs : MeasurableSet s) :
     IntegrableOn f s μ ↔ IntegrableOn g s μ :=
   ⟨fun h => h.congr_fun hst hs, fun h => h.congr_fun hst.symm hs⟩
 #align measure_theory.integrable_on_congr_fun MeasureTheory.integrableOn_congr_fun
+-/
 
 #print MeasureTheory.Integrable.integrableOn /-
 theorem Integrable.integrableOn (h : Integrable f μ) : IntegrableOn f s μ :=
@@ -171,29 +213,40 @@ theorem Integrable.integrableOn (h : Integrable f μ) : IntegrableOn f s μ :=
 #align measure_theory.integrable.integrable_on MeasureTheory.Integrable.integrableOn
 -/
 
+#print MeasureTheory.IntegrableOn.restrict /-
 theorem IntegrableOn.restrict (h : IntegrableOn f s μ) (hs : MeasurableSet s) :
     IntegrableOn f s (μ.restrict t) := by rw [integrable_on, measure.restrict_restrict hs];
   exact h.mono_set (inter_subset_left _ _)
 #align measure_theory.integrable_on.restrict MeasureTheory.IntegrableOn.restrict
+-/
 
+#print MeasureTheory.IntegrableOn.left_of_union /-
 theorem IntegrableOn.left_of_union (h : IntegrableOn f (s ∪ t) μ) : IntegrableOn f s μ :=
   h.mono_set <| subset_union_left _ _
 #align measure_theory.integrable_on.left_of_union MeasureTheory.IntegrableOn.left_of_union
+-/
 
+#print MeasureTheory.IntegrableOn.right_of_union /-
 theorem IntegrableOn.right_of_union (h : IntegrableOn f (s ∪ t) μ) : IntegrableOn f t μ :=
   h.mono_set <| subset_union_right _ _
 #align measure_theory.integrable_on.right_of_union MeasureTheory.IntegrableOn.right_of_union
+-/
 
+#print MeasureTheory.IntegrableOn.union /-
 theorem IntegrableOn.union (hs : IntegrableOn f s μ) (ht : IntegrableOn f t μ) :
     IntegrableOn f (s ∪ t) μ :=
   (hs.add_measure ht).mono_measure <| Measure.restrict_union_le _ _
 #align measure_theory.integrable_on.union MeasureTheory.IntegrableOn.union
+-/
 
+#print MeasureTheory.integrableOn_union /-
 @[simp]
 theorem integrableOn_union : IntegrableOn f (s ∪ t) μ ↔ IntegrableOn f s μ ∧ IntegrableOn f t μ :=
   ⟨fun h => ⟨h.left_of_union, h.right_of_union⟩, fun h => h.1.union h.2⟩
 #align measure_theory.integrable_on_union MeasureTheory.integrableOn_union
+-/
 
+#print MeasureTheory.integrableOn_singleton_iff /-
 @[simp]
 theorem integrableOn_singleton_iff {x : α} [MeasurableSingletonClass α] :
     IntegrableOn f {x} μ ↔ f x = 0 ∨ μ {x} < ∞ :=
@@ -205,7 +258,9 @@ theorem integrableOn_singleton_iff {x : α} [MeasurableSingletonClass α] :
   rw [integrable_on, integrable_congr this, integrable_const_iff]
   simp
 #align measure_theory.integrable_on_singleton_iff MeasureTheory.integrableOn_singleton_iff
+-/
 
+#print MeasureTheory.integrableOn_finite_biUnion /-
 @[simp]
 theorem integrableOn_finite_biUnion {s : Set β} (hs : s.Finite) {t : β → Set α} :
     IntegrableOn f (⋃ i ∈ s, t i) μ ↔ ∀ i ∈ s, IntegrableOn f (t i) μ :=
@@ -214,13 +269,17 @@ theorem integrableOn_finite_biUnion {s : Set β} (hs : s.Finite) {t : β → Set
   · simp
   · intro a s ha hs hf; simp [hf, or_imp, forall_and]
 #align measure_theory.integrable_on_finite_bUnion MeasureTheory.integrableOn_finite_biUnion
+-/
 
+#print MeasureTheory.integrableOn_finset_iUnion /-
 @[simp]
 theorem integrableOn_finset_iUnion {s : Finset β} {t : β → Set α} :
     IntegrableOn f (⋃ i ∈ s, t i) μ ↔ ∀ i ∈ s, IntegrableOn f (t i) μ :=
   integrableOn_finite_biUnion s.finite_toSet
 #align measure_theory.integrable_on_finset_Union MeasureTheory.integrableOn_finset_iUnion
+-/
 
+#print MeasureTheory.integrableOn_finite_iUnion /-
 @[simp]
 theorem integrableOn_finite_iUnion [Finite β] {t : β → Set α} :
     IntegrableOn f (⋃ i, t i) μ ↔ ∀ i, IntegrableOn f (t i) μ :=
@@ -228,12 +287,16 @@ theorem integrableOn_finite_iUnion [Finite β] {t : β → Set α} :
   cases nonempty_fintype β
   simpa using @integrable_on_finset_Union _ _ _ _ _ f μ Finset.univ t
 #align measure_theory.integrable_on_finite_Union MeasureTheory.integrableOn_finite_iUnion
+-/
 
+#print MeasureTheory.IntegrableOn.add_measure /-
 theorem IntegrableOn.add_measure (hμ : IntegrableOn f s μ) (hν : IntegrableOn f s ν) :
     IntegrableOn f s (μ + ν) := by delta integrable_on; rw [measure.restrict_add];
   exact hμ.integrable.add_measure hν
 #align measure_theory.integrable_on.add_measure MeasureTheory.IntegrableOn.add_measure
+-/
 
+#print MeasureTheory.integrableOn_add_measure /-
 @[simp]
 theorem integrableOn_add_measure :
     IntegrableOn f s (μ + ν) ↔ IntegrableOn f s μ ∧ IntegrableOn f s ν :=
@@ -241,51 +304,69 @@ theorem integrableOn_add_measure :
     ⟨h.mono_measure (Measure.le_add_right le_rfl), h.mono_measure (Measure.le_add_left le_rfl)⟩,
     fun h => h.1.add_measure h.2⟩
 #align measure_theory.integrable_on_add_measure MeasureTheory.integrableOn_add_measure
+-/
 
+#print MeasurableEmbedding.integrableOn_map_iff /-
 theorem MeasurableEmbedding.integrableOn_map_iff [MeasurableSpace β] {e : α → β}
     (he : MeasurableEmbedding e) {f : β → E} {μ : Measure α} {s : Set β} :
     IntegrableOn f s (Measure.map e μ) ↔ IntegrableOn (f ∘ e) (e ⁻¹' s) μ := by
   simp only [integrable_on, he.restrict_map, he.integrable_map_iff]
 #align measurable_embedding.integrable_on_map_iff MeasurableEmbedding.integrableOn_map_iff
+-/
 
+#print MeasureTheory.integrableOn_map_equiv /-
 theorem integrableOn_map_equiv [MeasurableSpace β] (e : α ≃ᵐ β) {f : β → E} {μ : Measure α}
     {s : Set β} : IntegrableOn f s (Measure.map e μ) ↔ IntegrableOn (f ∘ e) (e ⁻¹' s) μ := by
   simp only [integrable_on, e.restrict_map, integrable_map_equiv e]
 #align measure_theory.integrable_on_map_equiv MeasureTheory.integrableOn_map_equiv
+-/
 
+#print MeasureTheory.MeasurePreserving.integrableOn_comp_preimage /-
 theorem MeasurePreserving.integrableOn_comp_preimage [MeasurableSpace β] {e : α → β} {ν}
     (h₁ : MeasurePreserving e μ ν) (h₂ : MeasurableEmbedding e) {f : β → E} {s : Set β} :
     IntegrableOn (f ∘ e) (e ⁻¹' s) μ ↔ IntegrableOn f s ν :=
   (h₁.restrict_preimage_emb h₂ s).integrable_comp_emb h₂
 #align measure_theory.measure_preserving.integrable_on_comp_preimage MeasureTheory.MeasurePreserving.integrableOn_comp_preimage
+-/
 
+#print MeasureTheory.MeasurePreserving.integrableOn_image /-
 theorem MeasurePreserving.integrableOn_image [MeasurableSpace β] {e : α → β} {ν}
     (h₁ : MeasurePreserving e μ ν) (h₂ : MeasurableEmbedding e) {f : β → E} {s : Set α} :
     IntegrableOn f (e '' s) ν ↔ IntegrableOn (f ∘ e) s μ :=
   ((h₁.restrict_image_emb h₂ s).integrable_comp_emb h₂).symm
 #align measure_theory.measure_preserving.integrable_on_image MeasureTheory.MeasurePreserving.integrableOn_image
+-/
 
+#print MeasureTheory.integrable_indicator_iff /-
 theorem integrable_indicator_iff (hs : MeasurableSet s) :
     Integrable (indicator s f) μ ↔ IntegrableOn f s μ := by
   simp [integrable_on, integrable, has_finite_integral, nnnorm_indicator_eq_indicator_nnnorm,
     ENNReal.coe_indicator, lintegral_indicator _ hs, aestronglyMeasurable_indicator_iff hs]
 #align measure_theory.integrable_indicator_iff MeasureTheory.integrable_indicator_iff
+-/
 
+#print MeasureTheory.IntegrableOn.integrable_indicator /-
 theorem IntegrableOn.integrable_indicator (h : IntegrableOn f s μ) (hs : MeasurableSet s) :
     Integrable (indicator s f) μ :=
   (integrable_indicator_iff hs).2 h
 #align measure_theory.integrable_on.integrable_indicator MeasureTheory.IntegrableOn.integrable_indicator
+-/
 
+#print MeasureTheory.Integrable.indicator /-
 theorem Integrable.indicator (h : Integrable f μ) (hs : MeasurableSet s) :
     Integrable (indicator s f) μ :=
   h.IntegrableOn.integrable_indicator hs
 #align measure_theory.integrable.indicator MeasureTheory.Integrable.indicator
+-/
 
+#print MeasureTheory.IntegrableOn.indicator /-
 theorem IntegrableOn.indicator (h : IntegrableOn f s μ) (ht : MeasurableSet t) :
     IntegrableOn (indicator t f) s μ :=
   Integrable.indicator h ht
 #align measure_theory.integrable_on.indicator MeasureTheory.IntegrableOn.indicator
+-/
 
+#print MeasureTheory.integrable_indicatorConstLp /-
 theorem integrable_indicatorConstLp {E} [NormedAddCommGroup E] {p : ℝ≥0∞} {s : Set α}
     (hs : MeasurableSet s) (hμs : μ s ≠ ∞) (c : E) : Integrable (indicatorConstLp p hs hμs c) μ :=
   by
@@ -294,7 +375,9 @@ theorem integrable_indicatorConstLp {E} [NormedAddCommGroup E] {p : ℝ≥0∞}
   right
   simpa only [Set.univ_inter, MeasurableSet.univ, measure.restrict_apply] using hμs
 #align measure_theory.integrable_indicator_const_Lp MeasureTheory.integrable_indicatorConstLp
+-/
 
+#print MeasureTheory.IntegrableOn.restrict_toMeasurable /-
 /-- If a function is integrable on a set `s` and nonzero there, then the measurable hull of `s` is
 well behaved: the restriction of the measure to `to_measurable μ s` coincides with its restriction
 to `s`. -/
@@ -315,7 +398,9 @@ theorem IntegrableOn.restrict_toMeasurable (hf : IntegrableOn f s μ) (h's : ∀
   refine' mem_Union.2 ⟨n, _⟩
   exact subset_to_measurable _ _ hn.le
 #align measure_theory.integrable_on.restrict_to_measurable MeasureTheory.IntegrableOn.restrict_toMeasurable
+-/
 
+#print MeasureTheory.IntegrableOn.of_ae_diff_eq_zero /-
 /-- If a function is integrable on a set `s`, and vanishes on `t \ s`, then it is integrable on `t`
 if `t` is null-measurable. -/
 theorem IntegrableOn.of_ae_diff_eq_zero (hf : IntegrableOn f s μ) (ht : NullMeasurableSet t μ)
@@ -342,14 +427,18 @@ theorem IntegrableOn.of_ae_diff_eq_zero (hf : IntegrableOn f s μ) (ht : NullMea
   rw [union_diff_self]
   exact subset_union_right _ _
 #align measure_theory.integrable_on.of_ae_diff_eq_zero MeasureTheory.IntegrableOn.of_ae_diff_eq_zero
+-/
 
+#print MeasureTheory.IntegrableOn.of_forall_diff_eq_zero /-
 /-- If a function is integrable on a set `s`, and vanishes on `t \ s`, then it is integrable on `t`
 if `t` is measurable. -/
 theorem IntegrableOn.of_forall_diff_eq_zero (hf : IntegrableOn f s μ) (ht : MeasurableSet t)
     (h't : ∀ x ∈ t \ s, f x = 0) : IntegrableOn f t μ :=
   hf.of_ae_diff_eq_zero ht.NullMeasurableSet (eventually_of_forall h't)
 #align measure_theory.integrable_on.of_forall_diff_eq_zero MeasureTheory.IntegrableOn.of_forall_diff_eq_zero
+-/
 
+#print MeasureTheory.IntegrableOn.integrable_of_ae_not_mem_eq_zero /-
 /-- If a function is integrable on a set `s` and vanishes almost everywhere on its complement,
 then it is integrable. -/
 theorem IntegrableOn.integrable_of_ae_not_mem_eq_zero (hf : IntegrableOn f s μ)
@@ -359,15 +448,19 @@ theorem IntegrableOn.integrable_of_ae_not_mem_eq_zero (hf : IntegrableOn f s μ)
   apply hf.of_ae_diff_eq_zero null_measurable_set_univ
   filter_upwards [h't] with x hx h'x using hx h'x.2
 #align measure_theory.integrable_on.integrable_of_ae_not_mem_eq_zero MeasureTheory.IntegrableOn.integrable_of_ae_not_mem_eq_zero
+-/
 
 /- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (x «expr ∉ » s) -/
+#print MeasureTheory.IntegrableOn.integrable_of_forall_not_mem_eq_zero /-
 /-- If a function is integrable on a set `s` and vanishes everywhere on its complement,
 then it is integrable. -/
 theorem IntegrableOn.integrable_of_forall_not_mem_eq_zero (hf : IntegrableOn f s μ)
     (h't : ∀ (x) (_ : x ∉ s), f x = 0) : Integrable f μ :=
   hf.integrable_of_ae_not_mem_eq_zero (eventually_of_forall fun x hx => h't x hx)
 #align measure_theory.integrable_on.integrable_of_forall_not_mem_eq_zero MeasureTheory.IntegrableOn.integrable_of_forall_not_mem_eq_zero
+-/
 
+#print MeasureTheory.integrableOn_iff_integrable_of_support_subset /-
 theorem integrableOn_iff_integrable_of_support_subset (h1s : support f ⊆ s) :
     IntegrableOn f s μ ↔ Integrable f μ :=
   by
@@ -376,7 +469,9 @@ theorem integrableOn_iff_integrable_of_support_subset (h1s : support f ⊆ s) :
   contrapose! hx
   exact h1s (mem_support.2 hx)
 #align measure_theory.integrable_on_iff_integrable_of_support_subset MeasureTheory.integrableOn_iff_integrable_of_support_subset
+-/
 
+#print MeasureTheory.integrableOn_Lp_of_measure_ne_top /-
 theorem integrableOn_Lp_of_measure_ne_top {E} [NormedAddCommGroup E] {p : ℝ≥0∞} {s : Set α}
     (f : Lp E p μ) (hp : 1 ≤ p) (hμs : μ s ≠ ∞) : IntegrableOn f s μ :=
   by
@@ -386,18 +481,23 @@ theorem integrableOn_Lp_of_measure_ne_top {E} [NormedAddCommGroup E] {p : ℝ≥
   haveI hμ_finite : is_finite_measure (μ.restrict s) := ⟨hμ_restrict_univ⟩
   exact ((Lp.mem_ℒp _).restrict s).memℒp_of_exponent_le hp
 #align measure_theory.integrable_on_Lp_of_measure_ne_top MeasureTheory.integrableOn_Lp_of_measure_ne_top
+-/
 
+#print MeasureTheory.Integrable.lintegral_lt_top /-
 theorem Integrable.lintegral_lt_top {f : α → ℝ} (hf : Integrable f μ) :
     ∫⁻ x, ENNReal.ofReal (f x) ∂μ < ∞ :=
   calc
     ∫⁻ x, ENNReal.ofReal (f x) ∂μ ≤ ∫⁻ x, ↑‖f x‖₊ ∂μ := lintegral_ofReal_le_lintegral_nnnorm f
     _ < ∞ := hf.2
 #align measure_theory.integrable.lintegral_lt_top MeasureTheory.Integrable.lintegral_lt_top
+-/
 
+#print MeasureTheory.IntegrableOn.set_lintegral_lt_top /-
 theorem IntegrableOn.set_lintegral_lt_top {f : α → ℝ} {s : Set α} (hf : IntegrableOn f s μ) :
     ∫⁻ x in s, ENNReal.ofReal (f x) ∂μ < ∞ :=
   Integrable.lintegral_lt_top hf
 #align measure_theory.integrable_on.set_lintegral_lt_top MeasureTheory.IntegrableOn.set_lintegral_lt_top
+-/
 
 #print MeasureTheory.IntegrableAtFilter /-
 /-- We say that a function `f` is *integrable at filter* `l` if it is integrable on some
@@ -417,27 +517,36 @@ theorem Integrable.integrableAtFilter (h : Integrable f μ) (l : Filter α) :
 #align measure_theory.integrable.integrable_at_filter MeasureTheory.Integrable.integrableAtFilter
 -/
 
+#print MeasureTheory.IntegrableAtFilter.eventually /-
 protected theorem IntegrableAtFilter.eventually (h : IntegrableAtFilter f l μ) :
     ∀ᶠ s in l.smallSets, IntegrableOn f s μ :=
   Iff.mpr (eventually_small_sets' fun s t hst ht => ht.mono_set hst) h
 #align measure_theory.integrable_at_filter.eventually MeasureTheory.IntegrableAtFilter.eventually
+-/
 
+#print MeasureTheory.IntegrableAtFilter.filter_mono /-
 theorem IntegrableAtFilter.filter_mono (hl : l ≤ l') (hl' : IntegrableAtFilter f l' μ) :
     IntegrableAtFilter f l μ :=
   let ⟨s, hs, hsf⟩ := hl'
   ⟨s, hl hs, hsf⟩
 #align measure_theory.integrable_at_filter.filter_mono MeasureTheory.IntegrableAtFilter.filter_mono
+-/
 
+#print MeasureTheory.IntegrableAtFilter.inf_of_left /-
 theorem IntegrableAtFilter.inf_of_left (hl : IntegrableAtFilter f l μ) :
     IntegrableAtFilter f (l ⊓ l') μ :=
   hl.filter_mono inf_le_left
 #align measure_theory.integrable_at_filter.inf_of_left MeasureTheory.IntegrableAtFilter.inf_of_left
+-/
 
+#print MeasureTheory.IntegrableAtFilter.inf_of_right /-
 theorem IntegrableAtFilter.inf_of_right (hl : IntegrableAtFilter f l μ) :
     IntegrableAtFilter f (l' ⊓ l) μ :=
   hl.filter_mono inf_le_right
 #align measure_theory.integrable_at_filter.inf_of_right MeasureTheory.IntegrableAtFilter.inf_of_right
+-/
 
+#print MeasureTheory.IntegrableAtFilter.inf_ae_iff /-
 @[simp]
 theorem IntegrableAtFilter.inf_ae_iff {l : Filter α} :
     IntegrableAtFilter f (l ⊓ μ.ae) μ ↔ IntegrableAtFilter f l μ :=
@@ -450,10 +559,12 @@ theorem IntegrableAtFilter.inf_ae_iff {l : Filter α} :
   refine' measure_mono_ae (mem_of_superset hu fun x hx => _)
   exact fun ⟨hv, ht⟩ => ⟨hv, ⟨ht, hx⟩⟩
 #align measure_theory.integrable_at_filter.inf_ae_iff MeasureTheory.IntegrableAtFilter.inf_ae_iff
+-/
 
 alias integrable_at_filter.inf_ae_iff ↔ integrable_at_filter.of_inf_ae _
 #align measure_theory.integrable_at_filter.of_inf_ae MeasureTheory.IntegrableAtFilter.of_inf_ae
 
+#print MeasureTheory.Measure.FiniteAtFilter.integrableAtFilter /-
 /-- If `μ` is a measure finite at filter `l` and `f` is a function such that its norm is bounded
 above at `l`, then `f` is integrable at `l`. -/
 theorem Measure.FiniteAtFilter.integrableAtFilter {l : Filter α} [IsMeasurablyGenerated l]
@@ -469,28 +580,34 @@ theorem Measure.FiniteAtFilter.integrableAtFilter {l : Filter α} [IsMeasurablyG
   rw [ae_restrict_eq hsm, eventually_inf_principal]
   exact eventually_of_forall hC
 #align measure_theory.measure.finite_at_filter.integrable_at_filter MeasureTheory.Measure.FiniteAtFilter.integrableAtFilter
+-/
 
+#print MeasureTheory.Measure.FiniteAtFilter.integrableAtFilter_of_tendsto_ae /-
 theorem Measure.FiniteAtFilter.integrableAtFilter_of_tendsto_ae {l : Filter α}
     [IsMeasurablyGenerated l] (hfm : StronglyMeasurableAtFilter f l μ) (hμ : μ.FiniteAtFilter l) {b}
     (hf : Tendsto f (l ⊓ μ.ae) (𝓝 b)) : IntegrableAtFilter f l μ :=
   (hμ.inf_of_left.IntegrableAtFilter (hfm.filter_mono inf_le_left)
       hf.norm.isBoundedUnder_le).of_inf_ae
 #align measure_theory.measure.finite_at_filter.integrable_at_filter_of_tendsto_ae MeasureTheory.Measure.FiniteAtFilter.integrableAtFilter_of_tendsto_ae
+-/
 
 alias measure.finite_at_filter.integrable_at_filter_of_tendsto_ae ←
   _root_.filter.tendsto.integrable_at_filter_ae
 #align filter.tendsto.integrable_at_filter_ae Filter.Tendsto.integrableAtFilter_ae
 
+#print MeasureTheory.Measure.FiniteAtFilter.integrableAtFilter_of_tendsto /-
 theorem Measure.FiniteAtFilter.integrableAtFilter_of_tendsto {l : Filter α}
     [IsMeasurablyGenerated l] (hfm : StronglyMeasurableAtFilter f l μ) (hμ : μ.FiniteAtFilter l) {b}
     (hf : Tendsto f l (𝓝 b)) : IntegrableAtFilter f l μ :=
   hμ.IntegrableAtFilter hfm hf.norm.isBoundedUnder_le
 #align measure_theory.measure.finite_at_filter.integrable_at_filter_of_tendsto MeasureTheory.Measure.FiniteAtFilter.integrableAtFilter_of_tendsto
+-/
 
 alias measure.finite_at_filter.integrable_at_filter_of_tendsto ←
   _root_.filter.tendsto.integrable_at_filter
 #align filter.tendsto.integrable_at_filter Filter.Tendsto.integrableAtFilter
 
