measure_theory.integral.interval_integral ⟷ Mathlib.MeasureTheory.Integral.IntervalIntegral

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

@@ -3,7 +3,7 @@ Copyright (c) 2020 Yury G. Kudryashov. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury G. Kudryashov, Patrick Massot, Sébastien Gouëzel
 -/
-import Data.Set.Intervals.Disjoint
+import Order.Interval.Set.Disjoint
 import MeasureTheory.Integral.SetIntegral
 import MeasureTheory.Measure.Lebesgue.Basic
 

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

@@ -1782,7 +1782,7 @@ theorem abs_integral_mono_interval {c d} (h : Ι a b ⊆ Ι c d) (hf : 0 ≤ᵐ[
   calc
     |∫ x in a..b, f x ∂μ| = |∫ x in Ι a b, f x ∂μ| := abs_integral_eq_abs_integral_uIoc f
     _ = ∫ x in Ι a b, f x ∂μ := (abs_of_nonneg (MeasureTheory.integral_nonneg_of_ae hf'))
-    _ ≤ ∫ x in Ι c d, f x ∂μ := (set_integral_mono_set hfi.def hf h.EventuallyLE)
+    _ ≤ ∫ x in Ι c d, f x ∂μ := (setIntegral_mono_set hfi.def hf h.EventuallyLE)
     _ ≤ |∫ x in Ι c d, f x ∂μ| := (le_abs_self _)
     _ = |∫ x in c..d, f x ∂μ| := (abs_integral_eq_abs_integral_uIoc f).symm
 #align interval_integral.abs_integral_mono_interval intervalIntegral.abs_integral_mono_interval
@@ -1801,7 +1801,7 @@ theorem MeasureTheory.Integrable.hasSum_intervalIntegral (hfi : Integrable f μ)
     HasSum (fun n : ℤ => ∫ x in y + n..y + n + 1, f x ∂μ) (∫ x, f x ∂μ) :=
   by
   simp_rw [integral_of_le (le_add_of_nonneg_right zero_le_one)]
-  rw [← integral_univ, ← iUnion_Ioc_add_int_cast y]
+  rw [← integral_univ, ← iUnion_Ioc_add_intCast y]
   exact
     has_sum_integral_Union (fun i => measurableSet_Ioc) (pairwise_disjoint_Ioc_add_int_cast y)
       hfi.integrable_on

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

@@ -89,12 +89,12 @@ theorem intervalIntegrable_iff : IntervalIntegrable f μ a b ↔ IntegrableOn f
 #align interval_integrable_iff intervalIntegrable_iff
 -/
 
-#print IntervalIntegrable.def /-
+#print IntervalIntegrable.def' /-
 /-- If a function is interval integrable with respect to a given measure `μ` on `a..b` then
   it is integrable on `uIoc a b` with respect to `μ`. -/
-theorem IntervalIntegrable.def (h : IntervalIntegrable f μ a b) : IntegrableOn f (Ι a b) μ :=
+theorem IntervalIntegrable.def' (h : IntervalIntegrable f μ a b) : IntegrableOn f (Ι a b) μ :=
   intervalIntegrable_iff.mp h
-#align interval_integrable.def IntervalIntegrable.def
+#align interval_integrable.def IntervalIntegrable.def'
 -/
 
 #print intervalIntegrable_iff_integrableOn_Ioc_of_le /-
@@ -778,7 +778,7 @@ theorem integral_smul {𝕜 : Type _} [NontriviallyNormedField 𝕜] [NormedSpac
 
 #print intervalIntegral.integral_smul_const /-
 @[simp]
-theorem integral_smul_const {𝕜 : Type _} [IsROrC 𝕜] [NormedSpace 𝕜 E] (f : ℝ → 𝕜) (c : E) :
+theorem integral_smul_const {𝕜 : Type _} [RCLike 𝕜] [NormedSpace 𝕜 E] (f : ℝ → 𝕜) (c : E) :
     ∫ x in a..b, f x • c ∂μ = (∫ x in a..b, f x ∂μ) • c := by
   simp only [interval_integral_eq_integral_uIoc, integral_smul_const, smul_assoc]
 #align interval_integral.integral_smul_const intervalIntegral.integral_smul_const
@@ -786,7 +786,7 @@ theorem integral_smul_const {𝕜 : Type _} [IsROrC 𝕜] [NormedSpace 𝕜 E] (
 
 #print intervalIntegral.integral_const_mul /-
 @[simp]
-theorem integral_const_mul {𝕜 : Type _} [IsROrC 𝕜] (r : 𝕜) (f : ℝ → 𝕜) :
+theorem integral_const_mul {𝕜 : Type _} [RCLike 𝕜] (r : 𝕜) (f : ℝ → 𝕜) :
     ∫ x in a..b, r * f x ∂μ = r * ∫ x in a..b, f x ∂μ :=
   integral_smul r f
 #align interval_integral.integral_const_mul intervalIntegral.integral_const_mul
@@ -794,7 +794,7 @@ theorem integral_const_mul {𝕜 : Type _} [IsROrC 𝕜] (r : 𝕜) (f : ℝ →
 
 #print intervalIntegral.integral_mul_const /-
 @[simp]
-theorem integral_mul_const {𝕜 : Type _} [IsROrC 𝕜] (r : 𝕜) (f : ℝ → 𝕜) :
+theorem integral_mul_const {𝕜 : Type _} [RCLike 𝕜] (r : 𝕜) (f : ℝ → 𝕜) :
     ∫ x in a..b, f x * r ∂μ = (∫ x in a..b, f x ∂μ) * r := by
   simpa only [mul_comm r] using integral_const_mul r f
 #align interval_integral.integral_mul_const intervalIntegral.integral_mul_const
@@ -802,7 +802,7 @@ theorem integral_mul_const {𝕜 : Type _} [IsROrC 𝕜] (r : 𝕜) (f : ℝ →
 
 #print intervalIntegral.integral_div /-
 @[simp]
-theorem integral_div {𝕜 : Type _} [IsROrC 𝕜] (r : 𝕜) (f : ℝ → 𝕜) :
+theorem integral_div {𝕜 : Type _} [RCLike 𝕜] (r : 𝕜) (f : ℝ → 𝕜) :
     ∫ x in a..b, f x / r ∂μ = (∫ x in a..b, f x ∂μ) / r := by
   simpa only [div_eq_mul_inv] using integral_mul_const r⁻¹ f
 #align interval_integral.integral_div intervalIntegral.integral_div
@@ -843,7 +843,7 @@ section ContinuousLinearMap
 
 variable {a b : ℝ} {μ : Measure ℝ} {f : ℝ → E}
 
-variable [IsROrC 𝕜] [NormedSpace 𝕜 E] [NormedAddCommGroup F] [NormedSpace 𝕜 F]
+variable [RCLike 𝕜] [NormedSpace 𝕜 E] [NormedAddCommGroup F] [NormedSpace 𝕜 F]
 
 open ContinuousLinearMap
 
@@ -881,8 +881,8 @@ theorem integral_comp_mul_right (hc : c ≠ 0) :
   simp_rw [integral_smul_measure, intervalIntegral, A.set_integral_map,
     ENNReal.toReal_ofReal (abs_nonneg c)]
   cases hc.lt_or_lt
-  · simp [h, mul_div_cancel, hc, abs_of_neg, measure.restrict_congr_set Ico_ae_eq_Ioc]
-  · simp [h, mul_div_cancel, hc, abs_of_pos]
+  · simp [h, mul_div_cancel_right₀, hc, abs_of_neg, measure.restrict_congr_set Ico_ae_eq_Ioc]
+  · simp [h, mul_div_cancel_right₀, hc, abs_of_pos]
 #align interval_integral.integral_comp_mul_right intervalIntegral.integral_comp_mul_right
 -/
 

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

@@ -402,7 +402,7 @@ theorem comp_add_right (hf : IntervalIntegrable f volume a b) (c : ℝ) :
     (Homeomorph.addRight c).ClosedEmbedding.MeasurableEmbedding
   have Am : measure.map (fun x => x + c) volume = volume :=
     is_add_left_invariant.is_add_right_invariant.map_add_right_eq_self _
-  rw [← Am] at hf 
+  rw [← Am] at hf
   convert (MeasurableEmbedding.integrableOn_map_iff A).mp hf
   rw [preimage_add_const_uIcc]
 #align interval_integrable.comp_add_right IntervalIntegrable.comp_add_right
@@ -1238,7 +1238,7 @@ theorem integral_eq_integral_of_support_subset {a b} (h : support f ⊆ Ioc a b)
   ·
     rw [integral_of_le hab, ← integral_indicator measurableSet_Ioc, indicator_eq_self.2 h] <;>
       infer_instance
-  · rw [Ioc_eq_empty hab.not_lt, subset_empty_iff, support_eq_empty_iff] at h 
+  · rw [Ioc_eq_empty hab.not_lt, subset_empty_iff, support_eq_empty_iff] at h
     simp [h]
 #align interval_integral.integral_eq_integral_of_support_subset intervalIntegral.integral_eq_integral_of_support_subset
 -/
@@ -1607,12 +1607,12 @@ theorem integral_pos_iff_support_of_nonneg_ae' (hf : 0 ≤ᵐ[μ.restrict (Ι a
     0 < ∫ x in a..b, f x ∂μ ↔ a < b ∧ 0 < μ (support f ∩ Ioc a b) :=
   by
   cases' lt_or_le a b with hab hba
-  · rw [uIoc_of_le hab.le] at hf 
+  · rw [uIoc_of_le hab.le] at hf
     simp only [hab, true_and_iff, integral_of_le hab.le,
       set_integral_pos_iff_support_of_nonneg_ae hf hfi.1]
   · suffices ∫ x in a..b, f x ∂μ ≤ 0 by simp only [this.not_lt, hba.not_lt, false_and_iff]
     rw [integral_of_ge hba, neg_nonpos]
-    rw [uIoc_swap, uIoc_of_le hba] at hf 
+    rw [uIoc_swap, uIoc_of_le hba] at hf
     exact integral_nonneg_of_ae hf
 #align interval_integral.integral_pos_iff_support_of_nonneg_ae' intervalIntegral.integral_pos_iff_support_of_nonneg_ae'
 -/
@@ -1688,11 +1688,11 @@ theorem integral_lt_integral_of_continuousOn_of_le_of_exists_lt {f g : ℝ → 
   contrapose! hlt
   have h_eq : f =ᵐ[volume.restrict (Ioc a b)] g :=
     by
-    simp only [← not_le, ← ae_iff] at hlt 
+    simp only [← not_le, ← ae_iff] at hlt
     exact
       eventually_le.antisymm ((ae_restrict_iff' measurableSet_Ioc).2 <| eventually_of_forall hle)
         hlt
-  simp only [measure.restrict_congr_set Ioc_ae_eq_Icc] at h_eq 
+  simp only [measure.restrict_congr_set Ioc_ae_eq_Icc] at h_eq
   exact fun c hc => (measure.eq_on_Icc_of_ae_eq volume hab.ne h_eq hfc hgc hc).ge
 #align interval_integral.integral_lt_integral_of_continuous_on_of_le_of_exists_lt intervalIntegral.integral_lt_integral_of_continuousOn_of_le_of_exists_lt
 -/

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

@@ -97,11 +97,11 @@ theorem IntervalIntegrable.def (h : IntervalIntegrable f μ a b) : IntegrableOn
 #align interval_integrable.def IntervalIntegrable.def
 -/
 
-#print intervalIntegrable_iff_integrable_Ioc_of_le /-
-theorem intervalIntegrable_iff_integrable_Ioc_of_le (hab : a ≤ b) :
+#print intervalIntegrable_iff_integrableOn_Ioc_of_le /-
+theorem intervalIntegrable_iff_integrableOn_Ioc_of_le (hab : a ≤ b) :
     IntervalIntegrable f μ a b ↔ IntegrableOn f (Ioc a b) μ := by
   rw [intervalIntegrable_iff, uIoc_of_le hab]
-#align interval_integrable_iff_integrable_Ioc_of_le intervalIntegrable_iff_integrable_Ioc_of_le
+#align interval_integrable_iff_integrable_Ioc_of_le intervalIntegrable_iff_integrableOn_Ioc_of_le
 -/
 
 #print intervalIntegrable_iff' /-
@@ -111,11 +111,11 @@ theorem intervalIntegrable_iff' [NoAtoms μ] :
 #align interval_integrable_iff' intervalIntegrable_iff'
 -/
 
-#print intervalIntegrable_iff_integrable_Icc_of_le /-
-theorem intervalIntegrable_iff_integrable_Icc_of_le {f : ℝ → E} {a b : ℝ} (hab : a ≤ b)
+#print intervalIntegrable_iff_integrableOn_Icc_of_le /-
+theorem intervalIntegrable_iff_integrableOn_Icc_of_le {f : ℝ → E} {a b : ℝ} (hab : a ≤ b)
     {μ : Measure ℝ} [NoAtoms μ] : IntervalIntegrable f μ a b ↔ IntegrableOn f (Icc a b) μ := by
-  rw [intervalIntegrable_iff_integrable_Ioc_of_le hab, integrableOn_Icc_iff_integrableOn_Ioc]
-#align interval_integrable_iff_integrable_Icc_of_le intervalIntegrable_iff_integrable_Icc_of_le
+  rw [intervalIntegrable_iff_integrableOn_Ioc_of_le hab, integrableOn_Icc_iff_integrableOn_Ioc]
+#align interval_integrable_iff_integrable_Icc_of_le intervalIntegrable_iff_integrableOn_Icc_of_le
 -/
 