+#print MeasureTheory.integrable_add_of_disjoint /-
 theorem integrable_add_of_disjoint {f g : α → E} (h : Disjoint (support f) (support g))
     (hf : StronglyMeasurable f) (hg : StronglyMeasurable g) :
     Integrable (f + g) μ ↔ Integrable f μ ∧ Integrable g μ :=
@@ -499,6 +616,7 @@ theorem integrable_add_of_disjoint {f g : α → E} (h : Disjoint (support f) (s
   · rw [← indicator_add_eq_left h]; exact hfg.indicator hf.measurable_set_support
   · rw [← indicator_add_eq_right h]; exact hfg.indicator hg.measurable_set_support
 #align measure_theory.integrable_add_of_disjoint MeasureTheory.integrable_add_of_disjoint
+-/
 
 end NormedAddCommGroup
 
@@ -508,6 +626,7 @@ open MeasureTheory
 
 variable [NormedAddCommGroup E]
 
+#print ContinuousOn.aemeasurable /-
 /-- A function which is continuous on a set `s` is almost everywhere measurable with respect to
 `μ.restrict s`. -/
 theorem ContinuousOn.aemeasurable [TopologicalSpace α] [OpensMeasurableSpace α] [MeasurableSpace β]
@@ -524,7 +643,9 @@ theorem ContinuousOn.aemeasurable [TopologicalSpace α] [OpensMeasurableSpace α
   rw [piecewise_preimage, Set.ite, hu]
   exact (u_open.measurable_set.inter hs).union ((measurable_const ht.measurable_set).diffₓ hs)
 #align continuous_on.ae_measurable ContinuousOn.aemeasurable
+-/
 
+#print ContinuousOn.aestronglyMeasurable_of_isSeparable /-
 /-- A function which is continuous on a separable set `s` is almost everywhere strongly measurable
 with respect to `μ.restrict s`. -/
 theorem ContinuousOn.aestronglyMeasurable_of_isSeparable [TopologicalSpace α]
@@ -539,7 +660,9 @@ theorem ContinuousOn.aestronglyMeasurable_of_isSeparable [TopologicalSpace α]
   refine' ⟨hf.ae_measurable hs, f '' s, hf.is_separable_image h's, _⟩
   exact mem_of_superset (self_mem_ae_restrict hs) (subset_preimage_image _ _)
 #align continuous_on.ae_strongly_measurable_of_is_separable ContinuousOn.aestronglyMeasurable_of_isSeparable
+-/
 
+#print ContinuousOn.aestronglyMeasurable /-
 /-- A function which is continuous on a set `s` is almost everywhere strongly measurable with
 respect to `μ.restrict s` when either the source space or the target space is second-countable. -/
 theorem ContinuousOn.aestronglyMeasurable [TopologicalSpace α] [TopologicalSpace β]
@@ -561,7 +684,9 @@ theorem ContinuousOn.aestronglyMeasurable [TopologicalSpace α] [TopologicalSpac
     simp
   · exact is_separable_of_separable_space _
 #align continuous_on.ae_strongly_measurable ContinuousOn.aestronglyMeasurable
+-/
 
+#print ContinuousOn.aestronglyMeasurable_of_isCompact /-
 /-- A function which is continuous on a compact set `s` is almost everywhere strongly measurable
 with respect to `μ.restrict s`. -/
 theorem ContinuousOn.aestronglyMeasurable_of_isCompact [TopologicalSpace α] [OpensMeasurableSpace α]
@@ -576,7 +701,9 @@ theorem ContinuousOn.aestronglyMeasurable_of_isCompact [TopologicalSpace α] [Op
   · exact (hs.image_of_continuous_on hf).IsSeparable
   · exact mem_of_superset (self_mem_ae_restrict h's) (subset_preimage_image _ _)
 #align continuous_on.ae_strongly_measurable_of_is_compact ContinuousOn.aestronglyMeasurable_of_isCompact
+-/
 
+#print ContinuousOn.integrableAt_nhdsWithin_of_isSeparable /-
 theorem ContinuousOn.integrableAt_nhdsWithin_of_isSeparable [TopologicalSpace α]
     [PseudoMetrizableSpace α] [OpensMeasurableSpace α] {μ : Measure α} [IsLocallyFiniteMeasure μ]
     {a : α} {t : Set α} {f : α → E} (hft : ContinuousOn f t) (ht : MeasurableSet t)
@@ -586,7 +713,9 @@ theorem ContinuousOn.integrableAt_nhdsWithin_of_isSeparable [TopologicalSpace α
     ⟨_, self_mem_nhdsWithin, hft.ae_strongly_measurable_of_is_separable ht h't⟩
     (μ.finite_at_nhds_within _ _)
 #align continuous_on.integrable_at_nhds_within_of_is_separable ContinuousOn.integrableAt_nhdsWithin_of_isSeparable
+-/
 
+#print ContinuousOn.integrableAt_nhdsWithin /-
 theorem ContinuousOn.integrableAt_nhdsWithin [TopologicalSpace α]
     [SecondCountableTopologyEither α E] [OpensMeasurableSpace α] {μ : Measure α}
     [IsLocallyFiniteMeasure μ] {a : α} {t : Set α} {f : α → E} (hft : ContinuousOn f t)
@@ -595,7 +724,9 @@ theorem ContinuousOn.integrableAt_nhdsWithin [TopologicalSpace α]
   (hft a ha).IntegrableAtFilter ⟨_, self_mem_nhdsWithin, hft.ae_strongly_measurable ht⟩
     (μ.finite_at_nhds_within _ _)
 #align continuous_on.integrable_at_nhds_within ContinuousOn.integrableAt_nhdsWithin
+-/
 
+#print Continuous.integrableAt_nhds /-
 theorem Continuous.integrableAt_nhds [TopologicalSpace α] [SecondCountableTopologyEither α E]
     [OpensMeasurableSpace α] {μ : Measure α} [IsLocallyFiniteMeasure μ] {f : α → E}
     (hf : Continuous f) (a : α) : IntegrableAtFilter f (𝓝 a) μ :=
@@ -603,7 +734,9 @@ theorem Continuous.integrableAt_nhds [TopologicalSpace α] [SecondCountableTopol
   rw [← nhdsWithin_univ]
   exact hf.continuous_on.integrable_at_nhds_within MeasurableSet.univ (mem_univ a)
 #align continuous.integrable_at_nhds Continuous.integrableAt_nhds
+-/
 
+#print ContinuousOn.stronglyMeasurableAtFilter /-
 /-- If a function is continuous on an open set `s`, then it is strongly measurable at the filter
 `𝓝 x` for all `x ∈ s` if either the source space or the target space is second-countable. -/
 theorem ContinuousOn.stronglyMeasurableAtFilter [TopologicalSpace α] [OpensMeasurableSpace α]
@@ -612,19 +745,25 @@ theorem ContinuousOn.stronglyMeasurableAtFilter [TopologicalSpace α] [OpensMeas
     ∀ x ∈ s, StronglyMeasurableAtFilter f (𝓝 x) μ := fun x hx =>
   ⟨s, IsOpen.mem_nhds hs hx, hf.AEStronglyMeasurable hs.MeasurableSet⟩
 #align continuous_on.strongly_measurable_at_filter ContinuousOn.stronglyMeasurableAtFilter
+-/
 
+#print ContinuousAt.stronglyMeasurableAtFilter /-
 theorem ContinuousAt.stronglyMeasurableAtFilter [TopologicalSpace α] [OpensMeasurableSpace α]
     [SecondCountableTopologyEither α E] {f : α → E} {s : Set α} {μ : Measure α} (hs : IsOpen s)
     (hf : ∀ x ∈ s, ContinuousAt f x) : ∀ x ∈ s, StronglyMeasurableAtFilter f (𝓝 x) μ :=
   ContinuousOn.stronglyMeasurableAtFilter hs <| ContinuousAt.continuousOn hf
 #align continuous_at.strongly_measurable_at_filter ContinuousAt.stronglyMeasurableAtFilter
+-/
 
+#print Continuous.stronglyMeasurableAtFilter /-
 theorem Continuous.stronglyMeasurableAtFilter [TopologicalSpace α] [OpensMeasurableSpace α]
     [TopologicalSpace β] [PseudoMetrizableSpace β] [SecondCountableTopologyEither α β] {f : α → β}
     (hf : Continuous f) (μ : Measure α) (l : Filter α) : StronglyMeasurableAtFilter f l μ :=
   hf.StronglyMeasurable.StronglyMeasurableAtFilter
 #align continuous.strongly_measurable_at_filter Continuous.stronglyMeasurableAtFilter
+-/
 
+#print ContinuousOn.stronglyMeasurableAtFilter_nhdsWithin /-
 /-- If a function is continuous on a measurable set `s`, then it is measurable at the filter
   `𝓝[s] x` for all `x`. -/
 theorem ContinuousOn.stronglyMeasurableAtFilter_nhdsWithin {α β : Type _} [MeasurableSpace α]
@@ -634,6 +773,7 @@ theorem ContinuousOn.stronglyMeasurableAtFilter_nhdsWithin {α β : Type _} [Mea
     StronglyMeasurableAtFilter f (𝓝[s] x) μ :=
   ⟨s, self_mem_nhdsWithin, hf.AEStronglyMeasurable hs⟩
 #align continuous_on.strongly_measurable_at_filter_nhds_within ContinuousOn.stronglyMeasurableAtFilter_nhdsWithin
+-/
 
 /-! ### Lemmas about adding and removing interval boundaries
 
@@ -646,6 +786,7 @@ section PartialOrder
 
 variable [PartialOrder α] [MeasurableSingletonClass α] {f : α → E} {μ : Measure α} {a b : α}
 
+#print integrableOn_Icc_iff_integrableOn_Ioc' /-
 theorem integrableOn_Icc_iff_integrableOn_Ioc' (ha : μ {a} ≠ ∞) :
     IntegrableOn f (Icc a b) μ ↔ IntegrableOn f (Ioc a b) μ :=
   by
@@ -657,7 +798,9 @@ theorem integrableOn_Icc_iff_integrableOn_Ioc' (ha : μ {a} ≠ ∞) :
     contrapose! hab
     exact hab.le
 #align integrable_on_Icc_iff_integrable_on_Ioc' integrableOn_Icc_iff_integrableOn_Ioc'
+-/
 
+#print integrableOn_Icc_iff_integrableOn_Ico' /-
 theorem integrableOn_Icc_iff_integrableOn_Ico' (hb : μ {b} ≠ ∞) :
     IntegrableOn f (Icc a b) μ ↔ IntegrableOn f (Ico a b) μ :=
   by
@@ -669,7 +812,9 @@ theorem integrableOn_Icc_iff_integrableOn_Ico' (hb : μ {b} ≠ ∞) :
     contrapose! hab
     exact hab.le
 #align integrable_on_Icc_iff_integrable_on_Ico' integrableOn_Icc_iff_integrableOn_Ico'
+-/
 
+#print integrableOn_Ico_iff_integrableOn_Ioo' /-
 theorem integrableOn_Ico_iff_integrableOn_Ioo' (ha : μ {a} ≠ ∞) :
     IntegrableOn f (Ico a b) μ ↔ IntegrableOn f (Ioo a b) μ :=
   by
@@ -679,7 +824,9 @@ theorem integrableOn_Ico_iff_integrableOn_Ioo' (ha : μ {a} ≠ ∞) :
       eq_true (integrable_on_singleton_iff.mpr <| Or.inr ha.lt_top), and_true_iff]
   · rw [Ioo_eq_empty hab, Ico_eq_empty hab]
 #align integrable_on_Ico_iff_integrable_on_Ioo' integrableOn_Ico_iff_integrableOn_Ioo'
+-/
 
+#print integrableOn_Ioc_iff_integrableOn_Ioo' /-
 theorem integrableOn_Ioc_iff_integrableOn_Ioo' (hb : μ {b} ≠ ∞) :
     IntegrableOn f (Ioc a b) μ ↔ IntegrableOn f (Ioo a b) μ :=
   by
@@ -689,60 +836,81 @@ theorem integrableOn_Ioc_iff_integrableOn_Ioo' (hb : μ {b} ≠ ∞) :
       eq_true (integrable_on_singleton_iff.mpr <| Or.inr hb.lt_top), and_true_iff]
   · rw [Ioo_eq_empty hab, Ioc_eq_empty hab]
 #align integrable_on_Ioc_iff_integrable_on_Ioo' integrableOn_Ioc_iff_integrableOn_Ioo'
+-/
 
+#print integrableOn_Icc_iff_integrableOn_Ioo' /-
 theorem integrableOn_Icc_iff_integrableOn_Ioo' (ha : μ {a} ≠ ∞) (hb : μ {b} ≠ ∞) :
     IntegrableOn f (Icc a b) μ ↔ IntegrableOn f (Ioo a b) μ := by
   rw [integrableOn_Icc_iff_integrableOn_Ioc' ha, integrableOn_Ioc_iff_integrableOn_Ioo' hb]
 #align integrable_on_Icc_iff_integrable_on_Ioo' integrableOn_Icc_iff_integrableOn_Ioo'
+-/
 
+#print integrableOn_Ici_iff_integrableOn_Ioi' /-
 theorem integrableOn_Ici_iff_integrableOn_Ioi' (hb : μ {b} ≠ ∞) :
     IntegrableOn f (Ici b) μ ↔ IntegrableOn f (Ioi b) μ := by
   rw [← Ioi_union_left, integrable_on_union,
     eq_true (integrable_on_singleton_iff.mpr <| Or.inr hb.lt_top), and_true_iff]
 #align integrable_on_Ici_iff_integrable_on_Ioi' integrableOn_Ici_iff_integrableOn_Ioi'
+-/
 
+#print integrableOn_Iic_iff_integrableOn_Iio' /-
 theorem integrableOn_Iic_iff_integrableOn_Iio' (hb : μ {b} ≠ ∞) :
     IntegrableOn f (Iic b) μ ↔ IntegrableOn f (Iio b) μ := by
   rw [← Iio_union_right, integrable_on_union,
     eq_true (integrable_on_singleton_iff.mpr <| Or.inr hb.lt_top), and_true_iff]
 #align integrable_on_Iic_iff_integrable_on_Iio' integrableOn_Iic_iff_integrableOn_Iio'
+-/
 
 variable [NoAtoms μ]
 
+#print integrableOn_Icc_iff_integrableOn_Ioc /-
 theorem integrableOn_Icc_iff_integrableOn_Ioc :
     IntegrableOn f (Icc a b) μ ↔ IntegrableOn f (Ioc a b) μ :=
   integrableOn_Icc_iff_integrableOn_Ioc' (by rw [measure_singleton]; exact ENNReal.zero_ne_top)
 #align integrable_on_Icc_iff_integrable_on_Ioc integrableOn_Icc_iff_integrableOn_Ioc
+-/
 
+#print integrableOn_Icc_iff_integrableOn_Ico /-
 theorem integrableOn_Icc_iff_integrableOn_Ico :
     IntegrableOn f (Icc a b) μ ↔ IntegrableOn f (Ico a b) μ :=
   integrableOn_Icc_iff_integrableOn_Ico' (by rw [measure_singleton]; exact ENNReal.zero_ne_top)
 #align integrable_on_Icc_iff_integrable_on_Ico integrableOn_Icc_iff_integrableOn_Ico
+-/
 
+#print integrableOn_Ico_iff_integrableOn_Ioo /-
 theorem integrableOn_Ico_iff_integrableOn_Ioo :
     IntegrableOn f (Ico a b) μ ↔ IntegrableOn f (Ioo a b) μ :=
   integrableOn_Ico_iff_integrableOn_Ioo' (by rw [measure_singleton]; exact ENNReal.zero_ne_top)
 #align integrable_on_Ico_iff_integrable_on_Ioo integrableOn_Ico_iff_integrableOn_Ioo
+-/
 
+#print integrableOn_Ioc_iff_integrableOn_Ioo /-
 theorem integrableOn_Ioc_iff_integrableOn_Ioo :
     IntegrableOn f (Ioc a b) μ ↔ IntegrableOn f (Ioo a b) μ :=
   integrableOn_Ioc_iff_integrableOn_Ioo' (by rw [measure_singleton]; exact ENNReal.zero_ne_top)
 #align integrable_on_Ioc_iff_integrable_on_Ioo integrableOn_Ioc_iff_integrableOn_Ioo
+-/
 
+#print integrableOn_Icc_iff_integrableOn_Ioo /-
 theorem integrableOn_Icc_iff_integrableOn_Ioo :
     IntegrableOn f (Icc a b) μ ↔ IntegrableOn f (Ioo a b) μ := by
   rw [integrableOn_Icc_iff_integrableOn_Ioc, integrableOn_Ioc_iff_integrableOn_Ioo]
 #align integrable_on_Icc_iff_integrable_on_Ioo integrableOn_Icc_iff_integrableOn_Ioo
+-/
 
+#print integrableOn_Ici_iff_integrableOn_Ioi /-
 theorem integrableOn_Ici_iff_integrableOn_Ioi :
     IntegrableOn f (Ici b) μ ↔ IntegrableOn f (Ioi b) μ :=
   integrableOn_Ici_iff_integrableOn_Ioi' (by rw [measure_singleton]; exact ENNReal.zero_ne_top)
 #align integrable_on_Ici_iff_integrable_on_Ioi integrableOn_Ici_iff_integrableOn_Ioi
+-/
 
+#print integrableOn_Iic_iff_integrableOn_Iio /-
 theorem integrableOn_Iic_iff_integrableOn_Iio :
     IntegrableOn f (Iic b) μ ↔ IntegrableOn f (Iio b) μ :=
   integrableOn_Iic_iff_integrableOn_Iio' (by rw [measure_singleton]; exact ENNReal.zero_ne_top)
 #align integrable_on_Iic_iff_integrable_on_Iio integrableOn_Iic_iff_integrableOn_Iio
+-/
 
 end PartialOrder
 

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

@@ -388,14 +388,14 @@ theorem integrableOn_Lp_of_measure_ne_top {E} [NormedAddCommGroup E] {p : ℝ≥
 #align measure_theory.integrable_on_Lp_of_measure_ne_top MeasureTheory.integrableOn_Lp_of_measure_ne_top
 
 theorem Integrable.lintegral_lt_top {f : α → ℝ} (hf : Integrable f μ) :
-    (∫⁻ x, ENNReal.ofReal (f x) ∂μ) < ∞ :=
+    ∫⁻ x, ENNReal.ofReal (f x) ∂μ < ∞ :=
   calc
-    (∫⁻ x, ENNReal.ofReal (f x) ∂μ) ≤ ∫⁻ x, ↑‖f x‖₊ ∂μ := lintegral_ofReal_le_lintegral_nnnorm f
+    ∫⁻ x, ENNReal.ofReal (f x) ∂μ ≤ ∫⁻ x, ↑‖f x‖₊ ∂μ := lintegral_ofReal_le_lintegral_nnnorm f
     _ < ∞ := hf.2
 #align measure_theory.integrable.lintegral_lt_top MeasureTheory.Integrable.lintegral_lt_top
 
 theorem IntegrableOn.set_lintegral_lt_top {f : α → ℝ} {s : Set α} (hf : IntegrableOn f s μ) :
-    (∫⁻ x in s, ENNReal.ofReal (f x) ∂μ) < ∞ :=
+    ∫⁻ x in s, ENNReal.ofReal (f x) ∂μ < ∞ :=
   Integrable.lintegral_lt_top hf
 #align measure_theory.integrable_on.set_lintegral_lt_top MeasureTheory.IntegrableOn.set_lintegral_lt_top
 

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

@@ -392,7 +392,6 @@ theorem Integrable.lintegral_lt_top {f : α → ℝ} (hf : Integrable f μ) :
   calc
     (∫⁻ x, ENNReal.ofReal (f x) ∂μ) ≤ ∫⁻ x, ↑‖f x‖₊ ∂μ := lintegral_ofReal_le_lintegral_nnnorm f
     _ < ∞ := hf.2
-    
 #align measure_theory.integrable.lintegral_lt_top MeasureTheory.Integrable.lintegral_lt_top
 
 theorem IntegrableOn.set_lintegral_lt_top {f : α → ℝ} {s : Set α} (hf : IntegrableOn f s μ) :

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

@@ -360,7 +360,7 @@ theorem IntegrableOn.integrable_of_ae_not_mem_eq_zero (hf : IntegrableOn f s μ)
   filter_upwards [h't] with x hx h'x using hx h'x.2
 #align measure_theory.integrable_on.integrable_of_ae_not_mem_eq_zero MeasureTheory.IntegrableOn.integrable_of_ae_not_mem_eq_zero
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x «expr ∉ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (x «expr ∉ » s) -/
 /-- If a function is integrable on a set `s` and vanishes everywhere on its complement,
 then it is integrable. -/
 theorem IntegrableOn.integrable_of_forall_not_mem_eq_zero (hf : IntegrableOn f s μ)

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

@@ -200,7 +200,7 @@ theorem integrableOn_singleton_iff {x : α} [MeasurableSingletonClass α] :
   by
   have : f =ᵐ[μ.restrict {x}] fun y => f x :=
     by
-    filter_upwards [ae_restrict_mem (measurable_set_singleton x)]with _ ha
+    filter_upwards [ae_restrict_mem (measurable_set_singleton x)] with _ ha
     simp only [mem_singleton_iff.1 ha]
   rw [integrable_on, integrable_congr this, integrable_const_iff]
   simp
@@ -302,7 +302,7 @@ theorem IntegrableOn.restrict_toMeasurable (hf : IntegrableOn f s μ) (h's : ∀
     μ.restrict (toMeasurable μ s) = μ.restrict s :=
   by
   rcases exists_seq_strictAnti_tendsto (0 : ℝ) with ⟨u, u_anti, u_pos, u_lim⟩
-  let v n := to_measurable (μ.restrict s) { x | u n ≤ ‖f x‖ }
+  let v n := to_measurable (μ.restrict s) {x | u n ≤ ‖f x‖}
   have A : ∀ n, μ (s ∩ v n) ≠ ∞ := by
     intro n
     rw [inter_comm, ← measure.restrict_apply (measurable_set_to_measurable _ _),
@@ -321,7 +321,7 @@ if `t` is null-measurable. -/
 theorem IntegrableOn.of_ae_diff_eq_zero (hf : IntegrableOn f s μ) (ht : NullMeasurableSet t μ)
     (h't : ∀ᵐ x ∂μ, x ∈ t \ s → f x = 0) : IntegrableOn f t μ :=
   by
-  let u := { x ∈ s | f x ≠ 0 }
+  let u := {x ∈ s | f x ≠ 0}
   have hu : integrable_on f u μ := hf.mono_set fun x hx => hx.1
   let v := to_measurable μ u
   have A : integrable_on f v μ :=
@@ -333,7 +333,7 @@ theorem IntegrableOn.of_ae_diff_eq_zero (hf : IntegrableOn f s μ) (ht : NullMea
     by
     apply integrable_on_zero.congr
     filter_upwards [ae_restrict_of_ae h't,
-      ae_restrict_mem₀ (ht.diff (measurable_set_to_measurable μ u).NullMeasurableSet)]with x hxt hx
+      ae_restrict_mem₀ (ht.diff (measurable_set_to_measurable μ u).NullMeasurableSet)] with x hxt hx
     by_cases h'x : x ∈ s
     · by_contra H
       exact hx.2 (subset_to_measurable μ u ⟨h'x, Ne.symm H⟩)
@@ -357,7 +357,7 @@ theorem IntegrableOn.integrable_of_ae_not_mem_eq_zero (hf : IntegrableOn f s μ)
   by
   rw [← integrable_on_univ]
   apply hf.of_ae_diff_eq_zero null_measurable_set_univ
-  filter_upwards [h't]with x hx h'x using hx h'x.2
+  filter_upwards [h't] with x hx h'x using hx h'x.2
 #align measure_theory.integrable_on.integrable_of_ae_not_mem_eq_zero MeasureTheory.IntegrableOn.integrable_of_ae_not_mem_eq_zero
 