 #print MeasureTheory.Integrable.intervalIntegrable /-
@@ -1505,7 +1505,7 @@ theorem continuousOn_primitive [NoAtoms μ] (h_int : IntegrableOn f (Icc a b) μ
     rw [continuousOn_congr this]
     intro x₀ hx₀
     refine' continuous_within_at_primitive (measure_singleton x₀) _
-    simp only [intervalIntegrable_iff_integrable_Ioc_of_le, min_eq_left, max_eq_right, h]
+    simp only [intervalIntegrable_iff_integrableOn_Ioc_of_le, min_eq_left, max_eq_right, h]
     exact h_int.mono Ioc_subset_Icc_self le_rfl
   · rw [Icc_eq_empty h]
     exact continuousOn_empty _

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

@@ -1336,7 +1336,7 @@ theorem hasSum_intervalIntegral_of_summable_norm [Countable ι] {f : ι → C(
       (ae_of_all _ fun x hx => hf_sum) intervalIntegrable_const
       (ae_of_all _ fun x hx => Summable.hasSum _)
   -- next line is slow, & doesn't work with "exact" in place of "apply" -- ?
-  apply ContinuousMap.summable_apply (summable_of_summable_norm hf_sum) ⟨x, ⟨hx.1.le, hx.2⟩⟩
+  apply ContinuousMap.summable_apply (Summable.of_norm hf_sum) ⟨x, ⟨hx.1.le, hx.2⟩⟩
 #align interval_integral.has_sum_interval_integral_of_summable_norm intervalIntegral.hasSum_intervalIntegral_of_summable_norm
 -/
 

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

@@ -3,9 +3,9 @@ Copyright (c) 2020 Yury G. Kudryashov. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury G. Kudryashov, Patrick Massot, Sébastien Gouëzel
 -/
-import Mathbin.Data.Set.Intervals.Disjoint
-import Mathbin.MeasureTheory.Integral.SetIntegral
-import Mathbin.MeasureTheory.Measure.Lebesgue.Basic
+import Data.Set.Intervals.Disjoint
+import MeasureTheory.Integral.SetIntegral
+import MeasureTheory.Measure.Lebesgue.Basic
 
 #align_import measure_theory.integral.interval_integral from "leanprover-community/mathlib"@"7e5137f579de09a059a5ce98f364a04e221aabf0"
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/442a83d738cb208d3600056c489be16900ba701d

@@ -284,11 +284,11 @@ protected theorem aestronglyMeasurable (h : IntervalIntegrable f μ a b) :
 #align interval_integrable.ae_strongly_measurable IntervalIntegrable.aestronglyMeasurable
 -/
 
-#print IntervalIntegrable.ae_strongly_measurable' /-
-protected theorem ae_strongly_measurable' (h : IntervalIntegrable f μ a b) :
+#print IntervalIntegrable.aestronglyMeasurable' /-
+protected theorem aestronglyMeasurable' (h : IntervalIntegrable f μ a b) :
     AEStronglyMeasurable f (μ.restrict (Ioc b a)) :=
   h.2.AEStronglyMeasurable
-#align interval_integrable.ae_strongly_measurable' IntervalIntegrable.ae_strongly_measurable'
+#align interval_integrable.ae_strongly_measurable' IntervalIntegrable.aestronglyMeasurable'
 -/
 
 end

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

@@ -2,16 +2,13 @@
 Copyright (c) 2020 Yury G. Kudryashov. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury G. Kudryashov, Patrick Massot, Sébastien Gouëzel
-
-! This file was ported from Lean 3 source module measure_theory.integral.interval_integral
-! leanprover-community/mathlib commit 7e5137f579de09a059a5ce98f364a04e221aabf0
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Data.Set.Intervals.Disjoint
 import Mathbin.MeasureTheory.Integral.SetIntegral
 import Mathbin.MeasureTheory.Measure.Lebesgue.Basic
 
+#align_import measure_theory.integral.interval_integral from "leanprover-community/mathlib"@"7e5137f579de09a059a5ce98f364a04e221aabf0"
+
 /-!
 # Integral over an interval
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/9240e8be927a0955b9a82c6c85ef499ee3a626b8

@@ -379,7 +379,7 @@ theorem comp_mul_left (hf : IntervalIntegrable f volume a b) (c : ℝ) :
   have A : MeasurableEmbedding fun x => x * c⁻¹ :=
     (Homeomorph.mulRight₀ _ (inv_ne_zero hc)).ClosedEmbedding.MeasurableEmbedding
   rw [← Real.smul_map_volume_mul_right (inv_ne_zero hc), integrable_on, measure.restrict_smul,
-    integrable_smul_measure (by simpa : ENNReal.ofReal (|c⁻¹|) ≠ 0) ENNReal.ofReal_ne_top, ←
+    integrable_smul_measure (by simpa : ENNReal.ofReal |c⁻¹| ≠ 0) ENNReal.ofReal_ne_top, ←
     integrable_on, MeasurableEmbedding.integrableOn_map_iff A]
   convert hf using 1
   · ext; simp only [comp_app]; congr 1; field_simp; ring

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

@@ -100,10 +100,12 @@ theorem IntervalIntegrable.def (h : IntervalIntegrable f μ a b) : IntegrableOn
 #align interval_integrable.def IntervalIntegrable.def
 -/
 
+#print intervalIntegrable_iff_integrable_Ioc_of_le /-
 theorem intervalIntegrable_iff_integrable_Ioc_of_le (hab : a ≤ b) :
     IntervalIntegrable f μ a b ↔ IntegrableOn f (Ioc a b) μ := by
   rw [intervalIntegrable_iff, uIoc_of_le hab]
 #align interval_integrable_iff_integrable_Ioc_of_le intervalIntegrable_iff_integrable_Ioc_of_le
+-/
 
 #print intervalIntegrable_iff' /-
 theorem intervalIntegrable_iff' [NoAtoms μ] :
@@ -112,10 +114,12 @@ theorem intervalIntegrable_iff' [NoAtoms μ] :
 #align interval_integrable_iff' intervalIntegrable_iff'
 -/
 
+#print intervalIntegrable_iff_integrable_Icc_of_le /-
 theorem intervalIntegrable_iff_integrable_Icc_of_le {f : ℝ → E} {a b : ℝ} (hab : a ≤ b)
     {μ : Measure ℝ} [NoAtoms μ] : IntervalIntegrable f μ a b ↔ IntegrableOn f (Icc a b) μ := by
   rw [intervalIntegrable_iff_integrable_Ioc_of_le hab, integrableOn_Icc_iff_integrableOn_Ioc]
 #align interval_integrable_iff_integrable_Icc_of_le intervalIntegrable_iff_integrable_Icc_of_le
+-/
 
 #print MeasureTheory.Integrable.intervalIntegrable /-
 /-- If a function is integrable with respect to a given measure `μ` then it is interval integrable
@@ -134,10 +138,12 @@ theorem MeasureTheory.IntegrableOn.intervalIntegrable (hf : IntegrableOn f [a, b
 #align measure_theory.integrable_on.interval_integrable MeasureTheory.IntegrableOn.intervalIntegrable
 -/
 
+#print intervalIntegrable_const_iff /-
 theorem intervalIntegrable_const_iff {c : E} :
     IntervalIntegrable (fun _ => c) μ a b ↔ c = 0 ∨ μ (Ι a b) < ∞ := by
   simp only [intervalIntegrable_iff, integrable_on_const]
 #align interval_integrable_const_iff intervalIntegrable_const_iff
+-/
 
 #print intervalIntegrable_const /-
 @[simp]
@@ -292,10 +298,12 @@ end
 
 variable [NormedRing A] {f g : ℝ → E} {a b : ℝ} {μ : Measure ℝ}
 
+#print IntervalIntegrable.smul /-
 theorem smul [NormedField 𝕜] [NormedSpace 𝕜 E] {f : ℝ → E} {a b : ℝ} {μ : Measure ℝ}
     (h : IntervalIntegrable f μ a b) (r : 𝕜) : IntervalIntegrable (r • f) μ a b :=
   ⟨h.1.smul r, h.2.smul r⟩
 #align interval_integrable.smul IntervalIntegrable.smul
+-/
 
 #print IntervalIntegrable.add /-
 @[simp]
@@ -313,10 +321,12 @@ theorem sub (hf : IntervalIntegrable f μ a b) (hg : IntervalIntegrable g μ a b
 #align interval_integrable.sub IntervalIntegrable.sub
 -/
 
+#print IntervalIntegrable.sum /-
 theorem sum (s : Finset ι) {f : ι → ℝ → E} (h : ∀ i ∈ s, IntervalIntegrable (f i) μ a b) :
     IntervalIntegrable (∑ i in s, f i) μ a b :=
   ⟨integrable_finset_sum' s fun i hi => (h i hi).1, integrable_finset_sum' s fun i hi => (h i hi).2⟩
 #align interval_integrable.sum IntervalIntegrable.sum
+-/
 
 #print IntervalIntegrable.mul_continuousOn /-
 theorem mul_continuousOn {f g : ℝ → A} (hf : IntervalIntegrable f μ a b)
@@ -442,10 +452,12 @@ theorem ContinuousOn.intervalIntegrable {u : ℝ → E} {a b : ℝ} (hu : Contin
 #align continuous_on.interval_integrable ContinuousOn.intervalIntegrable
 -/
 
+#print ContinuousOn.intervalIntegrable_of_Icc /-
 theorem ContinuousOn.intervalIntegrable_of_Icc {u : ℝ → E} {a b : ℝ} (h : a ≤ b)
     (hu : ContinuousOn u (Icc a b)) : IntervalIntegrable u μ a b :=
   ContinuousOn.intervalIntegrable ((uIcc_of_le h).symm ▸ hu)
 #align continuous_on.interval_integrable_of_Icc ContinuousOn.intervalIntegrable_of_Icc
+-/
 
 #print Continuous.intervalIntegrable /-
 /-- A continuous function on `ℝ` is `interval_integrable` with respect to any locally finite measure
@@ -551,10 +563,8 @@ def intervalIntegral (f : ℝ → E) (a b : ℝ) (μ : Measure ℝ) : E :=
 #align interval_integral intervalIntegral
 -/
 
--- mathport name: «expr∫ in .. , ∂ »
 notation3"∫ "(...)" in "a".."b", "r:60:(scoped f => f)" ∂"μ:70 => intervalIntegral r a b μ
 
--- mathport name: «expr∫ in .. , »
 notation3"∫ "(...)" in "a".."b", "r:60:(scoped f => intervalIntegral f a b volume) => r
 
 namespace intervalIntegral
@@ -563,27 +573,38 @@ section Basic
 
 variable {a b : ℝ} {f g : ℝ → E} {μ : Measure ℝ}
 
+#print intervalIntegral.integral_zero /-
 @[simp]
 theorem integral_zero : ∫ x in a..b, (0 : E) ∂μ = 0 := by simp [intervalIntegral]
 #align interval_integral.integral_zero intervalIntegral.integral_zero
+-/
 
+#print intervalIntegral.integral_of_le /-
 theorem integral_of_le (h : a ≤ b) : ∫ x in a..b, f x ∂μ = ∫ x in Ioc a b, f x ∂μ := by
   simp [intervalIntegral, h]
 #align interval_integral.integral_of_le intervalIntegral.integral_of_le
+-/
 
+#print intervalIntegral.integral_same /-
 @[simp]
 theorem integral_same : ∫ x in a..a, f x ∂μ = 0 :=
   sub_self _
 #align interval_integral.integral_same intervalIntegral.integral_same
+-/
 
+#print intervalIntegral.integral_symm /-
 theorem integral_symm (a b) : ∫ x in b..a, f x ∂μ = -∫ x in a..b, f x ∂μ := by
   simp only [intervalIntegral, neg_sub]
 #align interval_integral.integral_symm intervalIntegral.integral_symm
+-/
 
+#print intervalIntegral.integral_of_ge /-
 theorem integral_of_ge (h : b ≤ a) : ∫ x in a..b, f x ∂μ = -∫ x in Ioc b a, f x ∂μ := by
   simp only [integral_symm b, integral_of_le h]
 #align interval_integral.integral_of_ge intervalIntegral.integral_of_ge
+-/
 
+#print intervalIntegral.intervalIntegral_eq_integral_uIoc /-
 theorem intervalIntegral_eq_integral_uIoc (f : ℝ → E) (a b : ℝ) (μ : Measure ℝ) :
     ∫ x in a..b, f x ∂μ = (if a ≤ b then 1 else -1 : ℝ) • ∫ x in Ι a b, f x ∂μ :=
   by
@@ -591,6 +612,7 @@ theorem intervalIntegral_eq_integral_uIoc (f : ℝ → E) (a b : ℝ) (μ : Meas
   · simp only [integral_of_le h, uIoc_of_le h, one_smul]
   · simp only [integral_of_ge (not_le.1 h).le, uIoc_of_lt (not_le.1 h), neg_one_smul]
 #align interval_integral.interval_integral_eq_integral_uIoc intervalIntegral.intervalIntegral_eq_integral_uIoc
+-/
 