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x «expr ∉ » s) -/
@@ -579,7 +579,7 @@ theorem ContinuousOn.aestronglyMeasurable_of_isCompact [TopologicalSpace α] [Op
 #align continuous_on.ae_strongly_measurable_of_is_compact ContinuousOn.aestronglyMeasurable_of_isCompact
 
 theorem ContinuousOn.integrableAt_nhdsWithin_of_isSeparable [TopologicalSpace α]
-    [PseudoMetrizableSpace α] [OpensMeasurableSpace α] {μ : Measure α} [LocallyFiniteMeasure μ]
+    [PseudoMetrizableSpace α] [OpensMeasurableSpace α] {μ : Measure α} [IsLocallyFiniteMeasure μ]
     {a : α} {t : Set α} {f : α → E} (hft : ContinuousOn f t) (ht : MeasurableSet t)
     (h't : TopologicalSpace.IsSeparable t) (ha : a ∈ t) : IntegrableAtFilter f (𝓝[t] a) μ :=
   haveI : (𝓝[t] a).IsMeasurablyGenerated := ht.nhds_within_is_measurably_generated _
@@ -590,7 +590,7 @@ theorem ContinuousOn.integrableAt_nhdsWithin_of_isSeparable [TopologicalSpace α
 
 theorem ContinuousOn.integrableAt_nhdsWithin [TopologicalSpace α]
     [SecondCountableTopologyEither α E] [OpensMeasurableSpace α] {μ : Measure α}
-    [LocallyFiniteMeasure μ] {a : α} {t : Set α} {f : α → E} (hft : ContinuousOn f t)
+    [IsLocallyFiniteMeasure μ] {a : α} {t : Set α} {f : α → E} (hft : ContinuousOn f t)
     (ht : MeasurableSet t) (ha : a ∈ t) : IntegrableAtFilter f (𝓝[t] a) μ :=
   haveI : (𝓝[t] a).IsMeasurablyGenerated := ht.nhds_within_is_measurably_generated _
   (hft a ha).IntegrableAtFilter ⟨_, self_mem_nhdsWithin, hft.ae_strongly_measurable ht⟩
@@ -598,7 +598,7 @@ theorem ContinuousOn.integrableAt_nhdsWithin [TopologicalSpace α]
 #align continuous_on.integrable_at_nhds_within ContinuousOn.integrableAt_nhdsWithin
 
 theorem Continuous.integrableAt_nhds [TopologicalSpace α] [SecondCountableTopologyEither α E]
-    [OpensMeasurableSpace α] {μ : Measure α} [LocallyFiniteMeasure μ] {f : α → E}
+    [OpensMeasurableSpace α] {μ : Measure α} [IsLocallyFiniteMeasure μ] {f : α → E}
     (hf : Continuous f) (a : α) : IntegrableAtFilter f (𝓝 a) μ :=
   by
   rw [← nhdsWithin_univ]

mathlib commit https://github.com/leanprover-community/mathlib/commit/34ebaffc1d1e8e783fc05438ec2e70af87275ac9

@@ -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.integrable_on
-! leanprover-community/mathlib commit 8b8ba04e2f326f3f7cf24ad129beda58531ada61
+! leanprover-community/mathlib commit 599fffe78f0e11eb6a034e834ec51882167b9688
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -13,6 +13,9 @@ import Mathbin.Analysis.NormedSpace.IndicatorFunction
 
 /-! # Functions integrable on a set and at a filter
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 We define `integrable_on f s μ := integrable f (μ.restrict s)` and prove theorems like
 `integrable_on_union : integrable_on f (s ∪ t) μ ↔ integrable_on f s μ ∧ integrable_on f t μ`.
 

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

@@ -36,17 +36,19 @@ section
 
 variable [TopologicalSpace β] {l l' : Filter α} {f g : α → β} {μ ν : Measure α}
 
+#print StronglyMeasurableAtFilter /-
 /-- A function `f` is strongly measurable at a filter `l` w.r.t. a measure `μ` if it is
 ae strongly measurable w.r.t. `μ.restrict s` for some `s ∈ l`. -/
 def StronglyMeasurableAtFilter (f : α → β) (l : Filter α)
     (μ : Measure α := by exact MeasureTheory.MeasureSpace.volume) :=
   ∃ s ∈ l, AEStronglyMeasurable f (μ.restrict s)
 #align strongly_measurable_at_filter StronglyMeasurableAtFilter
+-/
 
 @[simp]
-theorem strongly_measurable_at_bot {f : α → β} : StronglyMeasurableAtFilter f ⊥ μ :=
+theorem stronglyMeasurableAt_bot {f : α → β} : StronglyMeasurableAtFilter f ⊥ μ :=
   ⟨∅, mem_bot, by simp⟩
-#align strongly_measurable_at_bot strongly_measurable_at_bot
+#align strongly_measurable_at_bot stronglyMeasurableAt_bot
 
 protected theorem StronglyMeasurableAtFilter.eventually (h : StronglyMeasurableAtFilter f l μ) :
     ∀ᶠ s in l.smallSets, AEStronglyMeasurable f (μ.restrict s) :=
@@ -89,12 +91,14 @@ theorem hasFiniteIntegral_restrict_of_bounded [NormedAddCommGroup E] {f : α →
 
 variable [NormedAddCommGroup E] {f g : α → E} {s t : Set α} {μ ν : Measure α}
 
+#print MeasureTheory.IntegrableOn /-
 /-- A function is `integrable_on` a set `s` if it is almost everywhere strongly measurable on `s`
 and if the integral of its pointwise norm over `s` is less than infinity. -/
 def IntegrableOn (f : α → E) (s : Set α)
     (μ : Measure α := by exact MeasureTheory.MeasureSpace.volume) : Prop :=
   Integrable f (μ.restrict s)
 #align measure_theory.integrable_on MeasureTheory.IntegrableOn
+-/
 
 theorem IntegrableOn.integrable (h : IntegrableOn f s μ) : Integrable f (μ.restrict s) :=
   h
@@ -158,9 +162,11 @@ theorem integrableOn_congr_fun (hst : EqOn f g s) (hs : MeasurableSet s) :
   ⟨fun h => h.congr_fun hst hs, fun h => h.congr_fun hst.symm hs⟩
 #align measure_theory.integrable_on_congr_fun MeasureTheory.integrableOn_congr_fun
 
+#print MeasureTheory.Integrable.integrableOn /-
 theorem Integrable.integrableOn (h : Integrable f μ) : IntegrableOn f s μ :=
   h.mono_measure <| Measure.restrict_le_self
 #align measure_theory.integrable.integrable_on MeasureTheory.Integrable.integrableOn
+-/
 
 theorem IntegrableOn.restrict (h : IntegrableOn f s μ) (hs : MeasurableSet s) :
     IntegrableOn f s (μ.restrict t) := by rw [integrable_on, measure.restrict_restrict hs];
@@ -198,18 +204,18 @@ theorem integrableOn_singleton_iff {x : α} [MeasurableSingletonClass α] :
 #align measure_theory.integrable_on_singleton_iff MeasureTheory.integrableOn_singleton_iff
 
 @[simp]
-theorem integrableOn_finite_bUnion {s : Set β} (hs : s.Finite) {t : β → Set α} :
+theorem integrableOn_finite_biUnion {s : Set β} (hs : s.Finite) {t : β → Set α} :
     IntegrableOn f (⋃ i ∈ s, t i) μ ↔ ∀ i ∈ s, IntegrableOn f (t i) μ :=
   by
   apply hs.induction_on
   · simp
   · intro a s ha hs hf; simp [hf, or_imp, forall_and]
-#align measure_theory.integrable_on_finite_bUnion MeasureTheory.integrableOn_finite_bUnion
+#align measure_theory.integrable_on_finite_bUnion MeasureTheory.integrableOn_finite_biUnion
 
 @[simp]
 theorem integrableOn_finset_iUnion {s : Finset β} {t : β → Set α} :
     IntegrableOn f (⋃ i ∈ s, t i) μ ↔ ∀ i ∈ s, IntegrableOn f (t i) μ :=
-  integrableOn_finite_bUnion s.finite_toSet
+  integrableOn_finite_biUnion s.finite_toSet
 #align measure_theory.integrable_on_finset_Union MeasureTheory.integrableOn_finset_iUnion
 
 @[simp]
@@ -368,15 +374,15 @@ theorem integrableOn_iff_integrable_of_support_subset (h1s : support f ⊆ s) :
   exact h1s (mem_support.2 hx)
 #align measure_theory.integrable_on_iff_integrable_of_support_subset MeasureTheory.integrableOn_iff_integrable_of_support_subset
 
-theorem integrableOn_lp_of_measure_ne_top {E} [NormedAddCommGroup E] {p : ℝ≥0∞} {s : Set α}
-    (f : lp E p μ) (hp : 1 ≤ p) (hμs : μ s ≠ ∞) : IntegrableOn f s μ :=
+theorem integrableOn_Lp_of_measure_ne_top {E} [NormedAddCommGroup E] {p : ℝ≥0∞} {s : Set α}
+    (f : Lp E p μ) (hp : 1 ≤ p) (hμs : μ s ≠ ∞) : IntegrableOn f s μ :=
   by
   refine' mem_ℒp_one_iff_integrable.mp _
   have hμ_restrict_univ : (μ.restrict s) Set.univ < ∞ := by
     simpa only [Set.univ_inter, MeasurableSet.univ, measure.restrict_apply, lt_top_iff_ne_top]
   haveI hμ_finite : is_finite_measure (μ.restrict s) := ⟨hμ_restrict_univ⟩
   exact ((Lp.mem_ℒp _).restrict s).memℒp_of_exponent_le hp
-#align measure_theory.integrable_on_Lp_of_measure_ne_top MeasureTheory.integrableOn_lp_of_measure_ne_top
+#align measure_theory.integrable_on_Lp_of_measure_ne_top MeasureTheory.integrableOn_Lp_of_measure_ne_top
 
 theorem Integrable.lintegral_lt_top {f : α → ℝ} (hf : Integrable f μ) :
     (∫⁻ x, ENNReal.ofReal (f x) ∂μ) < ∞ :=
@@ -391,19 +397,23 @@ theorem IntegrableOn.set_lintegral_lt_top {f : α → ℝ} {s : Set α} (hf : In
   Integrable.lintegral_lt_top hf
 #align measure_theory.integrable_on.set_lintegral_lt_top MeasureTheory.IntegrableOn.set_lintegral_lt_top
 
+#print MeasureTheory.IntegrableAtFilter /-
 /-- We say that a function `f` is *integrable at filter* `l` if it is integrable on some
 set `s ∈ l`. Equivalently, it is eventually integrable on `s` in `l.small_sets`. -/
 def IntegrableAtFilter (f : α → E) (l : Filter α)
     (μ : Measure α := by exact MeasureTheory.MeasureSpace.volume) :=
   ∃ s ∈ l, IntegrableOn f s μ
 #align measure_theory.integrable_at_filter MeasureTheory.IntegrableAtFilter
+-/
 
 variable {l l' : Filter α}
 
+#print MeasureTheory.Integrable.integrableAtFilter /-
 theorem Integrable.integrableAtFilter (h : Integrable f μ) (l : Filter α) :
     IntegrableAtFilter f l μ :=
   ⟨univ, Filter.univ_mem, integrableOn_univ.2 h⟩
 #align measure_theory.integrable.integrable_at_filter MeasureTheory.Integrable.integrableAtFilter
+-/
 
 protected theorem IntegrableAtFilter.eventually (h : IntegrableAtFilter f l μ) :
     ∀ᶠ s in l.smallSets, IntegrableOn f s μ :=
@@ -498,7 +508,7 @@ variable [NormedAddCommGroup E]
 
 /-- A function which is continuous on a set `s` is almost everywhere measurable with respect to
 `μ.restrict s`. -/
-theorem ContinuousOn.aEMeasurable [TopologicalSpace α] [OpensMeasurableSpace α] [MeasurableSpace β]
+theorem ContinuousOn.aemeasurable [TopologicalSpace α] [OpensMeasurableSpace α] [MeasurableSpace β]
     [TopologicalSpace β] [BorelSpace β] {f : α → β} {s : Set α} {μ : Measure α}
     (hf : ContinuousOn f s) (hs : MeasurableSet s) : AEMeasurable f (μ.restrict s) :=
   by
@@ -511,11 +521,11 @@ theorem ContinuousOn.aEMeasurable [TopologicalSpace α] [OpensMeasurableSpace α
     _root_.continuous_on_iff'.1 hf t ht
   rw [piecewise_preimage, Set.ite, hu]
   exact (u_open.measurable_set.inter hs).union ((measurable_const ht.measurable_set).diffₓ hs)
-#align continuous_on.ae_measurable ContinuousOn.aEMeasurable
+#align continuous_on.ae_measurable ContinuousOn.aemeasurable
 
 /-- A function which is continuous on a separable set `s` is almost everywhere strongly measurable
 with respect to `μ.restrict s`. -/
-theorem ContinuousOn.aEStronglyMeasurable_of_isSeparable [TopologicalSpace α]
+theorem ContinuousOn.aestronglyMeasurable_of_isSeparable [TopologicalSpace α]
     [PseudoMetrizableSpace α] [OpensMeasurableSpace α] [TopologicalSpace β]
     [PseudoMetrizableSpace β] {f : α → β} {s : Set α} {μ : Measure α} (hf : ContinuousOn f s)
     (hs : MeasurableSet s) (h's : TopologicalSpace.IsSeparable s) :
@@ -526,11 +536,11 @@ theorem ContinuousOn.aEStronglyMeasurable_of_isSeparable [TopologicalSpace α]
   rw [aestronglyMeasurable_iff_aemeasurable_separable]
   refine' ⟨hf.ae_measurable hs, f '' s, hf.is_separable_image h's, _⟩
   exact mem_of_superset (self_mem_ae_restrict hs) (subset_preimage_image _ _)
-#align continuous_on.ae_strongly_measurable_of_is_separable ContinuousOn.aEStronglyMeasurable_of_isSeparable
+#align continuous_on.ae_strongly_measurable_of_is_separable ContinuousOn.aestronglyMeasurable_of_isSeparable
 
 /-- A function which is continuous on a set `s` is almost everywhere strongly measurable with
 respect to `μ.restrict s` when either the source space or the target space is second-countable. -/
-theorem ContinuousOn.aEStronglyMeasurable [TopologicalSpace α] [TopologicalSpace β]
+theorem ContinuousOn.aestronglyMeasurable [TopologicalSpace α] [TopologicalSpace β]
     [h : SecondCountableTopologyEither α β] [OpensMeasurableSpace α] [PseudoMetrizableSpace β]
     {f : α → β} {s : Set α} {μ : Measure α} (hf : ContinuousOn f s) (hs : MeasurableSet s) :
     AEStronglyMeasurable f (μ.restrict s) :=
@@ -548,11 +558,11 @@ theorem ContinuousOn.aEStronglyMeasurable [TopologicalSpace α] [TopologicalSpac
     ext x
     simp
   · exact is_separable_of_separable_space _
-#align continuous_on.ae_strongly_measurable ContinuousOn.aEStronglyMeasurable
+#align continuous_on.ae_strongly_measurable ContinuousOn.aestronglyMeasurable
 
 /-- A function which is continuous on a compact set `s` is almost everywhere strongly measurable
 with respect to `μ.restrict s`. -/
-theorem ContinuousOn.aEStronglyMeasurable_of_isCompact [TopologicalSpace α] [OpensMeasurableSpace α]
+theorem ContinuousOn.aestronglyMeasurable_of_isCompact [TopologicalSpace α] [OpensMeasurableSpace α]
     [TopologicalSpace β] [PseudoMetrizableSpace β] {f : α → β} {s : Set α} {μ : Measure α}
     (hf : ContinuousOn f s) (hs : IsCompact s) (h's : MeasurableSet s) :
     AEStronglyMeasurable f (μ.restrict s) :=
@@ -563,9 +573,9 @@ theorem ContinuousOn.aEStronglyMeasurable_of_isCompact [TopologicalSpace α] [Op
   refine' ⟨hf.ae_measurable h's, f '' s, _, _⟩
   · exact (hs.image_of_continuous_on hf).IsSeparable
   · exact mem_of_superset (self_mem_ae_restrict h's) (subset_preimage_image _ _)
-#align continuous_on.ae_strongly_measurable_of_is_compact ContinuousOn.aEStronglyMeasurable_of_isCompact
+#align continuous_on.ae_strongly_measurable_of_is_compact ContinuousOn.aestronglyMeasurable_of_isCompact
 
-theorem ContinuousOn.integrable_at_nhdsWithin_of_isSeparable [TopologicalSpace α]
+theorem ContinuousOn.integrableAt_nhdsWithin_of_isSeparable [TopologicalSpace α]
     [PseudoMetrizableSpace α] [OpensMeasurableSpace α] {μ : Measure α} [LocallyFiniteMeasure μ]
     {a : α} {t : Set α} {f : α → E} (hft : ContinuousOn f t) (ht : MeasurableSet t)
     (h't : TopologicalSpace.IsSeparable t) (ha : a ∈ t) : IntegrableAtFilter f (𝓝[t] a) μ :=
@@ -573,24 +583,24 @@ theorem ContinuousOn.integrable_at_nhdsWithin_of_isSeparable [TopologicalSpace 
   (hft a ha).IntegrableAtFilter
     ⟨_, self_mem_nhdsWithin, hft.ae_strongly_measurable_of_is_separable ht h't⟩
     (μ.finite_at_nhds_within _ _)
-#align continuous_on.integrable_at_nhds_within_of_is_separable ContinuousOn.integrable_at_nhdsWithin_of_isSeparable
+#align continuous_on.integrable_at_nhds_within_of_is_separable ContinuousOn.integrableAt_nhdsWithin_of_isSeparable
 
-theorem ContinuousOn.integrable_at_nhdsWithin [TopologicalSpace α]
+theorem ContinuousOn.integrableAt_nhdsWithin [TopologicalSpace α]
     [SecondCountableTopologyEither α E] [OpensMeasurableSpace α] {μ : Measure α}
     [LocallyFiniteMeasure μ] {a : α} {t : Set α} {f : α → E} (hft : ContinuousOn f t)
     (ht : MeasurableSet t) (ha : a ∈ t) : IntegrableAtFilter f (𝓝[t] a) μ :=
   haveI : (𝓝[t] a).IsMeasurablyGenerated := ht.nhds_within_is_measurably_generated _
   (hft a ha).IntegrableAtFilter ⟨_, self_mem_nhdsWithin, hft.ae_strongly_measurable ht⟩
     (μ.finite_at_nhds_within _ _)
-#align continuous_on.integrable_at_nhds_within ContinuousOn.integrable_at_nhdsWithin
+#align continuous_on.integrable_at_nhds_within ContinuousOn.integrableAt_nhdsWithin
 
-theorem Continuous.integrable_at_nhds [TopologicalSpace α] [SecondCountableTopologyEither α E]
+theorem Continuous.integrableAt_nhds [TopologicalSpace α] [SecondCountableTopologyEither α E]
     [OpensMeasurableSpace α] {μ : Measure α} [LocallyFiniteMeasure μ] {f : α → E}
     (hf : Continuous f) (a : α) : IntegrableAtFilter f (𝓝 a) μ :=
   by
   rw [← nhdsWithin_univ]
   exact hf.continuous_on.integrable_at_nhds_within MeasurableSet.univ (mem_univ a)
-#align continuous.integrable_at_nhds Continuous.integrable_at_nhds
+#align continuous.integrable_at_nhds Continuous.integrableAt_nhds
 
 /-- If a function is continuous on an open set `s`, then it is strongly measurable at the filter
 `𝓝 x` for all `x ∈ s` if either the source space or the target space is second-countable. -/

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

@@ -28,7 +28,7 @@ noncomputable section
 
 open Set Filter TopologicalSpace MeasureTheory Function
 
-open Classical Topology Interval BigOperators Filter ENNReal MeasureTheory
+open scoped Classical Topology Interval BigOperators Filter ENNReal MeasureTheory
 
 variable {α β E F : Type _} [MeasurableSpace α]
 

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

@@ -163,9 +163,7 @@ theorem Integrable.integrableOn (h : Integrable f μ) : IntegrableOn f s μ :=
 #align measure_theory.integrable.integrable_on MeasureTheory.Integrable.integrableOn
 
 theorem IntegrableOn.restrict (h : IntegrableOn f s μ) (hs : MeasurableSet s) :
-    IntegrableOn f s (μ.restrict t) :=
-  by
-  rw [integrable_on, measure.restrict_restrict hs]
+    IntegrableOn f s (μ.restrict t) := by rw [integrable_on, measure.restrict_restrict hs];
   exact h.mono_set (inter_subset_left _ _)
 #align measure_theory.integrable_on.restrict MeasureTheory.IntegrableOn.restrict
 
@@ -205,8 +203,7 @@ theorem integrableOn_finite_bUnion {s : Set β} (hs : s.Finite) {t : β → Set
   by
   apply hs.induction_on
   · simp
-  · intro a s ha hs hf
-    simp [hf, or_imp, forall_and]
+  · intro a s ha hs hf; simp [hf, or_imp, forall_and]
 #align measure_theory.integrable_on_finite_bUnion MeasureTheory.integrableOn_finite_bUnion
 
 @[simp]
@@ -224,9 +221,7 @@ theorem integrableOn_finite_iUnion [Finite β] {t : β → Set α} :
 #align measure_theory.integrable_on_finite_Union MeasureTheory.integrableOn_finite_iUnion
 
 theorem IntegrableOn.add_measure (hμ : IntegrableOn f s μ) (hν : IntegrableOn f s ν) :
-    IntegrableOn f s (μ + ν) := by
-  delta integrable_on
-  rw [measure.restrict_add]
+    IntegrableOn f s (μ + ν) := by delta integrable_on; rw [measure.restrict_add];
   exact hμ.integrable.add_measure hν
 #align measure_theory.integrable_on.add_measure MeasureTheory.IntegrableOn.add_measure
 
@@ -307,8 +302,7 @@ theorem IntegrableOn.restrict_toMeasurable (hf : IntegrableOn f s μ) (h's : ∀
   apply measure.restrict_to_measurable_of_cover _ A
   intro x hx
   have : 0 < ‖f x‖ := by simp only [h's x hx, norm_pos_iff, Ne.def, not_false_iff]
-  obtain ⟨n, hn⟩ : ∃ n, u n < ‖f x‖
-  exact ((tendsto_order.1 u_lim).2 _ this).exists
+  obtain ⟨n, hn⟩ : ∃ n, u n < ‖f x‖; exact ((tendsto_order.1 u_lim).2 _ this).exists
   refine' mem_Union.2 ⟨n, _⟩
   exact subset_to_measurable _ _ hn.le
 #align measure_theory.integrable_on.restrict_to_measurable MeasureTheory.IntegrableOn.restrict_toMeasurable
@@ -325,8 +319,7 @@ theorem IntegrableOn.of_ae_diff_eq_zero (hf : IntegrableOn f s μ) (ht : NullMea
     by
     rw [integrable_on, hu.restrict_to_measurable]
     · exact hu
-    · intro x hx
-      exact hx.2
+    · intro x hx; exact hx.2
   have B : integrable_on f (t \ v) μ :=
     by
     apply integrable_on_zero.congr
@@ -491,10 +484,8 @@ theorem integrable_add_of_disjoint {f g : α → E} (h : Disjoint (support f) (s
     Integrable (f + g) μ ↔ Integrable f μ ∧ Integrable g μ :=
   by
   refine' ⟨fun hfg => ⟨_, _⟩, fun h => h.1.add h.2⟩
-  · rw [← indicator_add_eq_left h]
-    exact hfg.indicator hf.measurable_set_support
-  · rw [← indicator_add_eq_right h]
-    exact hfg.indicator hg.measurable_set_support
+  · rw [← indicator_add_eq_left h]; exact hfg.indicator hf.measurable_set_support
+  · rw [← indicator_add_eq_right h]; exact hfg.indicator hg.measurable_set_support
 #align measure_theory.integrable_add_of_disjoint MeasureTheory.integrable_add_of_disjoint
 
 end NormedAddCommGroup
@@ -708,34 +699,22 @@ variable [NoAtoms μ]
 
 theorem integrableOn_Icc_iff_integrableOn_Ioc :
     IntegrableOn f (Icc a b) μ ↔ IntegrableOn f (Ioc a b) μ :=
-  integrableOn_Icc_iff_integrableOn_Ioc'
-    (by
-      rw [measure_singleton]
-      exact ENNReal.zero_ne_top)
+  integrableOn_Icc_iff_integrableOn_Ioc' (by rw [measure_singleton]; exact ENNReal.zero_ne_top)
 #align integrable_on_Icc_iff_integrable_on_Ioc integrableOn_Icc_iff_integrableOn_Ioc
 
 theorem integrableOn_Icc_iff_integrableOn_Ico :
     IntegrableOn f (Icc a b) μ ↔ IntegrableOn f (Ico a b) μ :=
-  integrableOn_Icc_iff_integrableOn_Ico'
-    (by
-      rw [measure_singleton]
-      exact ENNReal.zero_ne_top)
+  integrableOn_Icc_iff_integrableOn_Ico' (by rw [measure_singleton]; exact ENNReal.zero_ne_top)
 #align integrable_on_Icc_iff_integrable_on_Ico integrableOn_Icc_iff_integrableOn_Ico
 
 theorem integrableOn_Ico_iff_integrableOn_Ioo :
     IntegrableOn f (Ico a b) μ ↔ IntegrableOn f (Ioo a b) μ :=
-  integrableOn_Ico_iff_integrableOn_Ioo'
-    (by
-      rw [measure_singleton]
-      exact ENNReal.zero_ne_top)
+  integrableOn_Ico_iff_integrableOn_Ioo' (by rw [measure_singleton]; exact ENNReal.zero_ne_top)
 #align integrable_on_Ico_iff_integrable_on_Ioo integrableOn_Ico_iff_integrableOn_Ioo
 
 theorem integrableOn_Ioc_iff_integrableOn_Ioo :
     IntegrableOn f (Ioc a b) μ ↔ IntegrableOn f (Ioo a b) μ :=
-  integrableOn_Ioc_iff_integrableOn_Ioo'
-    (by
-      rw [measure_singleton]
-      exact ENNReal.zero_ne_top)
+  integrableOn_Ioc_iff_integrableOn_Ioo' (by rw [measure_singleton]; exact ENNReal.zero_ne_top)
 #align integrable_on_Ioc_iff_integrable_on_Ioo integrableOn_Ioc_iff_integrableOn_Ioo
 
 theorem integrableOn_Icc_iff_integrableOn_Ioo :
@@ -745,18 +724,12 @@ theorem integrableOn_Icc_iff_integrableOn_Ioo :
 
 theorem integrableOn_Ici_iff_integrableOn_Ioi :
     IntegrableOn f (Ici b) μ ↔ IntegrableOn f (Ioi b) μ :=
-  integrableOn_Ici_iff_integrableOn_Ioi'
-    (by
-      rw [measure_singleton]
-      exact ENNReal.zero_ne_top)
+  integrableOn_Ici_iff_integrableOn_Ioi' (by rw [measure_singleton]; exact ENNReal.zero_ne_top)
 #align integrable_on_Ici_iff_integrable_on_Ioi integrableOn_Ici_iff_integrableOn_Ioi
 
 theorem integrableOn_Iic_iff_integrableOn_Iio :
     IntegrableOn f (Iic b) μ ↔ IntegrableOn f (Iio b) μ :=
-  integrableOn_Iic_iff_integrableOn_Iio'
-    (by
-      rw [measure_singleton]
-      exact ENNReal.zero_ne_top)
+  integrableOn_Iic_iff_integrableOn_Iio' (by rw [measure_singleton]; exact ENNReal.zero_ne_top)
 #align integrable_on_Iic_iff_integrable_on_Iio integrableOn_Iic_iff_integrableOn_Iio
 
 end PartialOrder

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

@@ -40,7 +40,7 @@ variable [TopologicalSpace β] {l l' : Filter α} {f g : α → β} {μ ν : Mea
 ae strongly measurable w.r.t. `μ.restrict s` for some `s ∈ l`. -/
 def StronglyMeasurableAtFilter (f : α → β) (l : Filter α)
     (μ : Measure α := by exact MeasureTheory.MeasureSpace.volume) :=
-  ∃ s ∈ l, AeStronglyMeasurable f (μ.restrict s)
+  ∃ s ∈ l, AEStronglyMeasurable f (μ.restrict s)
 #align strongly_measurable_at_filter StronglyMeasurableAtFilter
 
 @[simp]
@@ -49,8 +49,8 @@ theorem strongly_measurable_at_bot {f : α → β} : StronglyMeasurableAtFilter
 #align strongly_measurable_at_bot strongly_measurable_at_bot
 
 protected theorem StronglyMeasurableAtFilter.eventually (h : StronglyMeasurableAtFilter f l μ) :
-    ∀ᶠ s in l.smallSets, AeStronglyMeasurable f (μ.restrict s) :=
-  (eventually_small_sets' fun s t => AeStronglyMeasurable.mono_set).2 h
+    ∀ᶠ s in l.smallSets, AEStronglyMeasurable f (μ.restrict s) :=
+  (eventually_small_sets' fun s t => AEStronglyMeasurable.mono_set).2 h
 #align strongly_measurable_at_filter.eventually StronglyMeasurableAtFilter.eventually
 
 protected theorem StronglyMeasurableAtFilter.filter_mono (h : StronglyMeasurableAtFilter f l μ)
@@ -59,19 +59,19 @@ protected theorem StronglyMeasurableAtFilter.filter_mono (h : StronglyMeasurable
   ⟨s, h' hsl, hs⟩
 #align strongly_measurable_at_filter.filter_mono StronglyMeasurableAtFilter.filter_mono
 
-protected theorem MeasureTheory.AeStronglyMeasurable.stronglyMeasurableAtFilter
-    (h : AeStronglyMeasurable f μ) : StronglyMeasurableAtFilter f l μ :=
+protected theorem MeasureTheory.AEStronglyMeasurable.stronglyMeasurableAtFilter
+    (h : AEStronglyMeasurable f μ) : StronglyMeasurableAtFilter f l μ :=
   ⟨univ, univ_mem, by rwa [measure.restrict_univ]⟩
-#align measure_theory.ae_strongly_measurable.strongly_measurable_at_filter MeasureTheory.AeStronglyMeasurable.stronglyMeasurableAtFilter
+#align measure_theory.ae_strongly_measurable.strongly_measurable_at_filter MeasureTheory.AEStronglyMeasurable.stronglyMeasurableAtFilter
 
 theorem AeStronglyMeasurable.stronglyMeasurableAtFilter_of_mem {s}
-    (h : AeStronglyMeasurable f (μ.restrict s)) (hl : s ∈ l) : StronglyMeasurableAtFilter f l μ :=
+    (h : AEStronglyMeasurable f (μ.restrict s)) (hl : s ∈ l) : StronglyMeasurableAtFilter f l μ :=
   ⟨s, hl, h⟩
 #align ae_strongly_measurable.strongly_measurable_at_filter_of_mem AeStronglyMeasurable.stronglyMeasurableAtFilter_of_mem
 
 protected theorem MeasureTheory.StronglyMeasurable.stronglyMeasurableAtFilter
     (h : StronglyMeasurable f) : StronglyMeasurableAtFilter f l μ :=
-  h.AeStronglyMeasurable.StronglyMeasurableAtFilter
+  h.AEStronglyMeasurable.StronglyMeasurableAtFilter
 #align measure_theory.strongly_measurable.strongly_measurable_at_filter MeasureTheory.StronglyMeasurable.stronglyMeasurableAtFilter
 
 end
@@ -264,7 +264,7 @@ theorem MeasurePreserving.integrableOn_image [MeasurableSpace β] {e : α → β
 theorem integrable_indicator_iff (hs : MeasurableSet s) :
     Integrable (indicator s f) μ ↔ IntegrableOn f s μ := by
   simp [integrable_on, integrable, has_finite_integral, nnnorm_indicator_eq_indicator_nnnorm,
-    ENNReal.coe_indicator, lintegral_indicator _ hs, aeStronglyMeasurable_indicator_iff hs]
+    ENNReal.coe_indicator, lintegral_indicator _ hs, aestronglyMeasurable_indicator_iff hs]
 #align measure_theory.integrable_indicator_iff MeasureTheory.integrable_indicator_iff
 
 theorem IntegrableOn.integrable_indicator (h : IntegrableOn f s μ) (hs : MeasurableSet s) :
@@ -524,29 +524,29 @@ theorem ContinuousOn.aEMeasurable [TopologicalSpace α] [OpensMeasurableSpace α
 
 /-- A function which is continuous on a separable set `s` is almost everywhere strongly measurable
 with respect to `μ.restrict s`. -/
-theorem ContinuousOn.aeStronglyMeasurable_of_isSeparable [TopologicalSpace α]
+theorem ContinuousOn.aEStronglyMeasurable_of_isSeparable [TopologicalSpace α]
     [PseudoMetrizableSpace α] [OpensMeasurableSpace α] [TopologicalSpace β]
     [PseudoMetrizableSpace β] {f : α → β} {s : Set α} {μ : Measure α} (hf : ContinuousOn f s)
     (hs : MeasurableSet s) (h's : TopologicalSpace.IsSeparable s) :
-    AeStronglyMeasurable f (μ.restrict s) :=
+    AEStronglyMeasurable f (μ.restrict s) :=
   by
   letI := pseudo_metrizable_space_pseudo_metric α
   borelize β
-  rw [aeStronglyMeasurable_iff_aEMeasurable_separable]
+  rw [aestronglyMeasurable_iff_aemeasurable_separable]
   refine' ⟨hf.ae_measurable hs, f '' s, hf.is_separable_image h's, _⟩
   exact mem_of_superset (self_mem_ae_restrict hs) (subset_preimage_image _ _)
-#align continuous_on.ae_strongly_measurable_of_is_separable ContinuousOn.aeStronglyMeasurable_of_isSeparable
+#align continuous_on.ae_strongly_measurable_of_is_separable ContinuousOn.aEStronglyMeasurable_of_isSeparable
 
 /-- A function which is continuous on a set `s` is almost everywhere strongly measurable with
 respect to `μ.restrict s` when either the source space or the target space is second-countable. -/
-theorem ContinuousOn.aeStronglyMeasurable [TopologicalSpace α] [TopologicalSpace β]
+theorem ContinuousOn.aEStronglyMeasurable [TopologicalSpace α] [TopologicalSpace β]
     [h : SecondCountableTopologyEither α β] [OpensMeasurableSpace α] [PseudoMetrizableSpace β]
     {f : α → β} {s : Set α} {μ : Measure α} (hf : ContinuousOn f s) (hs : MeasurableSet s) :
-    AeStronglyMeasurable f (μ.restrict s) :=
+    AEStronglyMeasurable f (μ.restrict s) :=
   by
   borelize β
   refine'
-    aeStronglyMeasurable_iff_aEMeasurable_separable.2
+    aestronglyMeasurable_iff_aemeasurable_separable.2
       ⟨hf.ae_measurable hs, f '' s, _,
         mem_of_superset (self_mem_ae_restrict hs) (subset_preimage_image _ _)⟩
   cases h.out
@@ -557,22 +557,22 @@ theorem ContinuousOn.aeStronglyMeasurable [TopologicalSpace α] [TopologicalSpac
     ext x
     simp
   · exact is_separable_of_separable_space _
-#align continuous_on.ae_strongly_measurable ContinuousOn.aeStronglyMeasurable
+#align continuous_on.ae_strongly_measurable ContinuousOn.aEStronglyMeasurable
 
 /-- A function which is continuous on a compact set `s` is almost everywhere strongly measurable
 with respect to `μ.restrict s`. -/
-theorem ContinuousOn.aeStronglyMeasurable_of_isCompact [TopologicalSpace α] [OpensMeasurableSpace α]
+theorem ContinuousOn.aEStronglyMeasurable_of_isCompact [TopologicalSpace α] [OpensMeasurableSpace α]
     [TopologicalSpace β] [PseudoMetrizableSpace β] {f : α → β} {s : Set α} {μ : Measure α}
     (hf : ContinuousOn f s) (hs : IsCompact s) (h's : MeasurableSet s) :
-    AeStronglyMeasurable f (μ.restrict s) :=
+    AEStronglyMeasurable f (μ.restrict s) :=
   by
   letI := pseudo_metrizable_space_pseudo_metric β
   borelize β
-  rw [aeStronglyMeasurable_iff_aEMeasurable_separable]
+  rw [aestronglyMeasurable_iff_aemeasurable_separable]
   refine' ⟨hf.ae_measurable h's, f '' s, _, _⟩
   · exact (hs.image_of_continuous_on hf).IsSeparable
   · exact mem_of_superset (self_mem_ae_restrict h's) (subset_preimage_image _ _)
-#align continuous_on.ae_strongly_measurable_of_is_compact ContinuousOn.aeStronglyMeasurable_of_isCompact
+#align continuous_on.ae_strongly_measurable_of_is_compact ContinuousOn.aEStronglyMeasurable_of_isCompact
 
 theorem ContinuousOn.integrable_at_nhdsWithin_of_isSeparable [TopologicalSpace α]
     [PseudoMetrizableSpace α] [OpensMeasurableSpace α] {μ : Measure α} [LocallyFiniteMeasure μ]
@@ -607,7 +607,7 @@ theorem ContinuousOn.stronglyMeasurableAtFilter [TopologicalSpace α] [OpensMeas
     [TopologicalSpace β] [PseudoMetrizableSpace β] [SecondCountableTopologyEither α β] {f : α → β}
     {s : Set α} {μ : Measure α} (hs : IsOpen s) (hf : ContinuousOn f s) :
     ∀ x ∈ s, StronglyMeasurableAtFilter f (𝓝 x) μ := fun x hx =>
-  ⟨s, IsOpen.mem_nhds hs hx, hf.AeStronglyMeasurable hs.MeasurableSet⟩
+  ⟨s, IsOpen.mem_nhds hs hx, hf.AEStronglyMeasurable hs.MeasurableSet⟩
 #align continuous_on.strongly_measurable_at_filter ContinuousOn.stronglyMeasurableAtFilter
 
 theorem ContinuousAt.stronglyMeasurableAtFilter [TopologicalSpace α] [OpensMeasurableSpace α]
@@ -629,7 +629,7 @@ theorem ContinuousOn.stronglyMeasurableAtFilter_nhdsWithin {α β : Type _} [Mea
     [SecondCountableTopologyEither α β] {f : α → β} {s : Set α} {μ : Measure α}
     (hf : ContinuousOn f s) (hs : MeasurableSet s) (x : α) :
     StronglyMeasurableAtFilter f (𝓝[s] x) μ :=
-  ⟨s, self_mem_nhdsWithin, hf.AeStronglyMeasurable hs⟩
+  ⟨s, self_mem_nhdsWithin, hf.AEStronglyMeasurable hs⟩
 #align continuous_on.strongly_measurable_at_filter_nhds_within ContinuousOn.stronglyMeasurableAtFilter_nhdsWithin
 
 /-! ### Lemmas about adding and removing interval boundaries

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

@@ -552,7 +552,7 @@ theorem ContinuousOn.aeStronglyMeasurable [TopologicalSpace α] [TopologicalSpac
   cases h.out
   · let f' : s → β := s.restrict f
     have A : Continuous f' := continuousOn_iff_continuous_restrict.1 hf
-    have B : is_separable (univ : Set s) := is_separable_of_separable_space _
+    have B : IsSeparable (univ : Set s) := is_separable_of_separable_space _
     convert is_separable.image B A using 1
     ext x
     simp

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

@@ -210,18 +210,18 @@ theorem integrableOn_finite_bUnion {s : Set β} (hs : s.Finite) {t : β → Set
 #align measure_theory.integrable_on_finite_bUnion MeasureTheory.integrableOn_finite_bUnion
 
 @[simp]
-theorem integrableOn_finset_unionᵢ {s : Finset β} {t : β → Set α} :
+theorem integrableOn_finset_iUnion {s : Finset β} {t : β → Set α} :
     IntegrableOn f (⋃ i ∈ s, t i) μ ↔ ∀ i ∈ s, IntegrableOn f (t i) μ :=
   integrableOn_finite_bUnion s.finite_toSet
-#align measure_theory.integrable_on_finset_Union MeasureTheory.integrableOn_finset_unionᵢ
+#align measure_theory.integrable_on_finset_Union MeasureTheory.integrableOn_finset_iUnion
 
 @[simp]
-theorem integrableOn_finite_unionᵢ [Finite β] {t : β → Set α} :
+theorem integrableOn_finite_iUnion [Finite β] {t : β → Set α} :
     IntegrableOn f (⋃ i, t i) μ ↔ ∀ i, IntegrableOn f (t i) μ :=
   by
   cases nonempty_fintype β
   simpa using @integrable_on_finset_Union _ _ _ _ _ f μ Finset.univ t
-#align measure_theory.integrable_on_finite_Union MeasureTheory.integrableOn_finite_unionᵢ
+#align measure_theory.integrable_on_finite_Union MeasureTheory.integrableOn_finite_iUnion
 
 theorem IntegrableOn.add_measure (hμ : IntegrableOn f s μ) (hν : IntegrableOn f s ν) :
     IntegrableOn f s (μ + ν) := by

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

@@ -575,7 +575,7 @@ theorem ContinuousOn.aeStronglyMeasurable_of_isCompact [TopologicalSpace α] [Op
 #align continuous_on.ae_strongly_measurable_of_is_compact ContinuousOn.aeStronglyMeasurable_of_isCompact
 
 theorem ContinuousOn.integrable_at_nhdsWithin_of_isSeparable [TopologicalSpace α]
-    [PseudoMetrizableSpace α] [OpensMeasurableSpace α] {μ : Measure α} [IsLocallyFiniteMeasure μ]
+    [PseudoMetrizableSpace α] [OpensMeasurableSpace α] {μ : Measure α} [LocallyFiniteMeasure μ]
     {a : α} {t : Set α} {f : α → E} (hft : ContinuousOn f t) (ht : MeasurableSet t)
     (h't : TopologicalSpace.IsSeparable t) (ha : a ∈ t) : IntegrableAtFilter f (𝓝[t] a) μ :=
   haveI : (𝓝[t] a).IsMeasurablyGenerated := ht.nhds_within_is_measurably_generated _
@@ -586,7 +586,7 @@ theorem ContinuousOn.integrable_at_nhdsWithin_of_isSeparable [TopologicalSpace 
 
 theorem ContinuousOn.integrable_at_nhdsWithin [TopologicalSpace α]
     [SecondCountableTopologyEither α E] [OpensMeasurableSpace α] {μ : Measure α}
-    [IsLocallyFiniteMeasure μ] {a : α} {t : Set α} {f : α → E} (hft : ContinuousOn f t)
+    [LocallyFiniteMeasure μ] {a : α} {t : Set α} {f : α → E} (hft : ContinuousOn f t)
     (ht : MeasurableSet t) (ha : a ∈ t) : IntegrableAtFilter f (𝓝[t] a) μ :=
   haveI : (𝓝[t] a).IsMeasurablyGenerated := ht.nhds_within_is_measurably_generated _
   (hft a ha).IntegrableAtFilter ⟨_, self_mem_nhdsWithin, hft.ae_strongly_measurable ht⟩
@@ -594,7 +594,7 @@ theorem ContinuousOn.integrable_at_nhdsWithin [TopologicalSpace α]
 #align continuous_on.integrable_at_nhds_within ContinuousOn.integrable_at_nhdsWithin
 
 theorem Continuous.integrable_at_nhds [TopologicalSpace α] [SecondCountableTopologyEither α E]
-    [OpensMeasurableSpace α] {μ : Measure α} [IsLocallyFiniteMeasure μ] {f : α → E}
+    [OpensMeasurableSpace α] {μ : Measure α} [LocallyFiniteMeasure μ] {f : α → E}
     (hf : Continuous f) (a : α) : IntegrableAtFilter f (𝓝 a) μ :=
   by
   rw [← nhdsWithin_univ]
@@ -704,7 +704,7 @@ theorem integrableOn_Iic_iff_integrableOn_Iio' (hb : μ {b} ≠ ∞) :
     eq_true (integrable_on_singleton_iff.mpr <| Or.inr hb.lt_top), and_true_iff]
 #align integrable_on_Iic_iff_integrable_on_Iio' integrableOn_Iic_iff_integrableOn_Iio'
 
-variable [HasNoAtoms μ]
+variable [NoAtoms μ]
 
 theorem integrableOn_Icc_iff_integrableOn_Ioc :
     IntegrableOn f (Icc a b) μ ↔ IntegrableOn f (Ioc a b) μ :=

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

@@ -44,30 +44,30 @@ def StronglyMeasurableAtFilter (f : α → β) (l : Filter α)
 #align strongly_measurable_at_filter StronglyMeasurableAtFilter
 
 @[simp]
-theorem stronglyMeasurableAtBot {f : α → β} : StronglyMeasurableAtFilter f ⊥ μ :=
+theorem strongly_measurable_at_bot {f : α → β} : StronglyMeasurableAtFilter f ⊥ μ :=
   ⟨∅, mem_bot, by simp⟩
-#align strongly_measurable_at_bot stronglyMeasurableAtBot
+#align strongly_measurable_at_bot strongly_measurable_at_bot
 
 protected theorem StronglyMeasurableAtFilter.eventually (h : StronglyMeasurableAtFilter f l μ) :
     ∀ᶠ s in l.smallSets, AeStronglyMeasurable f (μ.restrict s) :=
-  (eventually_small_sets' fun s t => AeStronglyMeasurable.monoSet).2 h
+  (eventually_small_sets' fun s t => AeStronglyMeasurable.mono_set).2 h
 #align strongly_measurable_at_filter.eventually StronglyMeasurableAtFilter.eventually
 
-protected theorem StronglyMeasurableAtFilter.filterMono (h : StronglyMeasurableAtFilter f l μ)
+protected theorem StronglyMeasurableAtFilter.filter_mono (h : StronglyMeasurableAtFilter f l μ)
     (h' : l' ≤ l) : StronglyMeasurableAtFilter f l' μ :=
   let ⟨s, hsl, hs⟩ := h
   ⟨s, h' hsl, hs⟩
-#align strongly_measurable_at_filter.filter_mono StronglyMeasurableAtFilter.filterMono
+#align strongly_measurable_at_filter.filter_mono StronglyMeasurableAtFilter.filter_mono
 
 protected theorem MeasureTheory.AeStronglyMeasurable.stronglyMeasurableAtFilter
     (h : AeStronglyMeasurable f μ) : StronglyMeasurableAtFilter f l μ :=
   ⟨univ, univ_mem, by rwa [measure.restrict_univ]⟩
 #align measure_theory.ae_strongly_measurable.strongly_measurable_at_filter MeasureTheory.AeStronglyMeasurable.stronglyMeasurableAtFilter
 