 #print intervalIntegral.norm_intervalIntegral_eq /-
 theorem norm_intervalIntegral_eq (f : ℝ → E) (a b : ℝ) (μ : Measure ℝ) :
@@ -601,16 +623,21 @@ theorem norm_intervalIntegral_eq (f : ℝ → E) (a b : ℝ) (μ : Measure ℝ)
 #align interval_integral.norm_interval_integral_eq intervalIntegral.norm_intervalIntegral_eq
 -/
 
+#print intervalIntegral.abs_intervalIntegral_eq /-
 theorem abs_intervalIntegral_eq (f : ℝ → ℝ) (a b : ℝ) (μ : Measure ℝ) :
     |∫ x in a..b, f x ∂μ| = |∫ x in Ι a b, f x ∂μ| :=
   norm_intervalIntegral_eq f a b μ
 #align interval_integral.abs_interval_integral_eq intervalIntegral.abs_intervalIntegral_eq
+-/
 
+#print intervalIntegral.integral_cases /-
 theorem integral_cases (f : ℝ → E) (a b) :
     ∫ x in a..b, f x ∂μ ∈ ({∫ x in Ι a b, f x ∂μ, -∫ x in Ι a b, f x ∂μ} : Set E) := by
   rw [interval_integral_eq_integral_uIoc]; split_ifs <;> simp
 #align interval_integral.integral_cases intervalIntegral.integral_cases
+-/
 
+#print intervalIntegral.integral_undef /-
 theorem integral_undef (h : ¬IntervalIntegrable f μ a b) : ∫ x in a..b, f x ∂μ = 0 := by
   cases' le_total a b with hab hab <;>
         simp only [integral_of_le, integral_of_ge, hab, neg_eq_zero] <;>
@@ -618,21 +645,28 @@ theorem integral_undef (h : ¬IntervalIntegrable f μ a b) : ∫ x in a..b, f x
     simpa only [hab, Ioc_eq_empty_of_le, integrable_on_empty, not_true, false_or_iff,
       or_false_iff] using not_and_distrib.mp h
 #align interval_integral.integral_undef intervalIntegral.integral_undef
+-/
 
+#print intervalIntegral.intervalIntegrable_of_integral_ne_zero /-
 theorem intervalIntegrable_of_integral_ne_zero {a b : ℝ} {f : ℝ → E} {μ : Measure ℝ}
     (h : ∫ x in a..b, f x ∂μ ≠ 0) : IntervalIntegrable f μ a b := by contrapose! h;
   exact intervalIntegral.integral_undef h
 #align interval_integral.interval_integrable_of_integral_ne_zero intervalIntegral.intervalIntegrable_of_integral_ne_zero
+-/
 
+#print intervalIntegral.integral_non_aestronglyMeasurable /-
 theorem integral_non_aestronglyMeasurable (hf : ¬AEStronglyMeasurable f (μ.restrict (Ι a b))) :
     ∫ x in a..b, f x ∂μ = 0 := by
   rw [interval_integral_eq_integral_uIoc, integral_non_ae_strongly_measurable hf, smul_zero]
 #align interval_integral.integral_non_ae_strongly_measurable intervalIntegral.integral_non_aestronglyMeasurable
+-/
 
+#print intervalIntegral.integral_non_aestronglyMeasurable_of_le /-
 theorem integral_non_aestronglyMeasurable_of_le (h : a ≤ b)
     (hf : ¬AEStronglyMeasurable f (μ.restrict (Ioc a b))) : ∫ x in a..b, f x ∂μ = 0 :=
   integral_non_aestronglyMeasurable <| by rwa [uIoc_of_le h]
 #align interval_integral.integral_non_ae_strongly_measurable_of_le intervalIntegral.integral_non_aestronglyMeasurable_of_le
+-/
 
 #print intervalIntegral.norm_integral_min_max /-
 theorem norm_integral_min_max (f : ℝ → E) :
@@ -648,27 +682,35 @@ theorem norm_integral_eq_norm_integral_Ioc (f : ℝ → E) :
 #align interval_integral.norm_integral_eq_norm_integral_Ioc intervalIntegral.norm_integral_eq_norm_integral_Ioc
 -/
 
+#print intervalIntegral.abs_integral_eq_abs_integral_uIoc /-
 theorem abs_integral_eq_abs_integral_uIoc (f : ℝ → ℝ) :
     |∫ x in a..b, f x ∂μ| = |∫ x in Ι a b, f x ∂μ| :=
   norm_integral_eq_norm_integral_Ioc f
 #align interval_integral.abs_integral_eq_abs_integral_uIoc intervalIntegral.abs_integral_eq_abs_integral_uIoc
+-/
 
+#print intervalIntegral.norm_integral_le_integral_norm_Ioc /-
 theorem norm_integral_le_integral_norm_Ioc : ‖∫ x in a..b, f x ∂μ‖ ≤ ∫ x in Ι a b, ‖f x‖ ∂μ :=
   calc
     ‖∫ x in a..b, f x ∂μ‖ = ‖∫ x in Ι a b, f x ∂μ‖ := norm_integral_eq_norm_integral_Ioc f
     _ ≤ ∫ x in Ι a b, ‖f x‖ ∂μ := norm_integral_le_integral_norm f
 #align interval_integral.norm_integral_le_integral_norm_Ioc intervalIntegral.norm_integral_le_integral_norm_Ioc
+-/
 
+#print intervalIntegral.norm_integral_le_abs_integral_norm /-
 theorem norm_integral_le_abs_integral_norm : ‖∫ x in a..b, f x ∂μ‖ ≤ |∫ x in a..b, ‖f x‖ ∂μ| :=
   by
   simp only [← Real.norm_eq_abs, norm_integral_eq_norm_integral_Ioc]
   exact le_trans (norm_integral_le_integral_norm _) (le_abs_self _)
 #align interval_integral.norm_integral_le_abs_integral_norm intervalIntegral.norm_integral_le_abs_integral_norm
+-/
 
+#print intervalIntegral.norm_integral_le_integral_norm /-
 theorem norm_integral_le_integral_norm (h : a ≤ b) :
     ‖∫ x in a..b, f x ∂μ‖ ≤ ∫ x in a..b, ‖f x‖ ∂μ :=
   norm_integral_le_integral_norm_Ioc.trans_eq <| by rw [uIoc_of_le h, integral_of_le h]
 #align interval_integral.norm_integral_le_integral_norm intervalIntegral.norm_integral_le_integral_norm
+-/
 
 #print intervalIntegral.norm_integral_le_of_norm_le /-
 theorem norm_integral_le_of_norm_le {g : ℝ → ℝ} (h : ∀ᵐ t ∂μ.restrict <| Ι a b, ‖f t‖ ≤ g t)
@@ -679,6 +721,7 @@ theorem norm_integral_le_of_norm_le {g : ℝ → ℝ} (h : ∀ᵐ t ∂μ.restri
 #align interval_integral.norm_integral_le_of_norm_le intervalIntegral.norm_integral_le_of_norm_le
 -/
 
+#print intervalIntegral.norm_integral_le_of_norm_le_const_ae /-
 theorem norm_integral_le_of_norm_le_const_ae {a b C : ℝ} {f : ℝ → E}
     (h : ∀ᵐ x, x ∈ Ι a b → ‖f x‖ ≤ C) : ‖∫ x in a..b, f x‖ ≤ C * |b - a| :=
   by
@@ -687,17 +730,22 @@ theorem norm_integral_le_of_norm_le_const_ae {a b C : ℝ} {f : ℝ → E}
   · rw [Real.volume_Ioc, max_sub_min_eq_abs, ENNReal.toReal_ofReal (abs_nonneg _)]
   · simp only [Real.volume_Ioc, ENNReal.ofReal_lt_top]
 #align interval_integral.norm_integral_le_of_norm_le_const_ae intervalIntegral.norm_integral_le_of_norm_le_const_ae
+-/
 
+#print intervalIntegral.norm_integral_le_of_norm_le_const /-
 theorem norm_integral_le_of_norm_le_const {a b C : ℝ} {f : ℝ → E} (h : ∀ x ∈ Ι a b, ‖f x‖ ≤ C) :
     ‖∫ x in a..b, f x‖ ≤ C * |b - a| :=
   norm_integral_le_of_norm_le_const_ae <| eventually_of_forall h
 #align interval_integral.norm_integral_le_of_norm_le_const intervalIntegral.norm_integral_le_of_norm_le_const
+-/
 
+#print intervalIntegral.integral_add /-
 @[simp]
 theorem integral_add (hf : IntervalIntegrable f μ a b) (hg : IntervalIntegrable g μ a b) :
     ∫ x in a..b, f x + g x ∂μ = ∫ x in a..b, f x ∂μ + ∫ x in a..b, g x ∂μ := by
   simp only [interval_integral_eq_integral_uIoc, integral_add hf.def hg.def, smul_add]
 #align interval_integral.integral_add intervalIntegral.integral_add
+-/
 
 #print intervalIntegral.integral_finset_sum /-
 theorem integral_finset_sum {ι} {s : Finset ι} {f : ι → ℝ → E}
@@ -708,16 +756,20 @@ theorem integral_finset_sum {ι} {s : Finset ι} {f : ι → ℝ → E}
 #align interval_integral.integral_finset_sum intervalIntegral.integral_finset_sum
 -/
 
+#print intervalIntegral.integral_neg /-
 @[simp]
 theorem integral_neg : ∫ x in a..b, -f x ∂μ = -∫ x in a..b, f x ∂μ := by
   simp only [intervalIntegral, integral_neg]; abel
 #align interval_integral.integral_neg intervalIntegral.integral_neg
+-/
 
+#print intervalIntegral.integral_sub /-
 @[simp]
 theorem integral_sub (hf : IntervalIntegrable f μ a b) (hg : IntervalIntegrable g μ a b) :
     ∫ x in a..b, f x - g x ∂μ = ∫ x in a..b, f x ∂μ - ∫ x in a..b, g x ∂μ := by
   simpa only [sub_eq_add_neg] using (integral_add hf hg.neg).trans (congr_arg _ integral_neg)
 #align interval_integral.integral_sub intervalIntegral.integral_sub
+-/
 
 #print intervalIntegral.integral_smul /-
 @[simp]
@@ -735,34 +787,44 @@ theorem integral_smul_const {𝕜 : Type _} [IsROrC 𝕜] [NormedSpace 𝕜 E] (
 #align interval_integral.integral_smul_const intervalIntegral.integral_smul_const
 -/
 
+#print intervalIntegral.integral_const_mul /-
 @[simp]
 theorem integral_const_mul {𝕜 : Type _} [IsROrC 𝕜] (r : 𝕜) (f : ℝ → 𝕜) :
     ∫ x in a..b, r * f x ∂μ = r * ∫ x in a..b, f x ∂μ :=
   integral_smul r f
 #align interval_integral.integral_const_mul intervalIntegral.integral_const_mul
+-/
 
+#print intervalIntegral.integral_mul_const /-
 @[simp]
 theorem integral_mul_const {𝕜 : Type _} [IsROrC 𝕜] (r : 𝕜) (f : ℝ → 𝕜) :
     ∫ x in a..b, f x * r ∂μ = (∫ x in a..b, f x ∂μ) * r := by
   simpa only [mul_comm r] using integral_const_mul r f
 #align interval_integral.integral_mul_const intervalIntegral.integral_mul_const
+-/
 
+#print intervalIntegral.integral_div /-
 @[simp]
 theorem integral_div {𝕜 : Type _} [IsROrC 𝕜] (r : 𝕜) (f : ℝ → 𝕜) :
     ∫ x in a..b, f x / r ∂μ = (∫ x in a..b, f x ∂μ) / r := by
   simpa only [div_eq_mul_inv] using integral_mul_const r⁻¹ f
 #align interval_integral.integral_div intervalIntegral.integral_div
+-/
 
+#print intervalIntegral.integral_const' /-
 theorem integral_const' (c : E) :
     ∫ x in a..b, c ∂μ = ((μ <| Ioc a b).toReal - (μ <| Ioc b a).toReal) • c := by
   simp only [intervalIntegral, set_integral_const, sub_smul]
 #align interval_integral.integral_const' intervalIntegral.integral_const'
+-/
 
+#print intervalIntegral.integral_const /-
 @[simp]
 theorem integral_const (c : E) : ∫ x in a..b, c = (b - a) • c := by
   simp only [integral_const', Real.volume_Ioc, ENNReal.toReal_ofReal', ← neg_sub b,
     max_zero_sub_eq_self]
 #align interval_integral.integral_const intervalIntegral.integral_const
+-/
 
 #print intervalIntegral.integral_smul_measure /-
 theorem integral_smul_measure (c : ℝ≥0∞) :
@@ -773,10 +835,12 @@ theorem integral_smul_measure (c : ℝ≥0∞) :
 
 end Basic
 
+#print intervalIntegral.integral_ofReal /-
 theorem integral_ofReal {a b : ℝ} {μ : Measure ℝ} {f : ℝ → ℝ} :
     ∫ x in a..b, (f x : ℂ) ∂μ = ↑(∫ x in a..b, f x ∂μ) := by
   simp only [intervalIntegral, integral_ofReal, Complex.ofReal_sub]
 #align interval_integral.integral_of_real intervalIntegral.integral_ofReal
+-/
 
 section ContinuousLinearMap
 
@@ -786,18 +850,22 @@ variable [IsROrC 𝕜] [NormedSpace 𝕜 E] [NormedAddCommGroup F] [NormedSpace
 
 open ContinuousLinearMap
 
+#print ContinuousLinearMap.intervalIntegral_apply /-
 theorem ContinuousLinearMap.intervalIntegral_apply {a b : ℝ} {φ : ℝ → F →L[𝕜] E}
     (hφ : IntervalIntegrable φ μ a b) (v : F) : (∫ x in a..b, φ x ∂μ) v = ∫ x in a..b, φ x v ∂μ :=
   by
   simp_rw [interval_integral_eq_integral_uIoc, ← integral_apply hφ.def v, coe_smul', Pi.smul_apply]
 #align continuous_linear_map.interval_integral_apply ContinuousLinearMap.intervalIntegral_apply
+-/
 
 variable [NormedSpace ℝ F] [CompleteSpace F]
 
+#print ContinuousLinearMap.intervalIntegral_comp_comm /-
 theorem ContinuousLinearMap.intervalIntegral_comp_comm (L : E →L[𝕜] F)
     (hf : IntervalIntegrable f μ a b) : ∫ x in a..b, L (f x) ∂μ = L (∫ x in a..b, f x ∂μ) := by
   simp_rw [intervalIntegral, L.integral_comp_comm hf.1, L.integral_comp_comm hf.2, L.map_sub]
 #align continuous_linear_map.interval_integral_comp_comm ContinuousLinearMap.intervalIntegral_comp_comm
+-/
 
 end ContinuousLinearMap
 
@@ -805,6 +873,7 @@ section Comp
 
 variable {a b c d : ℝ} (f : ℝ → E)
 
+#print intervalIntegral.integral_comp_mul_right /-
 @[simp]
 theorem integral_comp_mul_right (hc : c ≠ 0) :
     ∫ x in a..b, f (x * c) = c⁻¹ • ∫ x in a * c..b * c, f x :=
@@ -818,33 +887,45 @@ theorem integral_comp_mul_right (hc : c ≠ 0) :
   · simp [h, mul_div_cancel, hc, abs_of_neg, measure.restrict_congr_set Ico_ae_eq_Ioc]
   · simp [h, mul_div_cancel, hc, abs_of_pos]
 #align interval_integral.integral_comp_mul_right intervalIntegral.integral_comp_mul_right
+-/
 
+#print intervalIntegral.smul_integral_comp_mul_right /-
 @[simp]
 theorem smul_integral_comp_mul_right (c) : c • ∫ x in a..b, f (x * c) = ∫ x in a * c..b * c, f x :=
   by by_cases hc : c = 0 <;> simp [hc]
 #align interval_integral.smul_integral_comp_mul_right intervalIntegral.smul_integral_comp_mul_right
+-/
 
+#print intervalIntegral.integral_comp_mul_left /-
 @[simp]
 theorem integral_comp_mul_left (hc : c ≠ 0) :
     ∫ x in a..b, f (c * x) = c⁻¹ • ∫ x in c * a..c * b, f x := by
   simpa only [mul_comm c] using integral_comp_mul_right f hc
 #align interval_integral.integral_comp_mul_left intervalIntegral.integral_comp_mul_left
+-/
 
+#print intervalIntegral.smul_integral_comp_mul_left /-
 @[simp]
 theorem smul_integral_comp_mul_left (c) : c • ∫ x in a..b, f (c * x) = ∫ x in c * a..c * b, f x :=
   by by_cases hc : c = 0 <;> simp [hc]
 #align interval_integral.smul_integral_comp_mul_left intervalIntegral.smul_integral_comp_mul_left
+-/
 
+#print intervalIntegral.integral_comp_div /-
 @[simp]
 theorem integral_comp_div (hc : c ≠ 0) : ∫ x in a..b, f (x / c) = c • ∫ x in a / c..b / c, f x := by
   simpa only [inv_inv] using integral_comp_mul_right f (inv_ne_zero hc)
 #align interval_integral.integral_comp_div intervalIntegral.integral_comp_div
+-/
 
+#print intervalIntegral.inv_smul_integral_comp_div /-
 @[simp]
 theorem inv_smul_integral_comp_div (c) : c⁻¹ • ∫ x in a..b, f (x / c) = ∫ x in a / c..b / c, f x :=
   by by_cases hc : c = 0 <;> simp [hc]
 #align interval_integral.inv_smul_integral_comp_div intervalIntegral.inv_smul_integral_comp_div
+-/
 
+#print intervalIntegral.integral_comp_add_right /-
 @[simp]
 theorem integral_comp_add_right (d) : ∫ x in a..b, f (x + d) = ∫ x in a + d..b + d, f x :=
   have A : MeasurableEmbedding fun x => x + d :=
@@ -854,72 +935,96 @@ theorem integral_comp_add_right (d) : ∫ x in a..b, f (x + d) = ∫ x in a + d.
       simp [intervalIntegral, A.set_integral_map]
     _ = ∫ x in a + d..b + d, f x := by rw [map_add_right_eq_self]
 #align interval_integral.integral_comp_add_right intervalIntegral.integral_comp_add_right
+-/
 
+#print intervalIntegral.integral_comp_add_left /-
 @[simp]
 theorem integral_comp_add_left (d) : ∫ x in a..b, f (d + x) = ∫ x in d + a..d + b, f x := by
   simpa only [add_comm] using integral_comp_add_right f d
 #align interval_integral.integral_comp_add_left intervalIntegral.integral_comp_add_left
+-/
 
+#print intervalIntegral.integral_comp_mul_add /-
 @[simp]
 theorem integral_comp_mul_add (hc : c ≠ 0) (d) :
     ∫ x in a..b, f (c * x + d) = c⁻¹ • ∫ x in c * a + d..c * b + d, f x := by
   rw [← integral_comp_add_right, ← integral_comp_mul_left _ hc]
 #align interval_integral.integral_comp_mul_add intervalIntegral.integral_comp_mul_add
+-/
 
+#print intervalIntegral.smul_integral_comp_mul_add /-
 @[simp]
 theorem smul_integral_comp_mul_add (c d) :
     c • ∫ x in a..b, f (c * x + d) = ∫ x in c * a + d..c * b + d, f x := by
   by_cases hc : c = 0 <;> simp [hc]
 #align interval_integral.smul_integral_comp_mul_add intervalIntegral.smul_integral_comp_mul_add
+-/
 
+#print intervalIntegral.integral_comp_add_mul /-
 @[simp]
 theorem integral_comp_add_mul (hc : c ≠ 0) (d) :
     ∫ x in a..b, f (d + c * x) = c⁻¹ • ∫ x in d + c * a..d + c * b, f x := by
   rw [← integral_comp_add_left, ← integral_comp_mul_left _ hc]
 #align interval_integral.integral_comp_add_mul intervalIntegral.integral_comp_add_mul
+-/
 
+#print intervalIntegral.smul_integral_comp_add_mul /-
 @[simp]
 theorem smul_integral_comp_add_mul (c d) :
     c • ∫ x in a..b, f (d + c * x) = ∫ x in d + c * a..d + c * b, f x := by
   by_cases hc : c = 0 <;> simp [hc]
 #align interval_integral.smul_integral_comp_add_mul intervalIntegral.smul_integral_comp_add_mul
+-/
 
+#print intervalIntegral.integral_comp_div_add /-
 @[simp]
 theorem integral_comp_div_add (hc : c ≠ 0) (d) :
     ∫ x in a..b, f (x / c + d) = c • ∫ x in a / c + d..b / c + d, f x := by
   simpa only [div_eq_inv_mul, inv_inv] using integral_comp_mul_add f (inv_ne_zero hc) d
 #align interval_integral.integral_comp_div_add intervalIntegral.integral_comp_div_add
+-/
 
+#print intervalIntegral.inv_smul_integral_comp_div_add /-
 @[simp]
 theorem inv_smul_integral_comp_div_add (c d) :
     c⁻¹ • ∫ x in a..b, f (x / c + d) = ∫ x in a / c + d..b / c + d, f x := by
   by_cases hc : c = 0 <;> simp [hc]
 #align interval_integral.inv_smul_integral_comp_div_add intervalIntegral.inv_smul_integral_comp_div_add
+-/
 
+#print intervalIntegral.integral_comp_add_div /-
 @[simp]
 theorem integral_comp_add_div (hc : c ≠ 0) (d) :
     ∫ x in a..b, f (d + x / c) = c • ∫ x in d + a / c..d + b / c, f x := by
   simpa only [div_eq_inv_mul, inv_inv] using integral_comp_add_mul f (inv_ne_zero hc) d
 #align interval_integral.integral_comp_add_div intervalIntegral.integral_comp_add_div
+-/
 
+#print intervalIntegral.inv_smul_integral_comp_add_div /-
 @[simp]
 theorem inv_smul_integral_comp_add_div (c d) :
     c⁻¹ • ∫ x in a..b, f (d + x / c) = ∫ x in d + a / c..d + b / c, f x := by
   by_cases hc : c = 0 <;> simp [hc]
 #align interval_integral.inv_smul_integral_comp_add_div intervalIntegral.inv_smul_integral_comp_add_div
+-/
 
+#print intervalIntegral.integral_comp_mul_sub /-
 @[simp]
 theorem integral_comp_mul_sub (hc : c ≠ 0) (d) :
     ∫ x in a..b, f (c * x - d) = c⁻¹ • ∫ x in c * a - d..c * b - d, f x := by
   simpa only [sub_eq_add_neg] using integral_comp_mul_add f hc (-d)
 #align interval_integral.integral_comp_mul_sub intervalIntegral.integral_comp_mul_sub
+-/
 
+#print intervalIntegral.smul_integral_comp_mul_sub /-
 @[simp]
 theorem smul_integral_comp_mul_sub (c d) :
     c • ∫ x in a..b, f (c * x - d) = ∫ x in c * a - d..c * b - d, f x := by
   by_cases hc : c = 0 <;> simp [hc]
 #align interval_integral.smul_integral_comp_mul_sub intervalIntegral.smul_integral_comp_mul_sub
+-/
 
+#print intervalIntegral.integral_comp_sub_mul /-
 @[simp]
 theorem integral_comp_sub_mul (hc : c ≠ 0) (d) :
     ∫ x in a..b, f (d - c * x) = c⁻¹ • ∫ x in d - c * b..d - c * a, f x :=
@@ -928,51 +1033,68 @@ theorem integral_comp_sub_mul (hc : c ≠ 0) (d) :
   rw [integral_comp_add_mul f (neg_ne_zero.mpr hc) d, integral_symm]
   simp only [inv_neg, smul_neg, neg_neg, neg_smul]
 #align interval_integral.integral_comp_sub_mul intervalIntegral.integral_comp_sub_mul
+-/
 
+#print intervalIntegral.smul_integral_comp_sub_mul /-
 @[simp]
 theorem smul_integral_comp_sub_mul (c d) :
     c • ∫ x in a..b, f (d - c * x) = ∫ x in d - c * b..d - c * a, f x := by
   by_cases hc : c = 0 <;> simp [hc]
 #align interval_integral.smul_integral_comp_sub_mul intervalIntegral.smul_integral_comp_sub_mul
+-/
 
+#print intervalIntegral.integral_comp_div_sub /-
 @[simp]
 theorem integral_comp_div_sub (hc : c ≠ 0) (d) :
     ∫ x in a..b, f (x / c - d) = c • ∫ x in a / c - d..b / c - d, f x := by
   simpa only [div_eq_inv_mul, inv_inv] using integral_comp_mul_sub f (inv_ne_zero hc) d
 #align interval_integral.integral_comp_div_sub intervalIntegral.integral_comp_div_sub
+-/
 
+#print intervalIntegral.inv_smul_integral_comp_div_sub /-
 @[simp]
 theorem inv_smul_integral_comp_div_sub (c d) :
     c⁻¹ • ∫ x in a..b, f (x / c - d) = ∫ x in a / c - d..b / c - d, f x := by
   by_cases hc : c = 0 <;> simp [hc]
 #align interval_integral.inv_smul_integral_comp_div_sub intervalIntegral.inv_smul_integral_comp_div_sub
+-/
 
+#print intervalIntegral.integral_comp_sub_div /-
 @[simp]
 theorem integral_comp_sub_div (hc : c ≠ 0) (d) :
     ∫ x in a..b, f (d - x / c) = c • ∫ x in d - b / c..d - a / c, f x := by
   simpa only [div_eq_inv_mul, inv_inv] using integral_comp_sub_mul f (inv_ne_zero hc) d
 #align interval_integral.integral_comp_sub_div intervalIntegral.integral_comp_sub_div
+-/
 
+#print intervalIntegral.inv_smul_integral_comp_sub_div /-
 @[simp]
 theorem inv_smul_integral_comp_sub_div (c d) :
     c⁻¹ • ∫ x in a..b, f (d - x / c) = ∫ x in d - b / c..d - a / c, f x := by
   by_cases hc : c = 0 <;> simp [hc]
 #align interval_integral.inv_smul_integral_comp_sub_div intervalIntegral.inv_smul_integral_comp_sub_div
+-/
 