-theorem AeStronglyMeasurable.stronglyMeasurableAtFilterOfMem {s}
+theorem AeStronglyMeasurable.stronglyMeasurableAtFilter_of_mem {s}
     (h : AeStronglyMeasurable f (μ.restrict s)) (hl : s ∈ l) : StronglyMeasurableAtFilter f l μ :=
   ⟨s, hl, h⟩
-#align ae_strongly_measurable.strongly_measurable_at_filter_of_mem AeStronglyMeasurable.stronglyMeasurableAtFilterOfMem
+#align ae_strongly_measurable.strongly_measurable_at_filter_of_mem AeStronglyMeasurable.stronglyMeasurableAtFilter_of_mem
 
 protected theorem MeasureTheory.StronglyMeasurable.stronglyMeasurableAtFilter
     (h : StronglyMeasurable f) : StronglyMeasurableAtFilter f l μ :=
@@ -80,12 +80,12 @@ namespace MeasureTheory
 
 section NormedAddCommGroup
 
-theorem hasFiniteIntegralRestrictOfBounded [NormedAddCommGroup E] {f : α → E} {s : Set α}
+theorem hasFiniteIntegral_restrict_of_bounded [NormedAddCommGroup E] {f : α → E} {s : Set α}
     {μ : Measure α} {C} (hs : μ s < ∞) (hf : ∀ᵐ x ∂μ.restrict s, ‖f x‖ ≤ C) :
     HasFiniteIntegral f (μ.restrict s) :=
   haveI : is_finite_measure (μ.restrict s) := ⟨by rwa [measure.restrict_apply_univ]⟩
   has_finite_integral_of_bounded hf
-#align measure_theory.has_finite_integral_restrict_of_bounded MeasureTheory.hasFiniteIntegralRestrictOfBounded
+#align measure_theory.has_finite_integral_restrict_of_bounded MeasureTheory.hasFiniteIntegral_restrict_of_bounded
 
 variable [NormedAddCommGroup E] {f g : α → E} {s t : Set α} {μ ν : Measure α}
 
@@ -101,17 +101,17 @@ theorem IntegrableOn.integrable (h : IntegrableOn f s μ) : Integrable f (μ.res
 #align measure_theory.integrable_on.integrable MeasureTheory.IntegrableOn.integrable
 
 @[simp]
-theorem integrableOnEmpty : IntegrableOn f ∅ μ := by simp [integrable_on, integrable_zero_measure]
-#align measure_theory.integrable_on_empty MeasureTheory.integrableOnEmpty
+theorem integrableOn_empty : IntegrableOn f ∅ μ := by simp [integrable_on, integrable_zero_measure]
+#align measure_theory.integrable_on_empty MeasureTheory.integrableOn_empty
 
 @[simp]
 theorem integrableOn_univ : IntegrableOn f univ μ ↔ Integrable f μ := by
   rw [integrable_on, measure.restrict_univ]
 #align measure_theory.integrable_on_univ MeasureTheory.integrableOn_univ
 
-theorem integrableOnZero : IntegrableOn (fun _ => (0 : E)) s μ :=
-  integrableZero _ _ _
-#align measure_theory.integrable_on_zero MeasureTheory.integrableOnZero
+theorem integrableOn_zero : IntegrableOn (fun _ => (0 : E)) s μ :=
+  integrable_zero _ _ _
+#align measure_theory.integrable_on_zero MeasureTheory.integrableOn_zero
 
 @[simp]
 theorem integrableOn_const {C : E} : IntegrableOn (fun _ => C) s μ ↔ C = 0 ∨ μ s < ∞ :=
@@ -119,39 +119,39 @@ theorem integrableOn_const {C : E} : IntegrableOn (fun _ => C) s μ ↔ C = 0 
 #align measure_theory.integrable_on_const MeasureTheory.integrableOn_const
 
 theorem IntegrableOn.mono (h : IntegrableOn f t ν) (hs : s ⊆ t) (hμ : μ ≤ ν) : IntegrableOn f s μ :=
-  h.monoMeasure <| Measure.restrict_mono hs hμ
+  h.mono_measure <| Measure.restrict_mono hs hμ
 #align measure_theory.integrable_on.mono MeasureTheory.IntegrableOn.mono
 
-theorem IntegrableOn.monoSet (h : IntegrableOn f t μ) (hst : s ⊆ t) : IntegrableOn f s μ :=
+theorem IntegrableOn.mono_set (h : IntegrableOn f t μ) (hst : s ⊆ t) : IntegrableOn f s μ :=
   h.mono hst le_rfl
-#align measure_theory.integrable_on.mono_set MeasureTheory.IntegrableOn.monoSet
+#align measure_theory.integrable_on.mono_set MeasureTheory.IntegrableOn.mono_set
 
-theorem IntegrableOn.monoMeasure (h : IntegrableOn f s ν) (hμ : μ ≤ ν) : IntegrableOn f s μ :=
+theorem IntegrableOn.mono_measure (h : IntegrableOn f s ν) (hμ : μ ≤ ν) : IntegrableOn f s μ :=
   h.mono (Subset.refl _) hμ
-#align measure_theory.integrable_on.mono_measure MeasureTheory.IntegrableOn.monoMeasure
+#align measure_theory.integrable_on.mono_measure MeasureTheory.IntegrableOn.mono_measure
 
-theorem IntegrableOn.monoSetAe (h : IntegrableOn f t μ) (hst : s ≤ᵐ[μ] t) : IntegrableOn f s μ :=
-  h.Integrable.monoMeasure <| Measure.restrict_mono_ae hst
-#align measure_theory.integrable_on.mono_set_ae MeasureTheory.IntegrableOn.monoSetAe
+theorem IntegrableOn.mono_set_ae (h : IntegrableOn f t μ) (hst : s ≤ᵐ[μ] t) : IntegrableOn f s μ :=
+  h.Integrable.mono_measure <| Measure.restrict_mono_ae hst
+#align measure_theory.integrable_on.mono_set_ae MeasureTheory.IntegrableOn.mono_set_ae
 
-theorem IntegrableOn.congrSetAe (h : IntegrableOn f t μ) (hst : s =ᵐ[μ] t) : IntegrableOn f s μ :=
-  h.monoSetAe hst.le
-#align measure_theory.integrable_on.congr_set_ae MeasureTheory.IntegrableOn.congrSetAe
+theorem IntegrableOn.congr_set_ae (h : IntegrableOn f t μ) (hst : s =ᵐ[μ] t) : IntegrableOn f s μ :=
+  h.mono_set_ae hst.le
+#align measure_theory.integrable_on.congr_set_ae MeasureTheory.IntegrableOn.congr_set_ae
 
-theorem IntegrableOn.congrFunAe (h : IntegrableOn f s μ) (hst : f =ᵐ[μ.restrict s] g) :
+theorem IntegrableOn.congr_fun_ae (h : IntegrableOn f s μ) (hst : f =ᵐ[μ.restrict s] g) :
     IntegrableOn g s μ :=
   Integrable.congr h hst
-#align measure_theory.integrable_on.congr_fun_ae MeasureTheory.IntegrableOn.congrFunAe
+#align measure_theory.integrable_on.congr_fun_ae MeasureTheory.IntegrableOn.congr_fun_ae
 
 theorem integrableOn_congr_fun_ae (hst : f =ᵐ[μ.restrict s] g) :
     IntegrableOn f s μ ↔ IntegrableOn g s μ :=
-  ⟨fun h => h.congrFunAe hst, fun h => h.congrFunAe hst.symm⟩
+  ⟨fun h => h.congr_fun_ae hst, fun h => h.congr_fun_ae hst.symm⟩
 #align measure_theory.integrable_on_congr_fun_ae MeasureTheory.integrableOn_congr_fun_ae
 
-theorem IntegrableOn.congrFun (h : IntegrableOn f s μ) (hst : EqOn f g s) (hs : MeasurableSet s) :
+theorem IntegrableOn.congr_fun (h : IntegrableOn f s μ) (hst : EqOn f g s) (hs : MeasurableSet s) :
     IntegrableOn g s μ :=
-  h.congrFunAe ((ae_restrict_iff' hs).2 (eventually_of_forall hst))
-#align measure_theory.integrable_on.congr_fun MeasureTheory.IntegrableOn.congrFun
+  h.congr_fun_ae ((ae_restrict_iff' hs).2 (eventually_of_forall hst))
+#align measure_theory.integrable_on.congr_fun MeasureTheory.IntegrableOn.congr_fun
 
 theorem integrableOn_congr_fun (hst : EqOn f g s) (hs : MeasurableSet s) :
     IntegrableOn f s μ ↔ IntegrableOn g s μ :=
@@ -159,7 +159,7 @@ theorem integrableOn_congr_fun (hst : EqOn f g s) (hs : MeasurableSet s) :
 #align measure_theory.integrable_on_congr_fun MeasureTheory.integrableOn_congr_fun
 
 theorem Integrable.integrableOn (h : Integrable f μ) : IntegrableOn f s μ :=
-  h.monoMeasure <| Measure.restrict_le_self
+  h.mono_measure <| Measure.restrict_le_self
 #align measure_theory.integrable.integrable_on MeasureTheory.Integrable.integrableOn
 
 theorem IntegrableOn.restrict (h : IntegrableOn f s μ) (hs : MeasurableSet s) :
@@ -169,22 +169,22 @@ theorem IntegrableOn.restrict (h : IntegrableOn f s μ) (hs : MeasurableSet s) :
   exact h.mono_set (inter_subset_left _ _)
 #align measure_theory.integrable_on.restrict MeasureTheory.IntegrableOn.restrict
 
-theorem IntegrableOn.leftOfUnion (h : IntegrableOn f (s ∪ t) μ) : IntegrableOn f s μ :=
-  h.monoSet <| subset_union_left _ _
-#align measure_theory.integrable_on.left_of_union MeasureTheory.IntegrableOn.leftOfUnion
+theorem IntegrableOn.left_of_union (h : IntegrableOn f (s ∪ t) μ) : IntegrableOn f s μ :=
+  h.mono_set <| subset_union_left _ _
+#align measure_theory.integrable_on.left_of_union MeasureTheory.IntegrableOn.left_of_union
 
-theorem IntegrableOn.rightOfUnion (h : IntegrableOn f (s ∪ t) μ) : IntegrableOn f t μ :=
-  h.monoSet <| subset_union_right _ _
-#align measure_theory.integrable_on.right_of_union MeasureTheory.IntegrableOn.rightOfUnion
+theorem IntegrableOn.right_of_union (h : IntegrableOn f (s ∪ t) μ) : IntegrableOn f t μ :=
+  h.mono_set <| subset_union_right _ _
+#align measure_theory.integrable_on.right_of_union MeasureTheory.IntegrableOn.right_of_union
 
 theorem IntegrableOn.union (hs : IntegrableOn f s μ) (ht : IntegrableOn f t μ) :
     IntegrableOn f (s ∪ t) μ :=
-  (hs.addMeasure ht).monoMeasure <| Measure.restrict_union_le _ _
+  (hs.add_measure ht).mono_measure <| Measure.restrict_union_le _ _
 #align measure_theory.integrable_on.union MeasureTheory.IntegrableOn.union
 
 @[simp]
 theorem integrableOn_union : IntegrableOn f (s ∪ t) μ ↔ IntegrableOn f s μ ∧ IntegrableOn f t μ :=
-  ⟨fun h => ⟨h.leftOfUnion, h.rightOfUnion⟩, fun h => h.1.union h.2⟩
+  ⟨fun h => ⟨h.left_of_union, h.right_of_union⟩, fun h => h.1.union h.2⟩
 #align measure_theory.integrable_on_union MeasureTheory.integrableOn_union
 
 @[simp]
@@ -223,19 +223,19 @@ theorem integrableOn_finite_unionᵢ [Finite β] {t : β → Set α} :
   simpa using @integrable_on_finset_Union _ _ _ _ _ f μ Finset.univ t
 #align measure_theory.integrable_on_finite_Union MeasureTheory.integrableOn_finite_unionᵢ
 
-theorem IntegrableOn.addMeasure (hμ : IntegrableOn f s μ) (hν : IntegrableOn f s ν) :
+theorem IntegrableOn.add_measure (hμ : IntegrableOn f s μ) (hν : IntegrableOn f s ν) :
     IntegrableOn f s (μ + ν) := by
   delta integrable_on
   rw [measure.restrict_add]
   exact hμ.integrable.add_measure hν
-#align measure_theory.integrable_on.add_measure MeasureTheory.IntegrableOn.addMeasure
+#align measure_theory.integrable_on.add_measure MeasureTheory.IntegrableOn.add_measure
 
 @[simp]
 theorem integrableOn_add_measure :
     IntegrableOn f s (μ + ν) ↔ IntegrableOn f s μ ∧ IntegrableOn f s ν :=
   ⟨fun h =>
-    ⟨h.monoMeasure (Measure.le_add_right le_rfl), h.monoMeasure (Measure.le_add_left le_rfl)⟩,
-    fun h => h.1.addMeasure h.2⟩
+    ⟨h.mono_measure (Measure.le_add_right le_rfl), h.mono_measure (Measure.le_add_left le_rfl)⟩,
+    fun h => h.1.add_measure h.2⟩
 #align measure_theory.integrable_on_add_measure MeasureTheory.integrableOn_add_measure
 
 theorem MeasurableEmbedding.integrableOn_map_iff [MeasurableSpace β] {e : α → β}
@@ -252,13 +252,13 @@ theorem integrableOn_map_equiv [MeasurableSpace β] (e : α ≃ᵐ β) {f : β 
 theorem MeasurePreserving.integrableOn_comp_preimage [MeasurableSpace β] {e : α → β} {ν}
     (h₁ : MeasurePreserving e μ ν) (h₂ : MeasurableEmbedding e) {f : β → E} {s : Set β} :
     IntegrableOn (f ∘ e) (e ⁻¹' s) μ ↔ IntegrableOn f s ν :=
-  (h₁.restrictPreimageEmb h₂ s).integrable_comp_emb h₂
+  (h₁.restrict_preimage_emb h₂ s).integrable_comp_emb h₂
 #align measure_theory.measure_preserving.integrable_on_comp_preimage MeasureTheory.MeasurePreserving.integrableOn_comp_preimage
 
 theorem MeasurePreserving.integrableOn_image [MeasurableSpace β] {e : α → β} {ν}
     (h₁ : MeasurePreserving e μ ν) (h₂ : MeasurableEmbedding e) {f : β → E} {s : Set α} :
     IntegrableOn f (e '' s) ν ↔ IntegrableOn (f ∘ e) s μ :=
-  ((h₁.restrictImageEmb h₂ s).integrable_comp_emb h₂).symm
+  ((h₁.restrict_image_emb h₂ s).integrable_comp_emb h₂).symm
 #align measure_theory.measure_preserving.integrable_on_image MeasureTheory.MeasurePreserving.integrableOn_image
 
 theorem integrable_indicator_iff (hs : MeasurableSet s) :
@@ -267,14 +267,14 @@ theorem integrable_indicator_iff (hs : MeasurableSet s) :
     ENNReal.coe_indicator, lintegral_indicator _ hs, aeStronglyMeasurable_indicator_iff hs]
 #align measure_theory.integrable_indicator_iff MeasureTheory.integrable_indicator_iff
 
-theorem IntegrableOn.integrableIndicator (h : IntegrableOn f s μ) (hs : MeasurableSet s) :
+theorem IntegrableOn.integrable_indicator (h : IntegrableOn f s μ) (hs : MeasurableSet s) :
     Integrable (indicator s f) μ :=
   (integrable_indicator_iff hs).2 h
-#align measure_theory.integrable_on.integrable_indicator MeasureTheory.IntegrableOn.integrableIndicator
+#align measure_theory.integrable_on.integrable_indicator MeasureTheory.IntegrableOn.integrable_indicator
 
 theorem Integrable.indicator (h : Integrable f μ) (hs : MeasurableSet s) :
     Integrable (indicator s f) μ :=
-  h.IntegrableOn.integrableIndicator hs
+  h.IntegrableOn.integrable_indicator hs
 #align measure_theory.integrable.indicator MeasureTheory.Integrable.indicator
 
 theorem IntegrableOn.indicator (h : IntegrableOn f s μ) (ht : MeasurableSet t) :
@@ -282,14 +282,14 @@ theorem IntegrableOn.indicator (h : IntegrableOn f s μ) (ht : MeasurableSet t)
   Integrable.indicator h ht
 #align measure_theory.integrable_on.indicator MeasureTheory.IntegrableOn.indicator
 
-theorem integrableIndicatorConstLp {E} [NormedAddCommGroup E] {p : ℝ≥0∞} {s : Set α}
+theorem integrable_indicatorConstLp {E} [NormedAddCommGroup E] {p : ℝ≥0∞} {s : Set α}
     (hs : MeasurableSet s) (hμs : μ s ≠ ∞) (c : E) : Integrable (indicatorConstLp p hs hμs c) μ :=
   by
   rw [integrable_congr indicator_const_Lp_coe_fn, integrable_indicator_iff hs, integrable_on,
     integrable_const_iff, lt_top_iff_ne_top]
   right
   simpa only [Set.univ_inter, MeasurableSet.univ, measure.restrict_apply] using hμs
-#align measure_theory.integrable_indicator_const_Lp MeasureTheory.integrableIndicatorConstLp
+#align measure_theory.integrable_indicator_const_Lp MeasureTheory.integrable_indicatorConstLp
 
 /-- If a function is integrable on a set `s` and nonzero there, then the measurable hull of `s` is
 well behaved: the restriction of the measure to `to_measurable μ s` coincides with its restriction
@@ -315,7 +315,7 @@ theorem IntegrableOn.restrict_toMeasurable (hf : IntegrableOn f s μ) (h's : ∀
 
 /-- If a function is integrable on a set `s`, and vanishes on `t \ s`, then it is integrable on `t`
 if `t` is null-measurable. -/
-theorem IntegrableOn.ofAeDiffEqZero (hf : IntegrableOn f s μ) (ht : NullMeasurableSet t μ)
+theorem IntegrableOn.of_ae_diff_eq_zero (hf : IntegrableOn f s μ) (ht : NullMeasurableSet t μ)
     (h't : ∀ᵐ x ∂μ, x ∈ t \ s → f x = 0) : IntegrableOn f t μ :=
   by
   let u := { x ∈ s | f x ≠ 0 }
@@ -336,35 +336,35 @@ theorem IntegrableOn.ofAeDiffEqZero (hf : IntegrableOn f s μ) (ht : NullMeasura
     · by_contra H
       exact hx.2 (subset_to_measurable μ u ⟨h'x, Ne.symm H⟩)
     · exact (hxt ⟨hx.1, h'x⟩).symm
-  apply (A.union B).monoSet _
+  apply (A.union B).mono_set _
   rw [union_diff_self]
   exact subset_union_right _ _
-#align measure_theory.integrable_on.of_ae_diff_eq_zero MeasureTheory.IntegrableOn.ofAeDiffEqZero
+#align measure_theory.integrable_on.of_ae_diff_eq_zero MeasureTheory.IntegrableOn.of_ae_diff_eq_zero
 
 /-- If a function is integrable on a set `s`, and vanishes on `t \ s`, then it is integrable on `t`
 if `t` is measurable. -/
-theorem IntegrableOn.ofForallDiffEqZero (hf : IntegrableOn f s μ) (ht : MeasurableSet t)
+theorem IntegrableOn.of_forall_diff_eq_zero (hf : IntegrableOn f s μ) (ht : MeasurableSet t)
     (h't : ∀ x ∈ t \ s, f x = 0) : IntegrableOn f t μ :=
-  hf.ofAeDiffEqZero ht.NullMeasurableSet (eventually_of_forall h't)
-#align measure_theory.integrable_on.of_forall_diff_eq_zero MeasureTheory.IntegrableOn.ofForallDiffEqZero
+  hf.of_ae_diff_eq_zero ht.NullMeasurableSet (eventually_of_forall h't)
+#align measure_theory.integrable_on.of_forall_diff_eq_zero MeasureTheory.IntegrableOn.of_forall_diff_eq_zero
 
 /-- If a function is integrable on a set `s` and vanishes almost everywhere on its complement,
 then it is integrable. -/
-theorem IntegrableOn.integrableOfAeNotMemEqZero (hf : IntegrableOn f s μ)
+theorem IntegrableOn.integrable_of_ae_not_mem_eq_zero (hf : IntegrableOn f s μ)
     (h't : ∀ᵐ x ∂μ, x ∉ s → f x = 0) : Integrable f μ :=
   by
   rw [← integrable_on_univ]
   apply hf.of_ae_diff_eq_zero null_measurable_set_univ
   filter_upwards [h't]with x hx h'x using hx h'x.2
-#align measure_theory.integrable_on.integrable_of_ae_not_mem_eq_zero MeasureTheory.IntegrableOn.integrableOfAeNotMemEqZero
+#align measure_theory.integrable_on.integrable_of_ae_not_mem_eq_zero MeasureTheory.IntegrableOn.integrable_of_ae_not_mem_eq_zero
 
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x «expr ∉ » s) -/
 /-- If a function is integrable on a set `s` and vanishes everywhere on its complement,
 then it is integrable. -/
-theorem IntegrableOn.integrableOfForallNotMemEqZero (hf : IntegrableOn f s μ)
+theorem IntegrableOn.integrable_of_forall_not_mem_eq_zero (hf : IntegrableOn f s μ)
     (h't : ∀ (x) (_ : x ∉ s), f x = 0) : Integrable f μ :=
-  hf.integrableOfAeNotMemEqZero (eventually_of_forall fun x hx => h't x hx)
-#align measure_theory.integrable_on.integrable_of_forall_not_mem_eq_zero MeasureTheory.IntegrableOn.integrableOfForallNotMemEqZero
+  hf.integrable_of_ae_not_mem_eq_zero (eventually_of_forall fun x hx => h't x hx)
+#align measure_theory.integrable_on.integrable_of_forall_not_mem_eq_zero MeasureTheory.IntegrableOn.integrable_of_forall_not_mem_eq_zero
 
 theorem integrableOn_iff_integrable_of_support_subset (h1s : support f ⊆ s) :
     IntegrableOn f s μ ↔ Integrable f μ :=
@@ -375,15 +375,15 @@ theorem integrableOn_iff_integrable_of_support_subset (h1s : support f ⊆ s) :
   exact h1s (mem_support.2 hx)
 #align measure_theory.integrable_on_iff_integrable_of_support_subset MeasureTheory.integrableOn_iff_integrable_of_support_subset
 
-theorem integrableOnLpOfMeasureNeTop {E} [NormedAddCommGroup E] {p : ℝ≥0∞} {s : Set α}
+theorem integrableOn_lp_of_measure_ne_top {E} [NormedAddCommGroup E] {p : ℝ≥0∞} {s : Set α}
     (f : lp E p μ) (hp : 1 ≤ p) (hμs : μ s ≠ ∞) : IntegrableOn f s μ :=
   by
   refine' mem_ℒp_one_iff_integrable.mp _
   have hμ_restrict_univ : (μ.restrict s) Set.univ < ∞ := by
     simpa only [Set.univ_inter, MeasurableSet.univ, measure.restrict_apply, lt_top_iff_ne_top]
   haveI hμ_finite : is_finite_measure (μ.restrict s) := ⟨hμ_restrict_univ⟩
-  exact ((Lp.mem_ℒp _).restrict s).memℒpOfExponentLe hp
-#align measure_theory.integrable_on_Lp_of_measure_ne_top MeasureTheory.integrableOnLpOfMeasureNeTop
+  exact ((Lp.mem_ℒp _).restrict s).memℒp_of_exponent_le hp
+#align measure_theory.integrable_on_Lp_of_measure_ne_top MeasureTheory.integrableOn_lp_of_measure_ne_top
 
 theorem Integrable.lintegral_lt_top {f : α → ℝ} (hf : Integrable f μ) :
     (∫⁻ x, ENNReal.ofReal (f x) ∂μ) < ∞ :=
@@ -414,24 +414,24 @@ theorem Integrable.integrableAtFilter (h : Integrable f μ) (l : Filter α) :
 
 protected theorem IntegrableAtFilter.eventually (h : IntegrableAtFilter f l μ) :
     ∀ᶠ s in l.smallSets, IntegrableOn f s μ :=
-  Iff.mpr (eventually_small_sets' fun s t hst ht => ht.monoSet hst) h
+  Iff.mpr (eventually_small_sets' fun s t hst ht => ht.mono_set hst) h
 #align measure_theory.integrable_at_filter.eventually MeasureTheory.IntegrableAtFilter.eventually
 
-theorem IntegrableAtFilter.filterMono (hl : l ≤ l') (hl' : IntegrableAtFilter f l' μ) :
+theorem IntegrableAtFilter.filter_mono (hl : l ≤ l') (hl' : IntegrableAtFilter f l' μ) :
     IntegrableAtFilter f l μ :=
   let ⟨s, hs, hsf⟩ := hl'
   ⟨s, hl hs, hsf⟩
-#align measure_theory.integrable_at_filter.filter_mono MeasureTheory.IntegrableAtFilter.filterMono
+#align measure_theory.integrable_at_filter.filter_mono MeasureTheory.IntegrableAtFilter.filter_mono
 
-theorem IntegrableAtFilter.infOfLeft (hl : IntegrableAtFilter f l μ) :
+theorem IntegrableAtFilter.inf_of_left (hl : IntegrableAtFilter f l μ) :
     IntegrableAtFilter f (l ⊓ l') μ :=
   hl.filter_mono inf_le_left
-#align measure_theory.integrable_at_filter.inf_of_left MeasureTheory.IntegrableAtFilter.infOfLeft
+#align measure_theory.integrable_at_filter.inf_of_left MeasureTheory.IntegrableAtFilter.inf_of_left
 
-theorem IntegrableAtFilter.infOfRight (hl : IntegrableAtFilter f l μ) :
+theorem IntegrableAtFilter.inf_of_right (hl : IntegrableAtFilter f l μ) :
     IntegrableAtFilter f (l' ⊓ l) μ :=
   hl.filter_mono inf_le_right
-#align measure_theory.integrable_at_filter.inf_of_right MeasureTheory.IntegrableAtFilter.infOfRight
+#align measure_theory.integrable_at_filter.inf_of_right MeasureTheory.IntegrableAtFilter.inf_of_right
 
 @[simp]
 theorem IntegrableAtFilter.inf_ae_iff {l : Filter α} :
@@ -447,7 +447,7 @@ theorem IntegrableAtFilter.inf_ae_iff {l : Filter α} :
 #align measure_theory.integrable_at_filter.inf_ae_iff MeasureTheory.IntegrableAtFilter.inf_ae_iff
 
 alias integrable_at_filter.inf_ae_iff ↔ integrable_at_filter.of_inf_ae _
-#align measure_theory.integrable_at_filter.of_inf_ae MeasureTheory.IntegrableAtFilter.ofInfAe
+#align measure_theory.integrable_at_filter.of_inf_ae MeasureTheory.IntegrableAtFilter.of_inf_ae
 
 /-- If `μ` is a measure finite at filter `l` and `f` is a function such that its norm is bounded
 above at `l`, then `f` is integrable at `l`. -/
@@ -465,22 +465,22 @@ theorem Measure.FiniteAtFilter.integrableAtFilter {l : Filter α} [IsMeasurablyG
   exact eventually_of_forall hC
 #align measure_theory.measure.finite_at_filter.integrable_at_filter MeasureTheory.Measure.FiniteAtFilter.integrableAtFilter
 
-theorem Measure.FiniteAtFilter.integrableAtFilterOfTendstoAe {l : Filter α}
+theorem Measure.FiniteAtFilter.integrableAtFilter_of_tendsto_ae {l : Filter α}
     [IsMeasurablyGenerated l] (hfm : StronglyMeasurableAtFilter f l μ) (hμ : μ.FiniteAtFilter l) {b}
     (hf : Tendsto f (l ⊓ μ.ae) (𝓝 b)) : IntegrableAtFilter f l μ :=
   (hμ.inf_of_left.IntegrableAtFilter (hfm.filter_mono inf_le_left)
-      hf.norm.isBoundedUnder_le).ofInfAe
-#align measure_theory.measure.finite_at_filter.integrable_at_filter_of_tendsto_ae MeasureTheory.Measure.FiniteAtFilter.integrableAtFilterOfTendstoAe
+      hf.norm.isBoundedUnder_le).of_inf_ae
+#align measure_theory.measure.finite_at_filter.integrable_at_filter_of_tendsto_ae MeasureTheory.Measure.FiniteAtFilter.integrableAtFilter_of_tendsto_ae
 
 alias measure.finite_at_filter.integrable_at_filter_of_tendsto_ae ←
   _root_.filter.tendsto.integrable_at_filter_ae
-#align filter.tendsto.integrable_at_filter_ae Filter.Tendsto.integrableAtFilterAe
+#align filter.tendsto.integrable_at_filter_ae Filter.Tendsto.integrableAtFilter_ae
 
-theorem Measure.FiniteAtFilter.integrableAtFilterOfTendsto {l : Filter α} [IsMeasurablyGenerated l]
-    (hfm : StronglyMeasurableAtFilter f l μ) (hμ : μ.FiniteAtFilter l) {b}
+theorem Measure.FiniteAtFilter.integrableAtFilter_of_tendsto {l : Filter α}
+    [IsMeasurablyGenerated l] (hfm : StronglyMeasurableAtFilter f l μ) (hμ : μ.FiniteAtFilter l) {b}
     (hf : Tendsto f l (𝓝 b)) : IntegrableAtFilter f l μ :=
   hμ.IntegrableAtFilter hfm hf.norm.isBoundedUnder_le
-#align measure_theory.measure.finite_at_filter.integrable_at_filter_of_tendsto MeasureTheory.Measure.FiniteAtFilter.integrableAtFilterOfTendsto
+#align measure_theory.measure.finite_at_filter.integrable_at_filter_of_tendsto MeasureTheory.Measure.FiniteAtFilter.integrableAtFilter_of_tendsto
 
 alias measure.finite_at_filter.integrable_at_filter_of_tendsto ←
   _root_.filter.tendsto.integrable_at_filter
@@ -507,9 +507,9 @@ variable [NormedAddCommGroup E]
 
 /-- A function which is continuous on a set `s` is almost everywhere measurable with respect to
 `μ.restrict s`. -/
-theorem ContinuousOn.aeMeasurable [TopologicalSpace α] [OpensMeasurableSpace α] [MeasurableSpace β]
+theorem ContinuousOn.aEMeasurable [TopologicalSpace α] [OpensMeasurableSpace α] [MeasurableSpace β]
     [TopologicalSpace β] [BorelSpace β] {f : α → β} {s : Set α} {μ : Measure α}
-    (hf : ContinuousOn f s) (hs : MeasurableSet s) : AeMeasurable f (μ.restrict s) :=
+    (hf : ContinuousOn f s) (hs : MeasurableSet s) : AEMeasurable f (μ.restrict s) :=
   by
   nontriviality α; inhabit α
   have : (piecewise s f fun _ => f default) =ᵐ[μ.restrict s] f := piecewise_ae_eq_restrict hs
@@ -520,11 +520,11 @@ theorem ContinuousOn.aeMeasurable [TopologicalSpace α] [OpensMeasurableSpace α
     _root_.continuous_on_iff'.1 hf t ht
   rw [piecewise_preimage, Set.ite, hu]
   exact (u_open.measurable_set.inter hs).union ((measurable_const ht.measurable_set).diffₓ hs)
-#align continuous_on.ae_measurable ContinuousOn.aeMeasurable
+#align continuous_on.ae_measurable ContinuousOn.aEMeasurable
 
 /-- A function which is continuous on a separable set `s` is almost everywhere strongly measurable
 with respect to `μ.restrict s`. -/
-theorem ContinuousOn.aeStronglyMeasurableOfIsSeparable [TopologicalSpace α]
+theorem ContinuousOn.aeStronglyMeasurable_of_isSeparable [TopologicalSpace α]
     [PseudoMetrizableSpace α] [OpensMeasurableSpace α] [TopologicalSpace β]
     [PseudoMetrizableSpace β] {f : α → β} {s : Set α} {μ : Measure α} (hf : ContinuousOn f s)
     (hs : MeasurableSet s) (h's : TopologicalSpace.IsSeparable s) :
@@ -532,10 +532,10 @@ theorem ContinuousOn.aeStronglyMeasurableOfIsSeparable [TopologicalSpace α]
   by
   letI := pseudo_metrizable_space_pseudo_metric α
   borelize β
-  rw [aeStronglyMeasurable_iff_aeMeasurable_separable]
+  rw [aeStronglyMeasurable_iff_aEMeasurable_separable]
   refine' ⟨hf.ae_measurable hs, f '' s, hf.is_separable_image h's, _⟩
   exact mem_of_superset (self_mem_ae_restrict hs) (subset_preimage_image _ _)
-#align continuous_on.ae_strongly_measurable_of_is_separable ContinuousOn.aeStronglyMeasurableOfIsSeparable
+#align continuous_on.ae_strongly_measurable_of_is_separable ContinuousOn.aeStronglyMeasurable_of_isSeparable
 
 /-- A function which is continuous on a set `s` is almost everywhere strongly measurable with
 respect to `μ.restrict s` when either the source space or the target space is second-countable. -/
@@ -546,7 +546,7 @@ theorem ContinuousOn.aeStronglyMeasurable [TopologicalSpace α] [TopologicalSpac
   by
   borelize β
   refine'
-    aeStronglyMeasurable_iff_aeMeasurable_separable.2
+    aeStronglyMeasurable_iff_aEMeasurable_separable.2
       ⟨hf.ae_measurable hs, f '' s, _,
         mem_of_superset (self_mem_ae_restrict hs) (subset_preimage_image _ _)⟩
   cases h.out
@@ -561,20 +561,20 @@ theorem ContinuousOn.aeStronglyMeasurable [TopologicalSpace α] [TopologicalSpac
 
 /-- A function which is continuous on a compact set `s` is almost everywhere strongly measurable
 with respect to `μ.restrict s`. -/
-theorem ContinuousOn.aeStronglyMeasurableOfIsCompact [TopologicalSpace α] [OpensMeasurableSpace α]
+theorem ContinuousOn.aeStronglyMeasurable_of_isCompact [TopologicalSpace α] [OpensMeasurableSpace α]
     [TopologicalSpace β] [PseudoMetrizableSpace β] {f : α → β} {s : Set α} {μ : Measure α}
     (hf : ContinuousOn f s) (hs : IsCompact s) (h's : MeasurableSet s) :
     AeStronglyMeasurable f (μ.restrict s) :=
   by
   letI := pseudo_metrizable_space_pseudo_metric β
   borelize β
-  rw [aeStronglyMeasurable_iff_aeMeasurable_separable]
+  rw [aeStronglyMeasurable_iff_aEMeasurable_separable]
   refine' ⟨hf.ae_measurable h's, f '' s, _, _⟩
   · exact (hs.image_of_continuous_on hf).IsSeparable
   · exact mem_of_superset (self_mem_ae_restrict h's) (subset_preimage_image _ _)
-#align continuous_on.ae_strongly_measurable_of_is_compact ContinuousOn.aeStronglyMeasurableOfIsCompact
+#align continuous_on.ae_strongly_measurable_of_is_compact ContinuousOn.aeStronglyMeasurable_of_isCompact
 
-theorem ContinuousOn.integrableAtNhdsWithinOfIsSeparable [TopologicalSpace α]
+theorem ContinuousOn.integrable_at_nhdsWithin_of_isSeparable [TopologicalSpace α]
     [PseudoMetrizableSpace α] [OpensMeasurableSpace α] {μ : Measure α} [IsLocallyFiniteMeasure μ]
     {a : α} {t : Set α} {f : α → E} (hft : ContinuousOn f t) (ht : MeasurableSet t)
     (h't : TopologicalSpace.IsSeparable t) (ha : a ∈ t) : IntegrableAtFilter f (𝓝[t] a) μ :=
@@ -582,24 +582,24 @@ theorem ContinuousOn.integrableAtNhdsWithinOfIsSeparable [TopologicalSpace α]
   (hft a ha).IntegrableAtFilter
     ⟨_, self_mem_nhdsWithin, hft.ae_strongly_measurable_of_is_separable ht h't⟩
     (μ.finite_at_nhds_within _ _)
-#align continuous_on.integrable_at_nhds_within_of_is_separable ContinuousOn.integrableAtNhdsWithinOfIsSeparable
+#align continuous_on.integrable_at_nhds_within_of_is_separable ContinuousOn.integrable_at_nhdsWithin_of_isSeparable
 
-theorem ContinuousOn.integrableAtNhdsWithin [TopologicalSpace α] [SecondCountableTopologyEither α E]
-    [OpensMeasurableSpace α] {μ : Measure α} [IsLocallyFiniteMeasure μ] {a : α} {t : Set α}
-    {f : α → E} (hft : ContinuousOn f t) (ht : MeasurableSet t) (ha : a ∈ t) :
-    IntegrableAtFilter f (𝓝[t] a) μ :=
+theorem ContinuousOn.integrable_at_nhdsWithin [TopologicalSpace α]
+    [SecondCountableTopologyEither α E] [OpensMeasurableSpace α] {μ : Measure α}
+    [IsLocallyFiniteMeasure μ] {a : α} {t : Set α} {f : α → E} (hft : ContinuousOn f t)
+    (ht : MeasurableSet t) (ha : a ∈ t) : IntegrableAtFilter f (𝓝[t] a) μ :=
   haveI : (𝓝[t] a).IsMeasurablyGenerated := ht.nhds_within_is_measurably_generated _
   (hft a ha).IntegrableAtFilter ⟨_, self_mem_nhdsWithin, hft.ae_strongly_measurable ht⟩
     (μ.finite_at_nhds_within _ _)
-#align continuous_on.integrable_at_nhds_within ContinuousOn.integrableAtNhdsWithin
+#align continuous_on.integrable_at_nhds_within ContinuousOn.integrable_at_nhdsWithin
 
-theorem Continuous.integrableAtNhds [TopologicalSpace α] [SecondCountableTopologyEither α E]
+theorem Continuous.integrable_at_nhds [TopologicalSpace α] [SecondCountableTopologyEither α E]
     [OpensMeasurableSpace α] {μ : Measure α} [IsLocallyFiniteMeasure μ] {f : α → E}
     (hf : Continuous f) (a : α) : IntegrableAtFilter f (𝓝 a) μ :=
   by
   rw [← nhdsWithin_univ]
   exact hf.continuous_on.integrable_at_nhds_within MeasurableSet.univ (mem_univ a)
-#align continuous.integrable_at_nhds Continuous.integrableAtNhds
+#align continuous.integrable_at_nhds Continuous.integrable_at_nhds
 
 /-- If a function is continuous on an open set `s`, then it is strongly measurable at the filter
 `𝓝 x` for all `x ∈ s` if either the source space or the target space is second-countable. -/
@@ -624,13 +624,13 @@ theorem Continuous.stronglyMeasurableAtFilter [TopologicalSpace α] [OpensMeasur
 
 /-- If a function is continuous on a measurable set `s`, then it is measurable at the filter
   `𝓝[s] x` for all `x`. -/
-theorem ContinuousOn.stronglyMeasurableAtFilterNhdsWithin {α β : Type _} [MeasurableSpace α]
+theorem ContinuousOn.stronglyMeasurableAtFilter_nhdsWithin {α β : Type _} [MeasurableSpace α]
     [TopologicalSpace α] [OpensMeasurableSpace α] [TopologicalSpace β] [PseudoMetrizableSpace β]
     [SecondCountableTopologyEither α β] {f : α → β} {s : Set α} {μ : Measure α}
     (hf : ContinuousOn f s) (hs : MeasurableSet s) (x : α) :
     StronglyMeasurableAtFilter f (𝓝[s] x) μ :=
   ⟨s, self_mem_nhdsWithin, hf.AeStronglyMeasurable hs⟩
-#align continuous_on.strongly_measurable_at_filter_nhds_within ContinuousOn.stronglyMeasurableAtFilterNhdsWithin
+#align continuous_on.strongly_measurable_at_filter_nhds_within ContinuousOn.stronglyMeasurableAtFilter_nhdsWithin
 
 /-! ### Lemmas about adding and removing interval boundaries
 

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.integrable_on
-! 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.
 -/
@@ -632,3 +632,132 @@ theorem ContinuousOn.stronglyMeasurableAtFilterNhdsWithin {α β : Type _} [Meas
   ⟨s, self_mem_nhdsWithin, hf.AeStronglyMeasurable hs⟩
 #align continuous_on.strongly_measurable_at_filter_nhds_within ContinuousOn.stronglyMeasurableAtFilterNhdsWithin
 
+/-! ### Lemmas about adding and removing interval boundaries
+
+The primed lemmas take explicit arguments about the measure being finite at the endpoint, while
+the unprimed ones use `[has_no_atoms μ]`.
+-/
+
+
+section PartialOrder
+
+variable [PartialOrder α] [MeasurableSingletonClass α] {f : α → E} {μ : Measure α} {a b : α}
+
+theorem integrableOn_Icc_iff_integrableOn_Ioc' (ha : μ {a} ≠ ∞) :
+    IntegrableOn f (Icc a b) μ ↔ IntegrableOn f (Ioc a b) μ :=
+  by
+  by_cases hab : a ≤ b
+  ·
+    rw [← Ioc_union_left hab, integrable_on_union,
+      eq_true (integrable_on_singleton_iff.mpr <| Or.inr ha.lt_top), and_true_iff]
+  · rw [Icc_eq_empty hab, Ioc_eq_empty]
+    contrapose! hab
+    exact hab.le
+#align integrable_on_Icc_iff_integrable_on_Ioc' integrableOn_Icc_iff_integrableOn_Ioc'
+
+theorem integrableOn_Icc_iff_integrableOn_Ico' (hb : μ {b} ≠ ∞) :
+    IntegrableOn f (Icc a b) μ ↔ IntegrableOn f (Ico a b) μ :=
+  by
+  by_cases hab : a ≤ b
+  ·
+    rw [← Ico_union_right hab, integrable_on_union,
+      eq_true (integrable_on_singleton_iff.mpr <| Or.inr hb.lt_top), and_true_iff]
+  · rw [Icc_eq_empty hab, Ico_eq_empty]
+    contrapose! hab
+    exact hab.le
+#align integrable_on_Icc_iff_integrable_on_Ico' integrableOn_Icc_iff_integrableOn_Ico'
+
+theorem integrableOn_Ico_iff_integrableOn_Ioo' (ha : μ {a} ≠ ∞) :
+    IntegrableOn f (Ico a b) μ ↔ IntegrableOn f (Ioo a b) μ :=
+  by
+  by_cases hab : a < b
+  ·
+    rw [← Ioo_union_left hab, integrable_on_union,
+      eq_true (integrable_on_singleton_iff.mpr <| Or.inr ha.lt_top), and_true_iff]
+  · rw [Ioo_eq_empty hab, Ico_eq_empty hab]
+#align integrable_on_Ico_iff_integrable_on_Ioo' integrableOn_Ico_iff_integrableOn_Ioo'
+
+theorem integrableOn_Ioc_iff_integrableOn_Ioo' (hb : μ {b} ≠ ∞) :
+    IntegrableOn f (Ioc a b) μ ↔ IntegrableOn f (Ioo a b) μ :=
+  by
+  by_cases hab : a < b
+  ·
+    rw [← Ioo_union_right hab, integrable_on_union,
+      eq_true (integrable_on_singleton_iff.mpr <| Or.inr hb.lt_top), and_true_iff]
+  · rw [Ioo_eq_empty hab, Ioc_eq_empty hab]
+#align integrable_on_Ioc_iff_integrable_on_Ioo' integrableOn_Ioc_iff_integrableOn_Ioo'
+
+theorem integrableOn_Icc_iff_integrableOn_Ioo' (ha : μ {a} ≠ ∞) (hb : μ {b} ≠ ∞) :
+    IntegrableOn f (Icc a b) μ ↔ IntegrableOn f (Ioo a b) μ := by
+  rw [integrableOn_Icc_iff_integrableOn_Ioc' ha, integrableOn_Ioc_iff_integrableOn_Ioo' hb]
+#align integrable_on_Icc_iff_integrable_on_Ioo' integrableOn_Icc_iff_integrableOn_Ioo'
+
+theorem integrableOn_Ici_iff_integrableOn_Ioi' (hb : μ {b} ≠ ∞) :
+    IntegrableOn f (Ici b) μ ↔ IntegrableOn f (Ioi b) μ := by
+  rw [← Ioi_union_left, integrable_on_union,
+    eq_true (integrable_on_singleton_iff.mpr <| Or.inr hb.lt_top), and_true_iff]
+#align integrable_on_Ici_iff_integrable_on_Ioi' integrableOn_Ici_iff_integrableOn_Ioi'
+
+theorem integrableOn_Iic_iff_integrableOn_Iio' (hb : μ {b} ≠ ∞) :
+    IntegrableOn f (Iic b) μ ↔ IntegrableOn f (Iio b) μ := by
+  rw [← Iio_union_right, integrable_on_union,
+    eq_true (integrable_on_singleton_iff.mpr <| Or.inr hb.lt_top), and_true_iff]
+#align integrable_on_Iic_iff_integrable_on_Iio' integrableOn_Iic_iff_integrableOn_Iio'
+
+variable [HasNoAtoms μ]
+
+theorem integrableOn_Icc_iff_integrableOn_Ioc :
+    IntegrableOn f (Icc a b) μ ↔ IntegrableOn f (Ioc a b) μ :=
+  integrableOn_Icc_iff_integrableOn_Ioc'
+    (by
+      rw [measure_singleton]
+      exact ENNReal.zero_ne_top)
+#align integrable_on_Icc_iff_integrable_on_Ioc integrableOn_Icc_iff_integrableOn_Ioc
+
+theorem integrableOn_Icc_iff_integrableOn_Ico :
+    IntegrableOn f (Icc a b) μ ↔ IntegrableOn f (Ico a b) μ :=
+  integrableOn_Icc_iff_integrableOn_Ico'
+    (by
+      rw [measure_singleton]
+      exact ENNReal.zero_ne_top)
+#align integrable_on_Icc_iff_integrable_on_Ico integrableOn_Icc_iff_integrableOn_Ico
+
+theorem integrableOn_Ico_iff_integrableOn_Ioo :
+    IntegrableOn f (Ico a b) μ ↔ IntegrableOn f (Ioo a b) μ :=
+  integrableOn_Ico_iff_integrableOn_Ioo'
+    (by
+      rw [measure_singleton]
+      exact ENNReal.zero_ne_top)
+#align integrable_on_Ico_iff_integrable_on_Ioo integrableOn_Ico_iff_integrableOn_Ioo
+
+theorem integrableOn_Ioc_iff_integrableOn_Ioo :
+    IntegrableOn f (Ioc a b) μ ↔ IntegrableOn f (Ioo a b) μ :=
+  integrableOn_Ioc_iff_integrableOn_Ioo'
+    (by
+      rw [measure_singleton]
+      exact ENNReal.zero_ne_top)
+#align integrable_on_Ioc_iff_integrable_on_Ioo integrableOn_Ioc_iff_integrableOn_Ioo
+
+theorem integrableOn_Icc_iff_integrableOn_Ioo :
+    IntegrableOn f (Icc a b) μ ↔ IntegrableOn f (Ioo a b) μ := by
+  rw [integrableOn_Icc_iff_integrableOn_Ioc, integrableOn_Ioc_iff_integrableOn_Ioo]
+#align integrable_on_Icc_iff_integrable_on_Ioo integrableOn_Icc_iff_integrableOn_Ioo
+
+theorem integrableOn_Ici_iff_integrableOn_Ioi :
+    IntegrableOn f (Ici b) μ ↔ IntegrableOn f (Ioi b) μ :=
+  integrableOn_Ici_iff_integrableOn_Ioi'
+    (by
+      rw [measure_singleton]
+      exact ENNReal.zero_ne_top)
+#align integrable_on_Ici_iff_integrable_on_Ioi integrableOn_Ici_iff_integrableOn_Ioi
+
+theorem integrableOn_Iic_iff_integrableOn_Iio :
+    IntegrableOn f (Iic b) μ ↔ IntegrableOn f (Iio b) μ :=
+  integrableOn_Iic_iff_integrableOn_Iio'
+    (by
+      rw [measure_singleton]
+      exact ENNReal.zero_ne_top)
+#align integrable_on_Iic_iff_integrable_on_Iio integrableOn_Iic_iff_integrableOn_Iio
+
+end PartialOrder
+