+#print intervalIntegral.integral_comp_sub_right /-
 @[simp]
 theorem integral_comp_sub_right (d) : ∫ x in a..b, f (x - d) = ∫ x in a - d..b - d, f x := by
   simpa only [sub_eq_add_neg] using integral_comp_add_right f (-d)
 #align interval_integral.integral_comp_sub_right intervalIntegral.integral_comp_sub_right
+-/
 
+#print intervalIntegral.integral_comp_sub_left /-
 @[simp]
 theorem integral_comp_sub_left (d) : ∫ x in a..b, f (d - x) = ∫ x in d - b..d - a, f x := by
   simpa only [one_mul, one_smul, inv_one] using integral_comp_sub_mul f one_ne_zero d
 #align interval_integral.integral_comp_sub_left intervalIntegral.integral_comp_sub_left
+-/
 
+#print intervalIntegral.integral_comp_neg /-
 @[simp]
 theorem integral_comp_neg : ∫ x in a..b, f (-x) = ∫ x in -b..-a, f x := by
   simpa only [zero_sub] using integral_comp_sub_left f 0
 #align interval_integral.integral_comp_neg intervalIntegral.integral_comp_neg
+-/
 
 end Comp
 
@@ -999,6 +1121,7 @@ theorem integral_congr {a b : ℝ} (h : EqOn f g [a, b]) :
 #align interval_integral.integral_congr intervalIntegral.integral_congr
 -/
 
+#print intervalIntegral.integral_add_adjacent_intervals_cancel /-
 theorem integral_add_adjacent_intervals_cancel (hab : IntervalIntegrable f μ a b)
     (hbc : IntervalIntegrable f μ b c) :
     ∫ x in a..b, f x ∂μ + ∫ x in b..c, f x ∂μ + ∫ x in c..a, f x ∂μ = 0 :=
@@ -1013,13 +1136,17 @@ theorem integral_add_adjacent_intervals_cancel (hab : IntervalIntegrable f μ a
     simp [*, MeasurableSet.union, measurableSet_Ioc, Ioc_disjoint_Ioc_same,
       Ioc_disjoint_Ioc_same.symm, hab.1, hab.2, hbc.1, hbc.2, hac.1, hac.2]
 #align interval_integral.integral_add_adjacent_intervals_cancel intervalIntegral.integral_add_adjacent_intervals_cancel
+-/
 
+#print intervalIntegral.integral_add_adjacent_intervals /-
 theorem integral_add_adjacent_intervals (hab : IntervalIntegrable f μ a b)
     (hbc : IntervalIntegrable f μ b c) :
     ∫ x in a..b, f x ∂μ + ∫ x in b..c, f x ∂μ = ∫ x in a..c, f x ∂μ := by
   rw [← add_neg_eq_zero, ← integral_symm, integral_add_adjacent_intervals_cancel hab hbc]
 #align interval_integral.integral_add_adjacent_intervals intervalIntegral.integral_add_adjacent_intervals
+-/
 
+#print intervalIntegral.sum_integral_adjacent_intervals_Ico /-
 theorem sum_integral_adjacent_intervals_Ico {a : ℕ → ℝ} {m n : ℕ} (hmn : m ≤ n)
     (hint : ∀ k ∈ Ico m n, IntervalIntegrable f μ (a k) (a <| k + 1)) :
     ∑ k : ℕ in Finset.Ico m n, ∫ x in a k..a <| k + 1, f x ∂μ = ∫ x in a m..a n, f x ∂μ :=
@@ -1036,6 +1163,7 @@ theorem sum_integral_adjacent_intervals_Ico {a : ℕ → ℝ} {m n : ℕ} (hmn :
     · intro k hk
       exact h _ (Ico_subset_Ico_right p.le_succ hk)
 #align interval_integral.sum_integral_adjacent_intervals_Ico intervalIntegral.sum_integral_adjacent_intervals_Ico
+-/
 
 #print intervalIntegral.sum_integral_adjacent_intervals /-
 theorem sum_integral_adjacent_intervals {a : ℕ → ℝ} {n : ℕ}
@@ -1047,33 +1175,42 @@ theorem sum_integral_adjacent_intervals {a : ℕ → ℝ} {n : ℕ}
 #align interval_integral.sum_integral_adjacent_intervals intervalIntegral.sum_integral_adjacent_intervals
 -/
 
+#print intervalIntegral.integral_interval_sub_left /-
 theorem integral_interval_sub_left (hab : IntervalIntegrable f μ a b)
     (hac : IntervalIntegrable f μ a c) :
     ∫ x in a..b, f x ∂μ - ∫ x in a..c, f x ∂μ = ∫ x in c..b, f x ∂μ :=
   sub_eq_of_eq_add' <| Eq.symm <| integral_add_adjacent_intervals hac (hac.symm.trans hab)
 #align interval_integral.integral_interval_sub_left intervalIntegral.integral_interval_sub_left
+-/
 
+#print intervalIntegral.integral_interval_add_interval_comm /-
 theorem integral_interval_add_interval_comm (hab : IntervalIntegrable f μ a b)
     (hcd : IntervalIntegrable f μ c d) (hac : IntervalIntegrable f μ a c) :
     ∫ x in a..b, f x ∂μ + ∫ x in c..d, f x ∂μ = ∫ x in a..d, f x ∂μ + ∫ x in c..b, f x ∂μ := by
   rw [← integral_add_adjacent_intervals hac hcd, add_assoc, add_left_comm,
     integral_add_adjacent_intervals hac (hac.symm.trans hab), add_comm]
 #align interval_integral.integral_interval_add_interval_comm intervalIntegral.integral_interval_add_interval_comm
+-/
 
+#print intervalIntegral.integral_interval_sub_interval_comm /-
 theorem integral_interval_sub_interval_comm (hab : IntervalIntegrable f μ a b)
     (hcd : IntervalIntegrable f μ c d) (hac : IntervalIntegrable f μ a c) :
     ∫ x in a..b, f x ∂μ - ∫ x in c..d, f x ∂μ = ∫ x in a..c, f x ∂μ - ∫ x in b..d, f x ∂μ := by
   simp only [sub_eq_add_neg, ← integral_symm,
     integral_interval_add_interval_comm hab hcd.symm (hac.trans hcd)]
 #align interval_integral.integral_interval_sub_interval_comm intervalIntegral.integral_interval_sub_interval_comm
+-/
 
+#print intervalIntegral.integral_interval_sub_interval_comm' /-
 theorem integral_interval_sub_interval_comm' (hab : IntervalIntegrable f μ a b)
     (hcd : IntervalIntegrable f μ c d) (hac : IntervalIntegrable f μ a c) :
     ∫ x in a..b, f x ∂μ - ∫ x in c..d, f x ∂μ = ∫ x in d..b, f x ∂μ - ∫ x in c..a, f x ∂μ := by
   rw [integral_interval_sub_interval_comm hab hcd hac, integral_symm b d, integral_symm a c,
     sub_neg_eq_add, sub_eq_neg_add]
 #align interval_integral.integral_interval_sub_interval_comm' intervalIntegral.integral_interval_sub_interval_comm'
+-/
 
+#print intervalIntegral.integral_Iic_sub_Iic /-
 theorem integral_Iic_sub_Iic (ha : IntegrableOn f (Iic a) μ) (hb : IntegrableOn f (Iic b) μ) :
     ∫ x in Iic b, f x ∂μ - ∫ x in Iic a, f x ∂μ = ∫ x in a..b, f x ∂μ :=
   by
@@ -1083,7 +1220,9 @@ theorem integral_Iic_sub_Iic (ha : IntegrableOn f (Iic a) μ) (hb : IntegrableOn
     Iic_union_Ioc_eq_Iic hab]
   exacts [measurableSet_Ioc, ha, hb.mono_set fun _ => And.right]
 #align interval_integral.integral_Iic_sub_Iic intervalIntegral.integral_Iic_sub_Iic
+-/
 
+#print intervalIntegral.integral_const_of_cdf /-
 /-- If `μ` is a finite measure then `∫ x in a..b, c ∂μ = (μ (Iic b) - μ (Iic a)) • c`. -/
 theorem integral_const_of_cdf [IsFiniteMeasure μ] (c : E) :
     ∫ x in a..b, c ∂μ = ((μ (Iic b)).toReal - (μ (Iic a)).toReal) • c :=
@@ -1092,7 +1231,9 @@ theorem integral_const_of_cdf [IsFiniteMeasure μ] (c : E) :
   refine' (integral_Iic_sub_Iic _ _).symm <;>
     simp only [integrable_on_const, measure_lt_top, or_true_iff]
 #align interval_integral.integral_const_of_cdf intervalIntegral.integral_const_of_cdf
+-/
 
+#print intervalIntegral.integral_eq_integral_of_support_subset /-
 theorem integral_eq_integral_of_support_subset {a b} (h : support f ⊆ Ioc a b) :
     ∫ x in a..b, f x ∂μ = ∫ x, f x ∂μ :=
   by
@@ -1103,6 +1244,7 @@ theorem integral_eq_integral_of_support_subset {a b} (h : support f ⊆ Ioc a b)
   · rw [Ioc_eq_empty hab.not_lt, subset_empty_iff, support_eq_empty_iff] at h 
     simp [h]
 #align interval_integral.integral_eq_integral_of_support_subset intervalIntegral.integral_eq_integral_of_support_subset
+-/
 
 #print intervalIntegral.integral_congr_ae' /-
 theorem integral_congr_ae' (h : ∀ᵐ x ∂μ, x ∈ Ioc a b → f x = g x)
@@ -1119,12 +1261,15 @@ theorem integral_congr_ae (h : ∀ᵐ x ∂μ, x ∈ Ι a b → f x = g x) :
 #align interval_integral.integral_congr_ae intervalIntegral.integral_congr_ae
 -/
 
+#print intervalIntegral.integral_zero_ae /-
 theorem integral_zero_ae (h : ∀ᵐ x ∂μ, x ∈ Ι a b → f x = 0) : ∫ x in a..b, f x ∂μ = 0 :=
   calc
     ∫ x in a..b, f x ∂μ = ∫ x in a..b, 0 ∂μ := integral_congr_ae h
     _ = 0 := integral_zero
 #align interval_integral.integral_zero_ae intervalIntegral.integral_zero_ae
+-/
 
+#print intervalIntegral.integral_indicator /-
 theorem integral_indicator {a₁ a₂ a₃ : ℝ} (h : a₂ ∈ Icc a₁ a₃) :
     ∫ x in a₁..a₃, indicator {x | x ≤ a₂} f x ∂μ = ∫ x in a₁..a₂, f x ∂μ :=
   by
@@ -1134,7 +1279,9 @@ theorem integral_indicator {a₁ a₂ a₃ : ℝ} (h : a₂ ∈ Icc a₁ a₃) :
   exact measurableSet_Iic
   all_goals apply measurableSet_Iic
 #align interval_integral.integral_indicator intervalIntegral.integral_indicator
+-/
 
+#print intervalIntegral.tendsto_integral_filter_of_dominated_convergence /-
 /-- Lebesgue dominated convergence theorem for filters with a countable basis -/
 theorem tendsto_integral_filter_of_dominated_convergence {ι} {l : Filter ι} [l.IsCountablyGenerated]
     {F : ι → ℝ → E} (bound : ℝ → ℝ)
@@ -1151,7 +1298,9 @@ theorem tendsto_integral_filter_of_dominated_convergence {ι} {l : Filter ι} [l
       (tendsto_integral_filter_of_dominated_convergence bound hF_meas h_bound bound_integrable
         h_lim)
 #align interval_integral.tendsto_integral_filter_of_dominated_convergence intervalIntegral.tendsto_integral_filter_of_dominated_convergence
+-/
 
+#print intervalIntegral.hasSum_integral_of_dominated_convergence /-
 /-- Lebesgue dominated convergence theorem for series. -/
 theorem hasSum_integral_of_dominated_convergence {ι} [Countable ι] {F : ι → ℝ → E}
     (bound : ι → ℝ → ℝ) (hF_meas : ∀ n, AEStronglyMeasurable (F n) (μ.restrict (Ι a b)))
@@ -1168,9 +1317,11 @@ theorem hasSum_integral_of_dominated_convergence {ι} [Countable ι] {F : ι →
           h_lim).const_smul
       _
 #align interval_integral.has_sum_integral_of_dominated_convergence intervalIntegral.hasSum_integral_of_dominated_convergence
+-/
 
 open TopologicalSpace
 
+#print intervalIntegral.hasSum_intervalIntegral_of_summable_norm /-
 /-- Interval integrals commute with countable sums, when the supremum norms are summable (a
 special case of the dominated convergence theorem). -/
 theorem hasSum_intervalIntegral_of_summable_norm [Countable ι] {f : ι → C(ℝ, E)}
@@ -1190,15 +1341,19 @@ theorem hasSum_intervalIntegral_of_summable_norm [Countable ι] {f : ι → C(
   -- next line is slow, & doesn't work with "exact" in place of "apply" -- ?
   apply ContinuousMap.summable_apply (summable_of_summable_norm hf_sum) ⟨x, ⟨hx.1.le, hx.2⟩⟩
 #align interval_integral.has_sum_interval_integral_of_summable_norm intervalIntegral.hasSum_intervalIntegral_of_summable_norm
+-/
 
+#print intervalIntegral.tsum_intervalIntegral_eq_of_summable_norm /-
 theorem tsum_intervalIntegral_eq_of_summable_norm [Countable ι] {f : ι → C(ℝ, E)}
     (hf_sum : Summable fun i : ι => ‖(f i).restrict (⟨uIcc a b, isCompact_uIcc⟩ : Compacts ℝ)‖) :
     ∑' i : ι, ∫ x in a..b, f i x = ∫ x in a..b, ∑' i : ι, f i x :=
   (hasSum_intervalIntegral_of_summable_norm hf_sum).tsum_eq
 #align interval_integral.tsum_interval_integral_eq_of_summable_norm intervalIntegral.tsum_intervalIntegral_eq_of_summable_norm
+-/
 
 variable {X : Type _} [TopologicalSpace X] [FirstCountableTopology X]
 
+#print intervalIntegral.continuousWithinAt_of_dominated_interval /-
 /-- Continuity of interval integral with respect to a parameter, at a point within a set.
   Given `F : X → ℝ → E`, assume `F x` is ae-measurable on `[a, b]` for `x` in a
   neighborhood of `x₀` within `s` and at `x₀`, and assume it is bounded by a function integrable
@@ -1213,7 +1368,9 @@ theorem continuousWithinAt_of_dominated_interval {F : X → ℝ → E} {x₀ : X
     ContinuousWithinAt (fun x => ∫ t in a..b, F x t ∂μ) s x₀ :=
   tendsto_integral_filter_of_dominated_convergence bound hF_meas h_bound bound_integrable h_cont
 #align interval_integral.continuous_within_at_of_dominated_interval intervalIntegral.continuousWithinAt_of_dominated_interval
+-/
 
+#print intervalIntegral.continuousAt_of_dominated_interval /-
 /-- Continuity of interval integral with respect to a parameter at a point.
   Given `F : X → ℝ → E`, assume `F x` is ae-measurable on `[a, b]` for `x` in a
   neighborhood of `x₀`, and assume it is bounded by a function integrable on
@@ -1228,7 +1385,9 @@ theorem continuousAt_of_dominated_interval {F : X → ℝ → E} {x₀ : X} {bou
     ContinuousAt (fun x => ∫ t in a..b, F x t ∂μ) x₀ :=
   tendsto_integral_filter_of_dominated_convergence bound hF_meas h_bound bound_integrable h_cont
 #align interval_integral.continuous_at_of_dominated_interval intervalIntegral.continuousAt_of_dominated_interval
+-/
 
+#print intervalIntegral.continuous_of_dominated_interval /-
 /-- Continuity of interval integral with respect to a parameter.
   Given `F : X → ℝ → E`, assume each `F x` is ae-measurable on `[a, b]`,
   and assume it is bounded by a function integrable on `[a, b]` independent of `x`.
@@ -1245,6 +1404,7 @@ theorem continuous_of_dominated_interval {F : X → ℝ → E} {bound : ℝ →
         bound_integrable <|
       h_cont.mono fun x himp hx => (himp hx).ContinuousAt
 #align interval_integral.continuous_of_dominated_interval intervalIntegral.continuous_of_dominated_interval
+-/
 
 end OrderClosedTopology
 
@@ -1254,6 +1414,7 @@ open TopologicalSpace
 
 variable {a b b₀ b₁ b₂ : ℝ} {μ : Measure ℝ} {f g : ℝ → E}
 
+#print intervalIntegral.continuousWithinAt_primitive /-
 theorem continuousWithinAt_primitive (hb₀ : μ {b₀} = 0)
     (h_int : IntervalIntegrable f μ (min a b₁) (max a b₂)) :
     ContinuousWithinAt (fun b => ∫ x in a..b, f x ∂μ) (Icc b₁ b₂) b₀ :=
@@ -1333,6 +1494,7 @@ theorem continuousWithinAt_primitive (hb₀ : μ {b₀} = 0)
   · apply continuousWithinAt_of_not_mem_closure
     rwa [closure_Icc]
 #align interval_integral.continuous_within_at_primitive intervalIntegral.continuousWithinAt_primitive
+-/
 
 #print intervalIntegral.continuousOn_primitive /-
 theorem continuousOn_primitive [NoAtoms μ] (h_int : IntegrableOn f (Icc a b) μ) :
@@ -1420,10 +1582,12 @@ section
 
 variable {f g : ℝ → ℝ} {a b : ℝ} {μ : Measure ℝ}
 
+#print intervalIntegral.integral_eq_zero_iff_of_le_of_nonneg_ae /-
 theorem integral_eq_zero_iff_of_le_of_nonneg_ae (hab : a ≤ b) (hf : 0 ≤ᵐ[μ.restrict (Ioc a b)] f)
     (hfi : IntervalIntegrable f μ a b) : ∫ x in a..b, f x ∂μ = 0 ↔ f =ᵐ[μ.restrict (Ioc a b)] 0 :=
   by rw [integral_of_le hab, integral_eq_zero_iff_of_nonneg_ae hf hfi.1]
 #align interval_integral.integral_eq_zero_iff_of_le_of_nonneg_ae intervalIntegral.integral_eq_zero_iff_of_le_of_nonneg_ae
+-/
 
 #print intervalIntegral.integral_eq_zero_iff_of_nonneg_ae /-
 theorem integral_eq_zero_iff_of_nonneg_ae (hf : 0 ≤ᵐ[μ.restrict (Ioc a b ∪ Ioc b a)] f)
@@ -1456,6 +1620,7 @@ theorem integral_pos_iff_support_of_nonneg_ae' (hf : 0 ≤ᵐ[μ.restrict (Ι a
 #align interval_integral.integral_pos_iff_support_of_nonneg_ae' intervalIntegral.integral_pos_iff_support_of_nonneg_ae'
 -/
 
+#print intervalIntegral.integral_pos_iff_support_of_nonneg_ae /-
 /-- If `f` is nonnegative a.e.-everywhere and it is integrable on the unordered interval
 `set.uIoc a b`, then its integral over `a..b` is positive if and only if `a < b` and the
 measure of `function.support f ∩ set.Ioc a b` is positive. -/
@@ -1463,7 +1628,9 @@ theorem integral_pos_iff_support_of_nonneg_ae (hf : 0 ≤ᵐ[μ] f) (hfi : Inter
     0 < ∫ x in a..b, f x ∂μ ↔ a < b ∧ 0 < μ (support f ∩ Ioc a b) :=
   integral_pos_iff_support_of_nonneg_ae' (ae_mono Measure.restrict_le_self hf) hfi
 #align interval_integral.integral_pos_iff_support_of_nonneg_ae intervalIntegral.integral_pos_iff_support_of_nonneg_ae
+-/
 
+#print intervalIntegral.intervalIntegral_pos_of_pos_on /-
 /-- If `f : ℝ → ℝ` is integrable on `(a, b]` for real numbers `a < b`, and positive on the interior
 of the interval, then its integral over `a..b` is strictly positive. -/
 theorem intervalIntegral_pos_of_pos_on {f : ℝ → ℝ} {a b : ℝ} (hfi : IntervalIntegrable f volume a b)
@@ -1479,7 +1646,9 @@ theorem intervalIntegral_pos_of_pos_on {f : ℝ → ℝ} {a b : ℝ} (hfi : Inte
   rw [integral_pos_iff_support_of_nonneg_ae' h₀ hfi]
   exact ⟨hab, ((measure.measure_Ioo_pos _).mpr hab).trans_le (measure_mono hsupp)⟩
 #align interval_integral.interval_integral_pos_of_pos_on intervalIntegral.intervalIntegral_pos_of_pos_on
+-/
 
+#print intervalIntegral.intervalIntegral_pos_of_pos /-
 /-- If `f : ℝ → ℝ` is strictly positive everywhere, and integrable on `(a, b]` for real numbers
 `a < b`, then its integral over `a..b` is strictly positive. (See `interval_integral_pos_of_pos_on`
 for a version only assuming positivity of `f` on `(a, b)` rather than everywhere.) -/
@@ -1488,7 +1657,9 @@ theorem intervalIntegral_pos_of_pos {f : ℝ → ℝ} {a b : ℝ}
     0 < ∫ x in a..b, f x :=
   intervalIntegral_pos_of_pos_on hfi (fun x hx => hpos x) hab
 #align interval_integral.interval_integral_pos_of_pos intervalIntegral.intervalIntegral_pos_of_pos
+-/
 
+#print intervalIntegral.integral_lt_integral_of_ae_le_of_measure_setOf_lt_ne_zero /-
 /-- If `f` and `g` are two functions that are interval integrable on `a..b`, `a ≤ b`,
 `f x ≤ g x` for a.e. `x ∈ set.Ioc a b`, and `f x < g x` on a subset of `set.Ioc a b`
 of nonzero measure, then `∫ x in a..b, f x ∂μ < ∫ x in a..b, g x ∂μ`. -/
@@ -1503,7 +1674,9 @@ theorem integral_lt_integral_of_ae_le_of_measure_setOf_lt_ne_zero (hab : a ≤ b
     exact fun x hx => (sub_pos.2 hx).ne'
   exacts [hle.mono fun x => sub_nonneg.2, hgi.1.sub hfi.1]
 #align interval_integral.integral_lt_integral_of_ae_le_of_measure_set_of_lt_ne_zero intervalIntegral.integral_lt_integral_of_ae_le_of_measure_setOf_lt_ne_zero
+-/
 
+#print intervalIntegral.integral_lt_integral_of_continuousOn_of_le_of_exists_lt /-
 /-- If `f` and `g` are continuous on `[a, b]`, `a < b`, `f x ≤ g x` on this interval, and
 `f c < g c` at some point `c ∈ [a, b]`, then `∫ x in a..b, f x < ∫ x in a..b, g x`. -/
 theorem integral_lt_integral_of_continuousOn_of_le_of_exists_lt {f g : ℝ → ℝ} {a b : ℝ}
@@ -1525,61 +1698,77 @@ theorem integral_lt_integral_of_continuousOn_of_le_of_exists_lt {f g : ℝ → 
   simp only [measure.restrict_congr_set Ioc_ae_eq_Icc] at h_eq 
   exact fun c hc => (measure.eq_on_Icc_of_ae_eq volume hab.ne h_eq hfc hgc hc).ge
 #align interval_integral.integral_lt_integral_of_continuous_on_of_le_of_exists_lt intervalIntegral.integral_lt_integral_of_continuousOn_of_le_of_exists_lt
+-/
 
+#print intervalIntegral.integral_nonneg_of_ae_restrict /-
 theorem integral_nonneg_of_ae_restrict (hab : a ≤ b) (hf : 0 ≤ᵐ[μ.restrict (Icc a b)] f) :
     0 ≤ ∫ u in a..b, f u ∂μ :=
   by
   let H := ae_restrict_of_ae_restrict_of_subset Ioc_subset_Icc_self hf
   simpa only [integral_of_le hab] using set_integral_nonneg_of_ae_restrict H
 #align interval_integral.integral_nonneg_of_ae_restrict intervalIntegral.integral_nonneg_of_ae_restrict
+-/
 
+#print intervalIntegral.integral_nonneg_of_ae /-
 theorem integral_nonneg_of_ae (hab : a ≤ b) (hf : 0 ≤ᵐ[μ] f) : 0 ≤ ∫ u in a..b, f u ∂μ :=
   integral_nonneg_of_ae_restrict hab <| ae_restrict_of_ae hf
 #align interval_integral.integral_nonneg_of_ae intervalIntegral.integral_nonneg_of_ae
+-/
 
+#print intervalIntegral.integral_nonneg_of_forall /-
 theorem integral_nonneg_of_forall (hab : a ≤ b) (hf : ∀ u, 0 ≤ f u) : 0 ≤ ∫ u in a..b, f u ∂μ :=
   integral_nonneg_of_ae hab <| eventually_of_forall hf
 #align interval_integral.integral_nonneg_of_forall intervalIntegral.integral_nonneg_of_forall
+-/
 
+#print intervalIntegral.integral_nonneg /-
 theorem integral_nonneg (hab : a ≤ b) (hf : ∀ u, u ∈ Icc a b → 0 ≤ f u) : 0 ≤ ∫ u in a..b, f u ∂μ :=
   integral_nonneg_of_ae_restrict hab <| (ae_restrict_iff' measurableSet_Icc).mpr <| ae_of_all μ hf
 #align interval_integral.integral_nonneg intervalIntegral.integral_nonneg
+-/
 
+#print intervalIntegral.abs_integral_le_integral_abs /-
 theorem abs_integral_le_integral_abs (hab : a ≤ b) :
     |∫ x in a..b, f x ∂μ| ≤ ∫ x in a..b, |f x| ∂μ := by
   simpa only [← Real.norm_eq_abs] using norm_integral_le_integral_norm hab
 #align interval_integral.abs_integral_le_integral_abs intervalIntegral.abs_integral_le_integral_abs
+-/
 
 section Mono
 
 variable (hab : a ≤ b) (hf : IntervalIntegrable f μ a b) (hg : IntervalIntegrable g μ a b)
 