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.integrable_on
-! leanprover-community/mathlib commit a75898643b2d774cced9ae7c0b28c21663b99666
+! leanprover-community/mathlib commit 08a4542bec7242a5c60f179e4e49de8c0d677b1b
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -138,24 +138,30 @@ theorem IntegrableOn.congrSetAe (h : IntegrableOn f t μ) (hst : s =ᵐ[μ] t) :
   h.monoSetAe hst.le
 #align measure_theory.integrable_on.congr_set_ae MeasureTheory.IntegrableOn.congrSetAe
 
-theorem IntegrableOn.congrFun' (h : IntegrableOn f s μ) (hst : f =ᵐ[μ.restrict s] g) :
+theorem IntegrableOn.congrFunAe (h : IntegrableOn f s μ) (hst : f =ᵐ[μ.restrict s] g) :
     IntegrableOn g s μ :=
   Integrable.congr h hst
-#align measure_theory.integrable_on.congr_fun' MeasureTheory.IntegrableOn.congrFun'
+#align measure_theory.integrable_on.congr_fun_ae MeasureTheory.IntegrableOn.congrFunAe
+
+theorem integrableOn_congr_fun_ae (hst : f =ᵐ[μ.restrict s] g) :
+    IntegrableOn f s μ ↔ IntegrableOn g s μ :=
+  ⟨fun h => h.congrFunAe hst, fun h => h.congrFunAe hst.symm⟩
+#align measure_theory.integrable_on_congr_fun_ae MeasureTheory.integrableOn_congr_fun_ae
 
 theorem IntegrableOn.congrFun (h : IntegrableOn f s μ) (hst : EqOn f g s) (hs : MeasurableSet s) :
     IntegrableOn g s μ :=
-  h.congrFun' ((ae_restrict_iff' hs).2 (eventually_of_forall hst))
+  h.congrFunAe ((ae_restrict_iff' hs).2 (eventually_of_forall hst))
 #align measure_theory.integrable_on.congr_fun MeasureTheory.IntegrableOn.congrFun
 
+theorem integrableOn_congr_fun (hst : EqOn f g s) (hs : MeasurableSet s) :
+    IntegrableOn f s μ ↔ IntegrableOn g s μ :=
+  ⟨fun h => h.congr_fun hst hs, fun h => h.congr_fun hst.symm hs⟩
+#align measure_theory.integrable_on_congr_fun MeasureTheory.integrableOn_congr_fun
+
 theorem Integrable.integrableOn (h : Integrable f μ) : IntegrableOn f s μ :=
   h.monoMeasure <| Measure.restrict_le_self
 #align measure_theory.integrable.integrable_on MeasureTheory.Integrable.integrableOn
 
-theorem Integrable.integrableOn' (h : Integrable f (μ.restrict s)) : IntegrableOn f s μ :=
-  h
-#align measure_theory.integrable.integrable_on' MeasureTheory.Integrable.integrableOn'
-
 theorem IntegrableOn.restrict (h : IntegrableOn f s μ) (hs : MeasurableSet s) :
     IntegrableOn f s (μ.restrict t) :=
   by

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

@@ -352,7 +352,7 @@ theorem IntegrableOn.integrableOfAeNotMemEqZero (hf : IntegrableOn f s μ)
   filter_upwards [h't]with x hx h'x using hx h'x.2
 #align measure_theory.integrable_on.integrable_of_ae_not_mem_eq_zero MeasureTheory.IntegrableOn.integrableOfAeNotMemEqZero
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:628:2: warning: expanding binder collection (x «expr ∉ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x «expr ∉ » s) -/
 /-- If a function is integrable on a set `s` and vanishes everywhere on its complement,
 then it is integrable. -/
 theorem IntegrableOn.integrableOfForallNotMemEqZero (hf : IntegrableOn f s μ)

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

@@ -28,7 +28,7 @@ noncomputable section
 
 open Set Filter TopologicalSpace MeasureTheory Function
 
-open Classical Topology Interval BigOperators Filter Ennreal MeasureTheory
+open Classical Topology Interval BigOperators Filter ENNReal MeasureTheory
 
 variable {α β E F : Type _} [MeasurableSpace α]
 
@@ -258,7 +258,7 @@ theorem MeasurePreserving.integrableOn_image [MeasurableSpace β] {e : α → β
 theorem integrable_indicator_iff (hs : MeasurableSet s) :
     Integrable (indicator s f) μ ↔ IntegrableOn f s μ := by
   simp [integrable_on, integrable, has_finite_integral, nnnorm_indicator_eq_indicator_nnnorm,
-    Ennreal.coe_indicator, lintegral_indicator _ hs, aeStronglyMeasurable_indicator_iff hs]
+    ENNReal.coe_indicator, lintegral_indicator _ hs, aeStronglyMeasurable_indicator_iff hs]
 #align measure_theory.integrable_indicator_iff MeasureTheory.integrable_indicator_iff
 
 theorem IntegrableOn.integrableIndicator (h : IntegrableOn f s μ) (hs : MeasurableSet s) :
@@ -380,15 +380,15 @@ theorem integrableOnLpOfMeasureNeTop {E} [NormedAddCommGroup E] {p : ℝ≥0∞}
 #align measure_theory.integrable_on_Lp_of_measure_ne_top MeasureTheory.integrableOnLpOfMeasureNeTop
 
 theorem Integrable.lintegral_lt_top {f : α → ℝ} (hf : Integrable f μ) :
-    (∫⁻ x, Ennreal.ofReal (f x) ∂μ) < ∞ :=
+    (∫⁻ x, ENNReal.ofReal (f x) ∂μ) < ∞ :=
   calc
-    (∫⁻ x, Ennreal.ofReal (f x) ∂μ) ≤ ∫⁻ x, ↑‖f x‖₊ ∂μ := lintegral_ofReal_le_lintegral_nnnorm f
+    (∫⁻ x, ENNReal.ofReal (f x) ∂μ) ≤ ∫⁻ x, ↑‖f x‖₊ ∂μ := lintegral_ofReal_le_lintegral_nnnorm f
     _ < ∞ := hf.2
     
 #align measure_theory.integrable.lintegral_lt_top MeasureTheory.Integrable.lintegral_lt_top
 
 theorem IntegrableOn.set_lintegral_lt_top {f : α → ℝ} {s : Set α} (hf : IntegrableOn f s μ) :
-    (∫⁻ x in s, Ennreal.ofReal (f x) ∂μ) < ∞ :=
+    (∫⁻ x in s, ENNReal.ofReal (f x) ∂μ) < ∞ :=
   Integrable.lintegral_lt_top hf
 #align measure_theory.integrable_on.set_lintegral_lt_top MeasureTheory.IntegrableOn.set_lintegral_lt_top
 

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

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.

@@ -543,6 +543,22 @@ theorem integrable_add_of_disjoint {f g : α → E} (h : Disjoint (support f) (s
   · rw [← indicator_add_eq_right h]; exact hfg.indicator hg.measurableSet_support
 #align measure_theory.integrable_add_of_disjoint MeasureTheory.integrable_add_of_disjoint
 
+/-- If a function converges along a filter to a limit `a`, is integrable along this filter, and
+all elements of the filter have infinite measure, then the limit has to vanish. -/
+lemma IntegrableAtFilter.eq_zero_of_tendsto
+    (h : IntegrableAtFilter f l μ) (h' : ∀ s ∈ l, μ s = ∞) {a : E}
+    (hf : Tendsto f l (𝓝 a)) : a = 0 := by
+  by_contra H
+  obtain ⟨ε, εpos, hε⟩ : ∃ (ε : ℝ), 0 < ε ∧ ε < ‖a‖ := exists_between (norm_pos_iff'.mpr H)
+  rcases h with ⟨u, ul, hu⟩
+  let v := u ∩ {b | ε < ‖f b‖}
+  have hv : IntegrableOn f v μ := hu.mono_set (inter_subset_left _ _)
+  have vl : v ∈ l := inter_mem ul ((tendsto_order.1 hf.norm).1 _ hε)
+  have : μ.restrict v v < ∞ := lt_of_le_of_lt (measure_mono (inter_subset_right _ _))
+    (Integrable.measure_gt_lt_top hv.norm εpos)
+  have : μ v ≠ ∞ := ne_of_lt (by simpa only [Measure.restrict_apply_self])
+  exact this (h' v vl)
+
 end NormedAddCommGroup
 
 end MeasureTheory

Shortcuts for linearly ordered domains and/or continuous functions. As an example, I golf the existing integrable_of_isBigO_exp_neg.

Another example usage: https://github.com/AlexKontorovich/PrimeNumberTheoremAnd/blob/1909a40253607bd2df18a738fc504fe81b132974/PrimeNumberTheoremAnd/PerronFormula.lean#L414-L436

Co-authored-by: L Lllvvuu <git@llllvvuu.dev>

@@ -489,6 +489,12 @@ theorem integrableAtFilter_top : IntegrableAtFilter f ⊤ μ ↔ Integrable f μ
   obtain ⟨s, hsf, hs⟩ := h
   exact (integrableOn_iff_integrable_of_support_subset fun _ _ ↦ hsf _).mp hs
 
+theorem IntegrableAtFilter.sup_iff {l l' : Filter α} :
+    IntegrableAtFilter f (l ⊔ l') μ ↔ IntegrableAtFilter f l μ ∧ IntegrableAtFilter f l' μ := by
+  constructor
+  · exact fun h => ⟨h.filter_mono le_sup_left, h.filter_mono le_sup_right⟩
+  · exact fun ⟨⟨s, hsl, hs⟩, ⟨t, htl, ht⟩⟩ ↦ ⟨s ∪ t, union_mem_sup hsl htl, hs.union ht⟩
+
 /-- If `μ` is a measure finite at filter `l` and `f` is a function such that its norm is bounded
 above at `l`, then `f` is integrable at `l`. -/
 theorem Measure.FiniteAtFilter.integrableAtFilter {l : Filter α} [IsMeasurablyGenerated l]

@@ -310,7 +310,7 @@ theorem IntegrableOn.restrict_toMeasurable (hf : IntegrableOn f s μ) (h's : ∀
     exact (hf.measure_norm_ge_lt_top (u_pos n)).ne
   apply Measure.restrict_toMeasurable_of_cover _ A
   intro x hx
-  have : 0 < ‖f x‖ := by simp only [h's x hx, norm_pos_iff, Ne.def, not_false_iff]
+  have : 0 < ‖f x‖ := by simp only [h's x hx, norm_pos_iff, Ne, not_false_iff]
   obtain ⟨n, hn⟩ : ∃ n, u n < ‖f x‖ := ((tendsto_order.1 u_lim).2 _ this).exists
   exact mem_iUnion.2 ⟨n, subset_toMeasurable _ _ hn.le⟩
 #align measure_theory.integrable_on.restrict_to_measurable MeasureTheory.IntegrableOn.restrict_toMeasurable

These attributes are unused in Mathlib.

Many of them were workarounds for the now-resolved leanprover/lean4#2243; this also allows the lemmas themselves (hasFiniteIntegral_def, integrable_def, memℒp_def, and integrableOn_def) to be deleted.

We are currently experiencing problems with the @[eqns] attribute on the Lean nightlies. I'm uncertain yet what the outcome is going to be there, but it seems prudent to reduce our unnecessary exposure to a language feature added in Mathlib.

Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

@@ -91,13 +91,6 @@ def IntegrableOn (f : α → E) (s : Set α) (μ : Measure α := by volume_tac)
   Integrable f (μ.restrict s)
 #align measure_theory.integrable_on MeasureTheory.IntegrableOn
 
--- Porting note (#11215): TODO Delete this when leanprover/lean4#2243 is fixed.
-theorem integrableOn_def (f : α → E) (s : Set α) (μ : Measure α) :
-    IntegrableOn f s μ ↔ Integrable f (μ.restrict s) :=
-  Iff.rfl
-
-attribute [eqns integrableOn_def] IntegrableOn
-
 theorem IntegrableOn.integrable (h : IntegrableOn f s μ) : Integrable f (μ.restrict s) :=
   h
 #align measure_theory.integrable_on.integrable MeasureTheory.IntegrableOn.integrable

This PR establishes an easy topology comparison: the topology given by the Lévy-Prokhorov distance is finer than the topology of convergence in distribution.

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

@@ -531,6 +531,11 @@ alias _root_.Filter.Tendsto.integrableAtFilter :=
   Measure.FiniteAtFilter.integrableAtFilter_of_tendsto
 #align filter.tendsto.integrable_at_filter Filter.Tendsto.integrableAtFilter
 
+lemma Measure.integrableOn_of_bounded (s_finite : μ s ≠ ∞) (f_mble : AEStronglyMeasurable f μ)
+    {M : ℝ} (f_bdd : ∀ᵐ a ∂(μ.restrict s), ‖f a‖ ≤ M) :
+    IntegrableOn f s μ :=
+  ⟨f_mble.restrict, hasFiniteIntegral_restrict_of_bounded (C := M) s_finite.lt_top f_bdd⟩
+
 theorem integrable_add_of_disjoint {f g : α → E} (h : Disjoint (support f) (support g))
     (hf : StronglyMeasurable f) (hg : StronglyMeasurable g) :
     Integrable (f + g) μ ↔ Integrable f μ ∧ Integrable g μ := by

Classifies by adding issue number #11215 to porting notes claiming "TODO".

@@ -91,7 +91,7 @@ def IntegrableOn (f : α → E) (s : Set α) (μ : Measure α := by volume_tac)
   Integrable f (μ.restrict s)
 #align measure_theory.integrable_on MeasureTheory.IntegrableOn
 
--- Porting note: TODO Delete this when leanprover/lean4#2243 is fixed.
+-- Porting note (#11215): TODO Delete this when leanprover/lean4#2243 is fixed.
 theorem integrableOn_def (f : α → E) (s : Set α) (μ : Measure α) :
     IntegrableOn f s μ ↔ Integrable f (μ.restrict s) :=
   Iff.rfl

This covers many instances, but is not exhaustive.

Independently of whether that syntax should be avoided (similar to #10534), I think all these changes are small improvements.

@@ -318,9 +318,8 @@ theorem IntegrableOn.restrict_toMeasurable (hf : IntegrableOn f s μ) (h's : ∀
   apply Measure.restrict_toMeasurable_of_cover _ A
   intro x hx
   have : 0 < ‖f x‖ := by simp only [h's x hx, norm_pos_iff, Ne.def, not_false_iff]
-  obtain ⟨n, hn⟩ : ∃ n, u n < ‖f x‖; exact ((tendsto_order.1 u_lim).2 _ this).exists
-  refine' mem_iUnion.2 ⟨n, _⟩
-  exact subset_toMeasurable _ _ hn.le
+  obtain ⟨n, hn⟩ : ∃ n, u n < ‖f x‖ := ((tendsto_order.1 u_lim).2 _ this).exists
+  exact mem_iUnion.2 ⟨n, subset_toMeasurable _ _ hn.le⟩
 #align measure_theory.integrable_on.restrict_to_measurable MeasureTheory.IntegrableOn.restrict_toMeasurable
 
 /-- If a function is integrable on a set `s`, and vanishes on `t \ s`, then it is integrable on `t`

Redefine ≤ on MeasureTheory.Measure so that μ ≤ ν ↔ ∀ s, μ s ≤ ν s by definition instead of ∀ s, MeasurableSet s → μ s ≤ ν s.

Reasons

• this way it is defeq to ≤ on outer measures;
• if we decide to introduce an order on all DFunLike types and migrate measures to FunLike, then this is unavoidable;
• the reasoning for the old definition was "it's slightly easier to prove μ ≤ ν this way"; the counter-argument is "it's slightly harder to apply μ ≤ ν this way".

Other changes

• golf some proofs broken by this change;
• add @[gcongr] tags to some ENNReal lemmas;
• fix the name ENNReal.coe_lt_coe_of_le -> ENNReal.ENNReal.coe_lt_coe_of_lt;
• drop an unneeded MeasurableSet assumption in set_lintegral_pdf_le_map

@@ -482,13 +482,10 @@ theorem IntegrableAtFilter.inf_of_right (hl : IntegrableAtFilter f l μ) :
 @[simp]
 theorem IntegrableAtFilter.inf_ae_iff {l : Filter α} :
     IntegrableAtFilter f (l ⊓ μ.ae) μ ↔ IntegrableAtFilter f l μ := by
-  refine' ⟨_, fun h => h.filter_mono inf_le_left⟩
+  refine ⟨?_, fun h ↦ h.filter_mono inf_le_left⟩
   rintro ⟨s, ⟨t, ht, u, hu, rfl⟩, hf⟩
-  refine' ⟨t, ht, _⟩
-  refine' hf.integrable.mono_measure fun v hv => _
-  simp only [Measure.restrict_apply hv]
-  refine' measure_mono_ae (mem_of_superset hu fun x hx => _)
-  exact fun ⟨hv, ht⟩ => ⟨hv, ⟨ht, hx⟩⟩
+  refine ⟨t, ht, hf.congr_set_ae <| eventuallyEq_set.2 ?_⟩
+  filter_upwards [hu] with x hx using (and_iff_left hx).symm
 #align measure_theory.integrable_at_filter.inf_ae_iff MeasureTheory.IntegrableAtFilter.inf_ae_iff
 
 alias ⟨IntegrableAtFilter.of_inf_ae, _⟩ := IntegrableAtFilter.inf_ae_iff

part 1: corollaries such as for atTop ℝ yet to come

Co-authored-by: L Lllvvuu <git@llllvvuu.dev> Co-authored-by: L <git@llllvvuu.dev>

@@ -459,6 +459,10 @@ protected theorem IntegrableAtFilter.smul {𝕜 : Type*} [NormedAddCommGroup 
   rcases hf with ⟨s, sl, hs⟩
   exact ⟨s, sl, hs.smul c⟩
 
+protected theorem IntegrableAtFilter.norm (hf : IntegrableAtFilter f l μ) :
+    IntegrableAtFilter (fun x => ‖f x‖) l μ :=
+  Exists.casesOn hf fun s hs ↦ ⟨s, hs.1, hs.2.norm⟩
+
 theorem IntegrableAtFilter.filter_mono (hl : l ≤ l') (hl' : IntegrableAtFilter f l' μ) :
     IntegrableAtFilter f l μ :=
   let ⟨s, hs, hsf⟩ := hl'
@@ -490,6 +494,12 @@ theorem IntegrableAtFilter.inf_ae_iff {l : Filter α} :
 alias ⟨IntegrableAtFilter.of_inf_ae, _⟩ := IntegrableAtFilter.inf_ae_iff
 #align measure_theory.integrable_at_filter.of_inf_ae MeasureTheory.IntegrableAtFilter.of_inf_ae
 
+@[simp]
+theorem integrableAtFilter_top : IntegrableAtFilter f ⊤ μ ↔ Integrable f μ := by
+  refine ⟨fun h ↦ ?_, fun h ↦ h.integrableAtFilter ⊤⟩
+  obtain ⟨s, hsf, hs⟩ := h
+  exact (integrableOn_iff_integrable_of_support_subset fun _ _ ↦ hsf _).mp hs
+
 /-- If `μ` is a measure finite at filter `l` and `f` is a function such that its norm is bounded
 above at `l`, then `f` is integrable at `l`. -/
 theorem Measure.FiniteAtFilter.integrableAtFilter {l : Filter α} [IsMeasurablyGenerated l]

• upgrade isSeparable_iUnion to an Iff lemma, restore the original version as IsSeparable.iUnion;
• add isSeparable_union and isSeparable_closure;
• upgrade isSeparable_pi from [Finite ι] to [Countable ι], add IsSeparable.univ_pi version;
• add Dense.isSeparable_iff and isSeparable_range;
• rename isSeparable_of_separableSpace_subtype to IsSeparable.of_subtype;
• rename isSeparable_of_separableSpace to IsSeparable.of_separableSpace.

@@ -583,13 +583,9 @@ theorem ContinuousOn.aestronglyMeasurable [TopologicalSpace α] [TopologicalSpac
       ⟨hf.aemeasurable hs, f '' s, _,
         mem_of_superset (self_mem_ae_restrict hs) (subset_preimage_image _ _)⟩
   cases h.out
-  · let f' : s → β := s.restrict f
-    have A : Continuous f' := continuousOn_iff_continuous_restrict.1 hf
-    have B : IsSeparable (univ : Set s) := isSeparable_of_separableSpace _
-    convert IsSeparable.image B A using 1
-    ext x
-    simp
-  · exact isSeparable_of_separableSpace _
+  · rw [image_eq_range]
+    exact isSeparable_range <| continuousOn_iff_continuous_restrict.1 hf
+  · exact .of_separableSpace _
 #align continuous_on.ae_strongly_measurable ContinuousOn.aestronglyMeasurable
 
 /-- A function which is continuous on a compact set `s` is almost everywhere strongly measurable

A stronger version of #8800, the differences are:

• assume either IsSigmaCompact U or SigmaCompactSpace M;

• only need test functions satisfying tsupport g ⊆ U rather than support g ⊆ U;

• requires LocallyIntegrableOn U rather than LocallyIntegrable on the whole space.

Also fills in some missing APIs around the manifold and measure theory libraries.