-include hab hf hg
-
+#print intervalIntegral.integral_mono_ae_restrict /-
 theorem integral_mono_ae_restrict (h : f ≤ᵐ[μ.restrict (Icc a b)] g) :
     ∫ u in a..b, f u ∂μ ≤ ∫ u in a..b, g u ∂μ :=
   by
   let H := h.filter_mono <| ae_mono <| Measure.restrict_mono Ioc_subset_Icc_self <| le_refl μ
   simpa only [integral_of_le hab] using set_integral_mono_ae_restrict hf.1 hg.1 H
 #align interval_integral.integral_mono_ae_restrict intervalIntegral.integral_mono_ae_restrict
+-/
 
+#print intervalIntegral.integral_mono_ae /-
 theorem integral_mono_ae (h : f ≤ᵐ[μ] g) : ∫ u in a..b, f u ∂μ ≤ ∫ u in a..b, g u ∂μ := by
   simpa only [integral_of_le hab] using set_integral_mono_ae hf.1 hg.1 h
 #align interval_integral.integral_mono_ae intervalIntegral.integral_mono_ae
+-/
 
+#print intervalIntegral.integral_mono_on /-
 theorem integral_mono_on (h : ∀ x ∈ Icc a b, f x ≤ g x) :
     ∫ u in a..b, f u ∂μ ≤ ∫ u in a..b, g u ∂μ :=
   by
   let H x hx := h x <| Ioc_subset_Icc_self hx
   simpa only [integral_of_le hab] using set_integral_mono_on hf.1 hg.1 measurableSet_Ioc H
 #align interval_integral.integral_mono_on intervalIntegral.integral_mono_on
+-/
 
+#print intervalIntegral.integral_mono /-
 theorem integral_mono (h : f ≤ g) : ∫ u in a..b, f u ∂μ ≤ ∫ u in a..b, g u ∂μ :=
   integral_mono_ae hab hf hg <| ae_of_all _ h
 #align interval_integral.integral_mono intervalIntegral.integral_mono
+-/
 
-omit hg hab
-
+#print intervalIntegral.integral_mono_interval /-
 theorem integral_mono_interval {c d} (hca : c ≤ a) (hab : a ≤ b) (hbd : b ≤ d)
     (hf : 0 ≤ᵐ[μ.restrict (Ioc c d)] f) (hfi : IntervalIntegrable f μ c d) :
     ∫ x in a..b, f x ∂μ ≤ ∫ x in c..d, f x ∂μ :=
@@ -1587,6 +1776,7 @@ theorem integral_mono_interval {c d} (hca : c ≤ a) (hab : a ≤ b) (hbd : b 
   rw [integral_of_le hab, integral_of_le (hca.trans (hab.trans hbd))]
   exact set_integral_mono_set hfi.1 hf (Ioc_subset_Ioc hca hbd).EventuallyLE
 #align interval_integral.integral_mono_interval intervalIntegral.integral_mono_interval
+-/
 
 #print intervalIntegral.abs_integral_mono_interval /-
 theorem abs_integral_mono_interval {c d} (h : Ι a b ⊆ Ι c d) (hf : 0 ≤ᵐ[μ.restrict (Ι c d)] f)

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

@@ -547,15 +547,15 @@ variable [CompleteSpace E] [NormedSpace ℝ E]
 as `∫ x in Ioc a b, f x ∂μ - ∫ x in Ioc b a, f x ∂μ`. If `a ≤ b`, then it equals
 `∫ x in Ioc a b, f x ∂μ`, otherwise it equals `-∫ x in Ioc b a, f x ∂μ`. -/
 def intervalIntegral (f : ℝ → E) (a b : ℝ) (μ : Measure ℝ) : E :=
-  (∫ x in Ioc a b, f x ∂μ) - ∫ x in Ioc b a, f x ∂μ
+  ∫ x in Ioc a b, f x ∂μ - ∫ x in Ioc b a, f x ∂μ
 #align interval_integral intervalIntegral
 -/
 
 -- mathport name: «expr∫ in .. , ∂ »
-notation3"∫ "(...)" in "a".."b", "r:(scoped f => f)" ∂"μ => intervalIntegral r a b μ
+notation3"∫ "(...)" in "a".."b", "r:60:(scoped f => f)" ∂"μ:70 => intervalIntegral r a b μ
 
 -- mathport name: «expr∫ in .. , »
-notation3"∫ "(...)" in "a".."b", "r:(scoped f => intervalIntegral f a b volume) => r
+notation3"∫ "(...)" in "a".."b", "r:60:(scoped f => intervalIntegral f a b volume) => r
 
 namespace intervalIntegral
 
@@ -564,28 +564,28 @@ section Basic
 variable {a b : ℝ} {f g : ℝ → E} {μ : Measure ℝ}
 
 @[simp]
-theorem integral_zero : (∫ x in a..b, (0 : E) ∂μ) = 0 := by simp [intervalIntegral]
+theorem integral_zero : ∫ x in a..b, (0 : E) ∂μ = 0 := by simp [intervalIntegral]
 #align interval_integral.integral_zero intervalIntegral.integral_zero
 
-theorem integral_of_le (h : a ≤ b) : (∫ x in a..b, f x ∂μ) = ∫ x in Ioc a b, f x ∂μ := by
+theorem integral_of_le (h : a ≤ b) : ∫ x in a..b, f x ∂μ = ∫ x in Ioc a b, f x ∂μ := by
   simp [intervalIntegral, h]
 #align interval_integral.integral_of_le intervalIntegral.integral_of_le
 
 @[simp]
-theorem integral_same : (∫ x in a..a, f x ∂μ) = 0 :=
+theorem integral_same : ∫ x in a..a, f x ∂μ = 0 :=
   sub_self _
 #align interval_integral.integral_same intervalIntegral.integral_same
 
-theorem integral_symm (a b) : (∫ x in b..a, f x ∂μ) = -∫ x in a..b, f x ∂μ := by
+theorem integral_symm (a b) : ∫ x in b..a, f x ∂μ = -∫ x in a..b, f x ∂μ := by
   simp only [intervalIntegral, neg_sub]
 #align interval_integral.integral_symm intervalIntegral.integral_symm
 
-theorem integral_of_ge (h : b ≤ a) : (∫ x in a..b, f x ∂μ) = -∫ x in Ioc b a, f x ∂μ := by
+theorem integral_of_ge (h : b ≤ a) : ∫ x in a..b, f x ∂μ = -∫ x in Ioc b a, f x ∂μ := by
   simp only [integral_symm b, integral_of_le h]
 #align interval_integral.integral_of_ge intervalIntegral.integral_of_ge
 
 theorem intervalIntegral_eq_integral_uIoc (f : ℝ → E) (a b : ℝ) (μ : Measure ℝ) :
-    (∫ x in a..b, f x ∂μ) = (if a ≤ b then 1 else -1 : ℝ) • ∫ x in Ι a b, f x ∂μ :=
+    ∫ x in a..b, f x ∂μ = (if a ≤ b then 1 else -1 : ℝ) • ∫ x in Ι a b, f x ∂μ :=
   by
   split_ifs with h
   · simp only [integral_of_le h, uIoc_of_le h, one_smul]
@@ -607,11 +607,11 @@ theorem abs_intervalIntegral_eq (f : ℝ → ℝ) (a b : ℝ) (μ : Measure ℝ)
 #align interval_integral.abs_interval_integral_eq intervalIntegral.abs_intervalIntegral_eq
 
 theorem integral_cases (f : ℝ → E) (a b) :
-    (∫ x in a..b, f x ∂μ) ∈ ({∫ x in Ι a b, f x ∂μ, -∫ x in Ι a b, f x ∂μ} : Set E) := by
+    ∫ x in a..b, f x ∂μ ∈ ({∫ x in Ι a b, f x ∂μ, -∫ x in Ι a b, f x ∂μ} : Set E) := by
   rw [interval_integral_eq_integral_uIoc]; split_ifs <;> simp
 #align interval_integral.integral_cases intervalIntegral.integral_cases
 
-theorem integral_undef (h : ¬IntervalIntegrable f μ a b) : (∫ x in a..b, f x ∂μ) = 0 := by
+theorem integral_undef (h : ¬IntervalIntegrable f μ a b) : ∫ x in a..b, f x ∂μ = 0 := by
   cases' le_total a b with hab hab <;>
         simp only [integral_of_le, integral_of_ge, hab, neg_eq_zero] <;>
       refine' integral_undef (not_imp_not.mpr _ h) <;>
@@ -620,17 +620,17 @@ theorem integral_undef (h : ¬IntervalIntegrable f μ a b) : (∫ x in a..b, f x
 #align interval_integral.integral_undef intervalIntegral.integral_undef
 
 theorem intervalIntegrable_of_integral_ne_zero {a b : ℝ} {f : ℝ → E} {μ : Measure ℝ}
-    (h : (∫ x in a..b, f x ∂μ) ≠ 0) : IntervalIntegrable f μ a b := by contrapose! h;
+    (h : ∫ x in a..b, f x ∂μ ≠ 0) : IntervalIntegrable f μ a b := by contrapose! h;
   exact intervalIntegral.integral_undef h
 #align interval_integral.interval_integrable_of_integral_ne_zero intervalIntegral.intervalIntegrable_of_integral_ne_zero
 
 theorem integral_non_aestronglyMeasurable (hf : ¬AEStronglyMeasurable f (μ.restrict (Ι a b))) :
-    (∫ x in a..b, f x ∂μ) = 0 := by
+    ∫ x in a..b, f x ∂μ = 0 := by
   rw [interval_integral_eq_integral_uIoc, integral_non_ae_strongly_measurable hf, smul_zero]
 #align interval_integral.integral_non_ae_strongly_measurable intervalIntegral.integral_non_aestronglyMeasurable
 
 theorem integral_non_aestronglyMeasurable_of_le (h : a ≤ b)
-    (hf : ¬AEStronglyMeasurable f (μ.restrict (Ioc a b))) : (∫ x in a..b, f x ∂μ) = 0 :=
+    (hf : ¬AEStronglyMeasurable f (μ.restrict (Ioc a b))) : ∫ x in a..b, f x ∂μ = 0 :=
   integral_non_aestronglyMeasurable <| by rwa [uIoc_of_le h]
 #align interval_integral.integral_non_ae_strongly_measurable_of_le intervalIntegral.integral_non_aestronglyMeasurable_of_le
 
@@ -695,79 +695,78 @@ theorem norm_integral_le_of_norm_le_const {a b C : ℝ} {f : ℝ → E} (h : ∀
 
 @[simp]
 theorem integral_add (hf : IntervalIntegrable f μ a b) (hg : IntervalIntegrable g μ a b) :
-    (∫ x in a..b, f x + g x ∂μ) = (∫ x in a..b, f x ∂μ) + ∫ x in a..b, g x ∂μ := by
+    ∫ x in a..b, f x + g x ∂μ = ∫ x in a..b, f x ∂μ + ∫ x in a..b, g x ∂μ := by
   simp only [interval_integral_eq_integral_uIoc, integral_add hf.def hg.def, smul_add]
 #align interval_integral.integral_add intervalIntegral.integral_add
 
 #print intervalIntegral.integral_finset_sum /-
 theorem integral_finset_sum {ι} {s : Finset ι} {f : ι → ℝ → E}
     (h : ∀ i ∈ s, IntervalIntegrable (f i) μ a b) :
-    (∫ x in a..b, ∑ i in s, f i x ∂μ) = ∑ i in s, ∫ x in a..b, f i x ∂μ := by
+    ∫ x in a..b, ∑ i in s, f i x ∂μ = ∑ i in s, ∫ x in a..b, f i x ∂μ := by
   simp only [interval_integral_eq_integral_uIoc, integral_finset_sum s fun i hi => (h i hi).def,
     Finset.smul_sum]
 #align interval_integral.integral_finset_sum intervalIntegral.integral_finset_sum
 -/
 
 @[simp]
-theorem integral_neg : (∫ x in a..b, -f x ∂μ) = -∫ x in a..b, f x ∂μ := by
+theorem integral_neg : ∫ x in a..b, -f x ∂μ = -∫ x in a..b, f x ∂μ := by
   simp only [intervalIntegral, integral_neg]; abel
 #align interval_integral.integral_neg intervalIntegral.integral_neg
 
 @[simp]
 theorem integral_sub (hf : IntervalIntegrable f μ a b) (hg : IntervalIntegrable g μ a b) :
-    (∫ x in a..b, f x - g x ∂μ) = (∫ x in a..b, f x ∂μ) - ∫ x in a..b, g x ∂μ := by
+    ∫ x in a..b, f x - g x ∂μ = ∫ x in a..b, f x ∂μ - ∫ x in a..b, g x ∂μ := by
   simpa only [sub_eq_add_neg] using (integral_add hf hg.neg).trans (congr_arg _ integral_neg)
 #align interval_integral.integral_sub intervalIntegral.integral_sub
 