Co-authored-by: sgouezel <sebastien.gouezel@univ-rennes1.fr> Co-authored-by: Junyan Xu <junyanxu.math@gmail.com>

@@ -169,6 +169,11 @@ theorem IntegrableOn.restrict (h : IntegrableOn f s μ) (hs : MeasurableSet s) :
   rw [IntegrableOn, Measure.restrict_restrict hs]; exact h.mono_set (inter_subset_left _ _)
 #align measure_theory.integrable_on.restrict MeasureTheory.IntegrableOn.restrict
 
+theorem IntegrableOn.inter_of_restrict (h : IntegrableOn f s (μ.restrict t)) :
+    IntegrableOn f (s ∩ t) μ := by
+  have := h.mono_set (inter_subset_left s t)
+  rwa [IntegrableOn, μ.restrict_restrict_of_subset (inter_subset_right s t)] at this
+
 lemma Integrable.piecewise [DecidablePred (· ∈ s)]
     (hs : MeasurableSet s) (hf : IntegrableOn f s μ) (hg : IntegrableOn g sᶜ μ) :
     Integrable (s.piecewise f g) μ := by
@@ -240,12 +245,18 @@ theorem integrableOn_add_measure :
 
 theorem _root_.MeasurableEmbedding.integrableOn_map_iff [MeasurableSpace β] {e : α → β}
     (he : MeasurableEmbedding e) {f : β → E} {μ : Measure α} {s : Set β} :
-    IntegrableOn f s (Measure.map e μ) ↔ IntegrableOn (f ∘ e) (e ⁻¹' s) μ := by
-  simp only [IntegrableOn, he.restrict_map, he.integrable_map_iff]
+    IntegrableOn f s (μ.map e) ↔ IntegrableOn (f ∘ e) (e ⁻¹' s) μ := by
+  simp_rw [IntegrableOn, he.restrict_map, he.integrable_map_iff]
 #align measurable_embedding.integrable_on_map_iff MeasurableEmbedding.integrableOn_map_iff
 
+theorem _root_.MeasurableEmbedding.integrableOn_iff_comap [MeasurableSpace β] {e : α → β}
+    (he : MeasurableEmbedding e) {f : β → E} {μ : Measure β} {s : Set β} (hs : s ⊆ range e) :
+    IntegrableOn f s μ ↔ IntegrableOn (f ∘ e) (e ⁻¹' s) (μ.comap e) := by
+  simp_rw [← he.integrableOn_map_iff, he.map_comap, IntegrableOn,
+    Measure.restrict_restrict_of_subset hs]
+
 theorem integrableOn_map_equiv [MeasurableSpace β] (e : α ≃ᵐ β) {f : β → E} {μ : Measure α}
-    {s : Set β} : IntegrableOn f s (Measure.map e μ) ↔ IntegrableOn (f ∘ e) (e ⁻¹' s) μ := by
+    {s : Set β} : IntegrableOn f s (μ.map e) ↔ IntegrableOn (f ∘ e) (e ⁻¹' s) μ := by
   simp only [IntegrableOn, e.restrict_map, integrable_map_equiv e]
 #align measure_theory.integrable_on_map_equiv MeasureTheory.integrableOn_map_equiv
 
@@ -397,6 +408,22 @@ def IntegrableAtFilter (f : α → E) (l : Filter α) (μ : Measure α := by vol
 
 variable {l l' : Filter α}
 
+theorem _root_.MeasurableEmbedding.integrableAtFilter_map_iff [MeasurableSpace β] {e : α → β}
+    (he : MeasurableEmbedding e) {f : β → E} :
+    IntegrableAtFilter f (l.map e) (μ.map e) ↔ IntegrableAtFilter (f ∘ e) l μ := by
+  simp_rw [IntegrableAtFilter, he.integrableOn_map_iff]
+  constructor <;> rintro ⟨s, hs⟩
+  · exact ⟨_, hs⟩
+  · exact ⟨e '' s, by rwa [mem_map, he.injective.preimage_image]⟩
+
+theorem _root_.MeasurableEmbedding.integrableAtFilter_iff_comap [MeasurableSpace β] {e : α → β}
+    (he : MeasurableEmbedding e) {f : β → E} {μ : Measure β} :
+    IntegrableAtFilter f (l.map e) μ ↔ IntegrableAtFilter (f ∘ e) l (μ.comap e) := by
+  simp_rw [← he.integrableAtFilter_map_iff, IntegrableAtFilter, he.map_comap]
+  constructor <;> rintro ⟨s, hs, int⟩
+  · exact ⟨s, hs, int.mono_measure <| μ.restrict_le_self⟩
+  · exact ⟨_, inter_mem hs range_mem_map, int.inter_of_restrict⟩
+
 theorem Integrable.integrableAtFilter (h : Integrable f μ) (l : Filter α) :
     IntegrableAtFilter f l μ :=
   ⟨univ, Filter.univ_mem, integrableOn_univ.2 h⟩

@@ -169,6 +169,13 @@ theorem IntegrableOn.restrict (h : IntegrableOn f s μ) (hs : MeasurableSet s) :
   rw [IntegrableOn, Measure.restrict_restrict hs]; exact h.mono_set (inter_subset_left _ _)
 #align measure_theory.integrable_on.restrict MeasureTheory.IntegrableOn.restrict
 
+lemma Integrable.piecewise [DecidablePred (· ∈ s)]
+    (hs : MeasurableSet s) (hf : IntegrableOn f s μ) (hg : IntegrableOn g sᶜ μ) :
+    Integrable (s.piecewise f g) μ := by
+  rw [IntegrableOn] at hf hg
+  rw [← memℒp_one_iff_integrable] at hf hg ⊢
+  exact Memℒp.piecewise hs hf hg
+
 theorem IntegrableOn.left_of_union (h : IntegrableOn f (s ∪ t) μ) : IntegrableOn f s μ :=
   h.mono_set <| subset_union_left _ _
 #align measure_theory.integrable_on.left_of_union MeasureTheory.IntegrableOn.left_of_union

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

@@ -423,7 +423,7 @@ protected theorem IntegrableAtFilter.smul {𝕜 : Type*} [NormedAddCommGroup 
     [BoundedSMul 𝕜 E] {f : α → E} (hf : IntegrableAtFilter f l μ) (c : 𝕜) :
     IntegrableAtFilter (c • f) l μ := by
   rcases hf with ⟨s, sl, hs⟩
-  refine ⟨s, sl, hs.smul c⟩
+  exact ⟨s, sl, hs.smul c⟩
 
 theorem IntegrableAtFilter.filter_mono (hl : l ≤ l') (hl' : IntegrableAtFilter f l' μ) :
     IntegrableAtFilter f l μ :=

mathport was forgetting a space in filter_upwards [...]with instead of filter_upwards [...] with.

@@ -191,7 +191,7 @@ theorem integrableOn_union : IntegrableOn f (s ∪ t) μ ↔ IntegrableOn f s μ
 theorem integrableOn_singleton_iff {x : α} [MeasurableSingletonClass α] :
     IntegrableOn f {x} μ ↔ f x = 0 ∨ μ {x} < ∞ := by
   have : f =ᵐ[μ.restrict {x}] fun _ => f x := by
-    filter_upwards [ae_restrict_mem (measurableSet_singleton x)]with _ ha
+    filter_upwards [ae_restrict_mem (measurableSet_singleton x)] with _ ha
     simp only [mem_singleton_iff.1 ha]
   rw [IntegrableOn, integrable_congr this, integrable_const_iff]
   simp
@@ -342,7 +342,7 @@ theorem IntegrableOn.integrable_of_ae_not_mem_eq_zero (hf : IntegrableOn f s μ)
     (h't : ∀ᵐ x ∂μ, x ∉ s → f x = 0) : Integrable f μ := by
   rw [← integrableOn_univ]
   apply hf.of_ae_diff_eq_zero nullMeasurableSet_univ
-  filter_upwards [h't]with x hx h'x using hx h'x.2
+  filter_upwards [h't] with x hx h'x using hx h'x.2
 #align measure_theory.integrable_on.integrable_of_ae_not_mem_eq_zero MeasureTheory.IntegrableOn.integrable_of_ae_not_mem_eq_zero
 
 /-- If a function is integrable on a set `s` and vanishes everywhere on its complement,

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>

@@ -296,7 +296,7 @@ theorem IntegrableOn.restrict_toMeasurable (hf : IntegrableOn f s μ) (h's : ∀
     intro n
     rw [inter_comm, ← Measure.restrict_apply (measurableSet_toMeasurable _ _),
       measure_toMeasurable]
-    exact (hf.measure_ge_lt_top (u_pos n)).ne
+    exact (hf.measure_norm_ge_lt_top (u_pos n)).ne
   apply Measure.restrict_toMeasurable_of_cover _ A
   intro x hx
   have : 0 < ‖f x‖ := by simp only [h's x hx, norm_pos_iff, Ne.def, not_false_iff]

Measure theory prerequisites for Rademacher theorem in #7003.

@@ -419,6 +419,12 @@ protected theorem IntegrableAtFilter.sub {f g : α → E}
   rw [sub_eq_add_neg]
   exact hf.add hg.neg
 
+protected theorem IntegrableAtFilter.smul {𝕜 : Type*} [NormedAddCommGroup 𝕜] [SMulZeroClass 𝕜 E]
+    [BoundedSMul 𝕜 E] {f : α → E} (hf : IntegrableAtFilter f l μ) (c : 𝕜) :
+    IntegrableAtFilter (c • f) l μ := by
+  rcases hf with ⟨s, sl, hs⟩
+  refine ⟨s, sl, hs.smul c⟩
+
 theorem IntegrableAtFilter.filter_mono (hl : l ≤ l') (hl' : IntegrableAtFilter f l' μ) :
     IntegrableAtFilter f l μ :=
   let ⟨s, hs, hsf⟩ := hl'

@@ -455,12 +455,11 @@ above at `l`, then `f` is integrable at `l`. -/
 theorem Measure.FiniteAtFilter.integrableAtFilter {l : Filter α} [IsMeasurablyGenerated l]
     (hfm : StronglyMeasurableAtFilter f l μ) (hμ : μ.FiniteAtFilter l)
     (hf : l.IsBoundedUnder (· ≤ ·) (norm ∘ f)) : IntegrableAtFilter f l μ := by
-  obtain ⟨C, hC⟩ : ∃ C, ∀ᶠ s in l.smallSets, ∀ x ∈ s, ‖f x‖ ≤ C
-  exact hf.imp fun C hC => eventually_smallSets.2 ⟨_, hC, fun t => id⟩
-  rcases(hfm.eventually.and (hμ.eventually.and hC)).exists_measurable_mem_of_smallSets with
+  obtain ⟨C, hC⟩ : ∃ C, ∀ᶠ s in l.smallSets, ∀ x ∈ s, ‖f x‖ ≤ C :=
+    hf.imp fun C hC => eventually_smallSets.2 ⟨_, hC, fun t => id⟩
+  rcases (hfm.eventually.and (hμ.eventually.and hC)).exists_measurable_mem_of_smallSets with
     ⟨s, hsl, hsm, hfm, hμ, hC⟩
-  refine' ⟨s, hsl, ⟨hfm, hasFiniteIntegral_restrict_of_bounded hμ _⟩⟩
-  exact C
+  refine' ⟨s, hsl, ⟨hfm, hasFiniteIntegral_restrict_of_bounded hμ (C := C) _⟩⟩
   rw [ae_restrict_eq hsm, eventually_inf_principal]
   exact eventually_of_forall hC
 #align measure_theory.measure.finite_at_filter.integrable_at_filter MeasureTheory.Measure.FiniteAtFilter.integrableAtFilter

@@ -447,7 +447,7 @@ theorem IntegrableAtFilter.inf_ae_iff {l : Filter α} :
   exact fun ⟨hv, ht⟩ => ⟨hv, ⟨ht, hx⟩⟩
 #align measure_theory.integrable_at_filter.inf_ae_iff MeasureTheory.IntegrableAtFilter.inf_ae_iff
 
-alias IntegrableAtFilter.inf_ae_iff ↔ IntegrableAtFilter.of_inf_ae _
+alias ⟨IntegrableAtFilter.of_inf_ae, _⟩ := IntegrableAtFilter.inf_ae_iff
 #align measure_theory.integrable_at_filter.of_inf_ae MeasureTheory.IntegrableAtFilter.of_inf_ae
 
 /-- If `μ` is a measure finite at filter `l` and `f` is a function such that its norm is bounded
@@ -472,8 +472,8 @@ theorem Measure.FiniteAtFilter.integrableAtFilter_of_tendsto_ae {l : Filter α}
       hf.norm.isBoundedUnder_le).of_inf_ae
 #align measure_theory.measure.finite_at_filter.integrable_at_filter_of_tendsto_ae MeasureTheory.Measure.FiniteAtFilter.integrableAtFilter_of_tendsto_ae
 
-alias Measure.FiniteAtFilter.integrableAtFilter_of_tendsto_ae ←
-  _root_.Filter.Tendsto.integrableAtFilter_ae
+alias _root_.Filter.Tendsto.integrableAtFilter_ae :=
+  Measure.FiniteAtFilter.integrableAtFilter_of_tendsto_ae
 #align filter.tendsto.integrable_at_filter_ae Filter.Tendsto.integrableAtFilter_ae
 
 theorem Measure.FiniteAtFilter.integrableAtFilter_of_tendsto {l : Filter α}
@@ -482,8 +482,8 @@ theorem Measure.FiniteAtFilter.integrableAtFilter_of_tendsto {l : Filter α}
   hμ.integrableAtFilter hfm hf.norm.isBoundedUnder_le
 #align measure_theory.measure.finite_at_filter.integrable_at_filter_of_tendsto MeasureTheory.Measure.FiniteAtFilter.integrableAtFilter_of_tendsto
 
-alias Measure.FiniteAtFilter.integrableAtFilter_of_tendsto ←
-  _root_.Filter.Tendsto.integrableAtFilter
+alias _root_.Filter.Tendsto.integrableAtFilter :=
+  Measure.FiniteAtFilter.integrableAtFilter_of_tendsto
 #align filter.tendsto.integrable_at_filter Filter.Tendsto.integrableAtFilter
 
 theorem integrable_add_of_disjoint {f g : α → E} (h : Disjoint (support f) (support g))

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

This has nice performance benefits.

@@ -27,7 +27,7 @@ open Set Filter TopologicalSpace MeasureTheory Function
 
 open scoped Classical Topology Interval BigOperators Filter ENNReal MeasureTheory
 
-variable {α β E F : Type _} [MeasurableSpace α]
+variable {α β E F : Type*} [MeasurableSpace α]
 
 section
 
@@ -616,7 +616,7 @@ theorem Continuous.stronglyMeasurableAtFilter [TopologicalSpace α] [OpensMeasur
 
 /-- If a function is continuous on a measurable set `s`, then it is measurable at the filter
   `𝓝[s] x` for all `x`. -/
-theorem ContinuousOn.stronglyMeasurableAtFilter_nhdsWithin {α β : Type _} [MeasurableSpace α]
+theorem ContinuousOn.stronglyMeasurableAtFilter_nhdsWithin {α β : Type*} [MeasurableSpace α]
     [TopologicalSpace α] [OpensMeasurableSpace α] [TopologicalSpace β] [PseudoMetrizableSpace β]
     [SecondCountableTopologyEither α β] {f : α → β} {s : Set α} {μ : Measure α}
     (hf : ContinuousOn f s) (hs : MeasurableSet s) (x : α) :

@@ -46,7 +46,7 @@ theorem stronglyMeasurableAt_bot {f : α → β} : StronglyMeasurableAtFilter f
 
 protected theorem StronglyMeasurableAtFilter.eventually (h : StronglyMeasurableAtFilter f l μ) :
     ∀ᶠ s in l.smallSets, AEStronglyMeasurable f (μ.restrict s) :=
-  (eventually_small_sets' fun _ _ => AEStronglyMeasurable.mono_set).2 h
+  (eventually_smallSets' fun _ _ => AEStronglyMeasurable.mono_set).2 h
 #align strongly_measurable_at_filter.eventually StronglyMeasurableAtFilter.eventually
 
 protected theorem StronglyMeasurableAtFilter.filter_mono (h : StronglyMeasurableAtFilter f l μ)
@@ -397,7 +397,7 @@ theorem Integrable.integrableAtFilter (h : Integrable f μ) (l : Filter α) :
 
 protected theorem IntegrableAtFilter.eventually (h : IntegrableAtFilter f l μ) :
     ∀ᶠ s in l.smallSets, IntegrableOn f s μ :=
-  Iff.mpr (eventually_small_sets' fun _s _t hst ht => ht.mono_set hst) h
+  Iff.mpr (eventually_smallSets' fun _s _t hst ht => ht.mono_set hst) h
 #align measure_theory.integrable_at_filter.eventually MeasureTheory.IntegrableAtFilter.eventually
 
 protected theorem IntegrableAtFilter.add {f g : α → E}

We show that, if a locally integrable function has zero integral on all compact sets, then it vanishes almost everywhere.

@@ -400,6 +400,25 @@ protected theorem IntegrableAtFilter.eventually (h : IntegrableAtFilter f l μ)
   Iff.mpr (eventually_small_sets' fun _s _t hst ht => ht.mono_set hst) h
 #align measure_theory.integrable_at_filter.eventually MeasureTheory.IntegrableAtFilter.eventually
 
+protected theorem IntegrableAtFilter.add {f g : α → E}
+    (hf : IntegrableAtFilter f l μ) (hg : IntegrableAtFilter g l μ) :
+    IntegrableAtFilter (f + g) l μ := by
+  rcases hf with ⟨s, sl, hs⟩
+  rcases hg with ⟨t, tl, ht⟩
+  refine ⟨s ∩ t, inter_mem sl tl, ?_⟩
+  exact (hs.mono_set (inter_subset_left _ _)).add (ht.mono_set (inter_subset_right _ _))
+
+protected theorem IntegrableAtFilter.neg {f : α → E} (hf : IntegrableAtFilter f l μ) :
+    IntegrableAtFilter (-f) l μ := by
+  rcases hf with ⟨s, sl, hs⟩
+  exact ⟨s, sl, hs.neg⟩
+
+protected theorem IntegrableAtFilter.sub {f g : α → E}
+    (hf : IntegrableAtFilter f l μ) (hg : IntegrableAtFilter g l μ) :
+    IntegrableAtFilter (f - g) l μ := by
+  rw [sub_eq_add_neg]
+  exact hf.add hg.neg
+
 theorem IntegrableAtFilter.filter_mono (hl : l ≤ l') (hl' : IntegrableAtFilter f l' μ) :
     IntegrableAtFilter f l μ :=
   let ⟨s, hs, hsf⟩ := hl'

• depends on: #5966

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

@@ -2,15 +2,12 @@
 Copyright (c) 2021 Rémy Degenne. 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.integrable_on
-! leanprover-community/mathlib commit 8b8ba04e2f326f3f7cf24ad129beda58531ada61
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.MeasureTheory.Function.L1Space
 import Mathlib.Analysis.NormedSpace.IndicatorFunction
 
+#align_import measure_theory.integral.integrable_on from "leanprover-community/mathlib"@"8b8ba04e2f326f3f7cf24ad129beda58531ada61"
+
 /-! # Functions integrable on a set and at a filter
 
 We define `IntegrableOn f s μ := Integrable f (μ.restrict s)` and prove theorems like

I have misported is_foo to Foo because I misunderstood the rule for IsLawfulFoo. This PR recover Is of Foo which is ported from is_foo. This PR also renames some misported theorems.

@@ -82,7 +82,7 @@ section NormedAddCommGroup
 theorem hasFiniteIntegral_restrict_of_bounded [NormedAddCommGroup E] {f : α → E} {s : Set α}
     {μ : Measure α} {C} (hs : μ s < ∞) (hf : ∀ᵐ x ∂μ.restrict s, ‖f x‖ ≤ C) :
     HasFiniteIntegral f (μ.restrict s) :=
-  haveI : FiniteMeasure (μ.restrict s) := ⟨by rwa [Measure.restrict_apply_univ]⟩
+  haveI : IsFiniteMeasure (μ.restrict s) := ⟨by rwa [Measure.restrict_apply_univ]⟩
   hasFiniteIntegral_of_bounded hf
 #align measure_theory.has_finite_integral_restrict_of_bounded MeasureTheory.hasFiniteIntegral_restrict_of_bounded
 
@@ -368,7 +368,7 @@ theorem integrableOn_Lp_of_measure_ne_top {E} [NormedAddCommGroup E] {p : ℝ≥
   refine' memℒp_one_iff_integrable.mp _
   have hμ_restrict_univ : (μ.restrict s) Set.univ < ∞ := by
     simpa only [Set.univ_inter, MeasurableSet.univ, Measure.restrict_apply, lt_top_iff_ne_top]
-  haveI hμ_finite : FiniteMeasure (μ.restrict s) := ⟨hμ_restrict_univ⟩
+  haveI hμ_finite : IsFiniteMeasure (μ.restrict s) := ⟨hμ_restrict_univ⟩
   exact ((Lp.memℒp _).restrict s).memℒp_of_exponent_le hp
 set_option linter.uppercaseLean3 false in
 #align measure_theory.integrable_on_Lp_of_measure_ne_top MeasureTheory.integrableOn_Lp_of_measure_ne_top
@@ -552,7 +552,7 @@ theorem ContinuousOn.aestronglyMeasurable_of_isCompact [TopologicalSpace α] [Op
 #align continuous_on.ae_strongly_measurable_of_is_compact ContinuousOn.aestronglyMeasurable_of_isCompact
 
 theorem ContinuousOn.integrableAt_nhdsWithin_of_isSeparable [TopologicalSpace α]
-    [PseudoMetrizableSpace α] [OpensMeasurableSpace α] {μ : Measure α} [LocallyFiniteMeasure μ]
+    [PseudoMetrizableSpace α] [OpensMeasurableSpace α] {μ : Measure α} [IsLocallyFiniteMeasure μ]
     {a : α} {t : Set α} {f : α → E} (hft : ContinuousOn f t) (ht : MeasurableSet t)
     (h't : TopologicalSpace.IsSeparable t) (ha : a ∈ t) : IntegrableAtFilter f (𝓝[t] a) μ :=
   haveI : (𝓝[t] a).IsMeasurablyGenerated := ht.nhdsWithin_isMeasurablyGenerated _
@@ -563,7 +563,7 @@ theorem ContinuousOn.integrableAt_nhdsWithin_of_isSeparable [TopologicalSpace α
 
 theorem ContinuousOn.integrableAt_nhdsWithin [TopologicalSpace α]
     [SecondCountableTopologyEither α E] [OpensMeasurableSpace α] {μ : Measure α}
-    [LocallyFiniteMeasure μ] {a : α} {t : Set α} {f : α → E} (hft : ContinuousOn f t)
+    [IsLocallyFiniteMeasure μ] {a : α} {t : Set α} {f : α → E} (hft : ContinuousOn f t)
     (ht : MeasurableSet t) (ha : a ∈ t) : IntegrableAtFilter f (𝓝[t] a) μ :=
   haveI : (𝓝[t] a).IsMeasurablyGenerated := ht.nhdsWithin_isMeasurablyGenerated _
   (hft a ha).integrableAtFilter ⟨_, self_mem_nhdsWithin, hft.aestronglyMeasurable ht⟩
@@ -571,7 +571,7 @@ theorem ContinuousOn.integrableAt_nhdsWithin [TopologicalSpace α]
 #align continuous_on.integrable_at_nhds_within ContinuousOn.integrableAt_nhdsWithin
 
 theorem Continuous.integrableAt_nhds [TopologicalSpace α] [SecondCountableTopologyEither α E]
-    [OpensMeasurableSpace α] {μ : Measure α} [LocallyFiniteMeasure μ] {f : α → E}
+    [OpensMeasurableSpace α] {μ : Measure α} [IsLocallyFiniteMeasure μ] {f : α → E}
     (hf : Continuous f) (a : α) : IntegrableAtFilter f (𝓝 a) μ := by
   rw [← nhdsWithin_univ]
   exact hf.continuousOn.integrableAt_nhdsWithin MeasurableSet.univ (mem_univ a)