 #print intervalIntegral.integral_smul /-
 @[simp]
 theorem integral_smul {𝕜 : Type _} [NontriviallyNormedField 𝕜] [NormedSpace 𝕜 E]
-    [SMulCommClass ℝ 𝕜 E] (r : 𝕜) (f : ℝ → E) :
-    (∫ x in a..b, r • f x ∂μ) = r • ∫ x in a..b, f x ∂μ := by
-  simp only [intervalIntegral, integral_smul, smul_sub]
+    [SMulCommClass ℝ 𝕜 E] (r : 𝕜) (f : ℝ → E) : ∫ x in a..b, r • f x ∂μ = r • ∫ x in a..b, f x ∂μ :=
+  by simp only [intervalIntegral, integral_smul, smul_sub]
 #align interval_integral.integral_smul intervalIntegral.integral_smul
 -/
 
 #print intervalIntegral.integral_smul_const /-
 @[simp]
 theorem integral_smul_const {𝕜 : Type _} [IsROrC 𝕜] [NormedSpace 𝕜 E] (f : ℝ → 𝕜) (c : E) :
-    (∫ x in a..b, f x • c ∂μ) = (∫ x in a..b, f x ∂μ) • c := by
+    ∫ x in a..b, f x • c ∂μ = (∫ x in a..b, f x ∂μ) • c := by
   simp only [interval_integral_eq_integral_uIoc, integral_smul_const, smul_assoc]
 #align interval_integral.integral_smul_const intervalIntegral.integral_smul_const
 -/
 
 @[simp]
 theorem integral_const_mul {𝕜 : Type _} [IsROrC 𝕜] (r : 𝕜) (f : ℝ → 𝕜) :
-    (∫ x in a..b, r * f x ∂μ) = r * ∫ x in a..b, f x ∂μ :=
+    ∫ x in a..b, r * f x ∂μ = r * ∫ x in a..b, f x ∂μ :=
   integral_smul r f
 #align interval_integral.integral_const_mul intervalIntegral.integral_const_mul
 
 @[simp]
 theorem integral_mul_const {𝕜 : Type _} [IsROrC 𝕜] (r : 𝕜) (f : ℝ → 𝕜) :
-    (∫ x in a..b, f x * r ∂μ) = (∫ x in a..b, f x ∂μ) * r := by
+    ∫ x in a..b, f x * r ∂μ = (∫ x in a..b, f x ∂μ) * r := by
   simpa only [mul_comm r] using integral_const_mul r f
 #align interval_integral.integral_mul_const intervalIntegral.integral_mul_const
 
 @[simp]
 theorem integral_div {𝕜 : Type _} [IsROrC 𝕜] (r : 𝕜) (f : ℝ → 𝕜) :
-    (∫ x in a..b, f x / r ∂μ) = (∫ x in a..b, f x ∂μ) / r := by
+    ∫ x in a..b, f x / r ∂μ = (∫ x in a..b, f x ∂μ) / r := by
   simpa only [div_eq_mul_inv] using integral_mul_const r⁻¹ f
 #align interval_integral.integral_div intervalIntegral.integral_div
 
 theorem integral_const' (c : E) :
-    (∫ x in a..b, c ∂μ) = ((μ <| Ioc a b).toReal - (μ <| Ioc b a).toReal) • c := by
+    ∫ x in a..b, c ∂μ = ((μ <| Ioc a b).toReal - (μ <| Ioc b a).toReal) • c := by
   simp only [intervalIntegral, set_integral_const, sub_smul]
 #align interval_integral.integral_const' intervalIntegral.integral_const'
 
 @[simp]
-theorem integral_const (c : E) : (∫ x in a..b, c) = (b - a) • c := by
+theorem integral_const (c : E) : ∫ x in a..b, c = (b - a) • c := by
   simp only [integral_const', Real.volume_Ioc, ENNReal.toReal_ofReal', ← neg_sub b,
     max_zero_sub_eq_self]
 #align interval_integral.integral_const intervalIntegral.integral_const
 
 #print intervalIntegral.integral_smul_measure /-
 theorem integral_smul_measure (c : ℝ≥0∞) :
-    (∫ x in a..b, f x ∂c • μ) = c.toReal • ∫ x in a..b, f x ∂μ := by
+    ∫ x in a..b, f x ∂c • μ = c.toReal • ∫ x in a..b, f x ∂μ := by
   simp only [intervalIntegral, measure.restrict_smul, integral_smul_measure, smul_sub]
 #align interval_integral.integral_smul_measure intervalIntegral.integral_smul_measure
 -/
@@ -775,7 +774,7 @@ theorem integral_smul_measure (c : ℝ≥0∞) :
 end Basic
 
 theorem integral_ofReal {a b : ℝ} {μ : Measure ℝ} {f : ℝ → ℝ} :
-    (∫ x in a..b, (f x : ℂ) ∂μ) = ↑(∫ x in a..b, f x ∂μ) := by
+    ∫ x in a..b, (f x : ℂ) ∂μ = ↑(∫ x in a..b, f x ∂μ) := by
   simp only [intervalIntegral, integral_ofReal, Complex.ofReal_sub]
 #align interval_integral.integral_of_real intervalIntegral.integral_ofReal
 
@@ -796,7 +795,7 @@ theorem ContinuousLinearMap.intervalIntegral_apply {a b : ℝ} {φ : ℝ → F 
 variable [NormedSpace ℝ F] [CompleteSpace F]
 
 theorem ContinuousLinearMap.intervalIntegral_comp_comm (L : E →L[𝕜] F)
-    (hf : IntervalIntegrable f μ a b) : (∫ x in a..b, L (f x) ∂μ) = L (∫ x in a..b, f x ∂μ) := by
+    (hf : IntervalIntegrable f μ a b) : ∫ x in a..b, L (f x) ∂μ = L (∫ x in a..b, f x ∂μ) := by
   simp_rw [intervalIntegral, L.integral_comp_comm hf.1, L.integral_comp_comm hf.2, L.map_sub]
 #align continuous_linear_map.interval_integral_comp_comm ContinuousLinearMap.intervalIntegral_comp_comm
 
@@ -808,7 +807,7 @@ variable {a b c d : ℝ} (f : ℝ → E)
 
 @[simp]
 theorem integral_comp_mul_right (hc : c ≠ 0) :
-    (∫ x in a..b, f (x * c)) = c⁻¹ • ∫ x in a * c..b * c, f x :=
+    ∫ x in a..b, f (x * c) = c⁻¹ • ∫ x in a * c..b * c, f x :=
   by
   have A : MeasurableEmbedding fun x => x * c :=
     (Homeomorph.mulRight₀ c hc).ClosedEmbedding.MeasurableEmbedding
@@ -821,110 +820,109 @@ theorem integral_comp_mul_right (hc : c ≠ 0) :
 #align interval_integral.integral_comp_mul_right intervalIntegral.integral_comp_mul_right
 
 @[simp]
-theorem smul_integral_comp_mul_right (c) :
-    (c • ∫ x in a..b, f (x * c)) = ∫ x in a * c..b * c, f x := by by_cases hc : c = 0 <;> simp [hc]
+theorem smul_integral_comp_mul_right (c) : c • ∫ x in a..b, f (x * c) = ∫ x in a * c..b * c, f x :=
+  by by_cases hc : c = 0 <;> simp [hc]
 #align interval_integral.smul_integral_comp_mul_right intervalIntegral.smul_integral_comp_mul_right
 
 @[simp]
 theorem integral_comp_mul_left (hc : c ≠ 0) :
-    (∫ x in a..b, f (c * x)) = c⁻¹ • ∫ x in c * a..c * b, f x := by
+    ∫ x in a..b, f (c * x) = c⁻¹ • ∫ x in c * a..c * b, f x := by
   simpa only [mul_comm c] using integral_comp_mul_right f hc
 #align interval_integral.integral_comp_mul_left intervalIntegral.integral_comp_mul_left
 
 @[simp]
-theorem smul_integral_comp_mul_left (c) : (c • ∫ x in a..b, f (c * x)) = ∫ x in c * a..c * b, f x :=
+theorem smul_integral_comp_mul_left (c) : c • ∫ x in a..b, f (c * x) = ∫ x in c * a..c * b, f x :=
   by by_cases hc : c = 0 <;> simp [hc]
 #align interval_integral.smul_integral_comp_mul_left intervalIntegral.smul_integral_comp_mul_left
 
 @[simp]
-theorem integral_comp_div (hc : c ≠ 0) : (∫ x in a..b, f (x / c)) = c • ∫ x in a / c..b / c, f x :=
-  by simpa only [inv_inv] using integral_comp_mul_right f (inv_ne_zero hc)
+theorem integral_comp_div (hc : c ≠ 0) : ∫ x in a..b, f (x / c) = c • ∫ x in a / c..b / c, f x := by
+  simpa only [inv_inv] using integral_comp_mul_right f (inv_ne_zero hc)
 #align interval_integral.integral_comp_div intervalIntegral.integral_comp_div
 
 @[simp]
-theorem inv_smul_integral_comp_div (c) :
-    (c⁻¹ • ∫ x in a..b, f (x / c)) = ∫ x in a / c..b / c, f x := by
-  by_cases hc : c = 0 <;> simp [hc]
+theorem inv_smul_integral_comp_div (c) : c⁻¹ • ∫ x in a..b, f (x / c) = ∫ x in a / c..b / c, f x :=
+  by by_cases hc : c = 0 <;> simp [hc]
 #align interval_integral.inv_smul_integral_comp_div intervalIntegral.inv_smul_integral_comp_div
 
 @[simp]
-theorem integral_comp_add_right (d) : (∫ x in a..b, f (x + d)) = ∫ x in a + d..b + d, f x :=
+theorem integral_comp_add_right (d) : ∫ x in a..b, f (x + d) = ∫ x in a + d..b + d, f x :=
   have A : MeasurableEmbedding fun x => x + d :=
     (Homeomorph.addRight d).ClosedEmbedding.MeasurableEmbedding
   calc
-    (∫ x in a..b, f (x + d)) = ∫ x in a + d..b + d, f x ∂Measure.map (fun x => x + d) volume := by
+    ∫ x in a..b, f (x + d) = ∫ x in a + d..b + d, f x ∂Measure.map (fun x => x + d) volume := by
       simp [intervalIntegral, A.set_integral_map]
     _ = ∫ x in a + d..b + d, f x := by rw [map_add_right_eq_self]
 #align interval_integral.integral_comp_add_right intervalIntegral.integral_comp_add_right
 
 @[simp]
-theorem integral_comp_add_left (d) : (∫ x in a..b, f (d + x)) = ∫ x in d + a..d + b, f x := by
+theorem integral_comp_add_left (d) : ∫ x in a..b, f (d + x) = ∫ x in d + a..d + b, f x := by
   simpa only [add_comm] using integral_comp_add_right f d
 #align interval_integral.integral_comp_add_left intervalIntegral.integral_comp_add_left
 
 @[simp]
 theorem integral_comp_mul_add (hc : c ≠ 0) (d) :
-    (∫ x in a..b, f (c * x + d)) = c⁻¹ • ∫ x in c * a + d..c * b + d, f x := by
+    ∫ x in a..b, f (c * x + d) = c⁻¹ • ∫ x in c * a + d..c * b + d, f x := by
   rw [← integral_comp_add_right, ← integral_comp_mul_left _ hc]
 #align interval_integral.integral_comp_mul_add intervalIntegral.integral_comp_mul_add
 
 @[simp]
 theorem smul_integral_comp_mul_add (c d) :
-    (c • ∫ x in a..b, f (c * x + d)) = ∫ x in c * a + d..c * b + d, f x := by
+    c • ∫ x in a..b, f (c * x + d) = ∫ x in c * a + d..c * b + d, f x := by
   by_cases hc : c = 0 <;> simp [hc]
 #align interval_integral.smul_integral_comp_mul_add intervalIntegral.smul_integral_comp_mul_add
 
 @[simp]
 theorem integral_comp_add_mul (hc : c ≠ 0) (d) :
-    (∫ x in a..b, f (d + c * x)) = c⁻¹ • ∫ x in d + c * a..d + c * b, f x := by
+    ∫ x in a..b, f (d + c * x) = c⁻¹ • ∫ x in d + c * a..d + c * b, f x := by
   rw [← integral_comp_add_left, ← integral_comp_mul_left _ hc]
 #align interval_integral.integral_comp_add_mul intervalIntegral.integral_comp_add_mul
 
 @[simp]
 theorem smul_integral_comp_add_mul (c d) :
-    (c • ∫ x in a..b, f (d + c * x)) = ∫ x in d + c * a..d + c * b, f x := by
+    c • ∫ x in a..b, f (d + c * x) = ∫ x in d + c * a..d + c * b, f x := by
   by_cases hc : c = 0 <;> simp [hc]
 #align interval_integral.smul_integral_comp_add_mul intervalIntegral.smul_integral_comp_add_mul
 
 @[simp]
 theorem integral_comp_div_add (hc : c ≠ 0) (d) :
-    (∫ x in a..b, f (x / c + d)) = c • ∫ x in a / c + d..b / c + d, f x := by
+    ∫ x in a..b, f (x / c + d) = c • ∫ x in a / c + d..b / c + d, f x := by
   simpa only [div_eq_inv_mul, inv_inv] using integral_comp_mul_add f (inv_ne_zero hc) d
 #align interval_integral.integral_comp_div_add intervalIntegral.integral_comp_div_add
 
 @[simp]
 theorem inv_smul_integral_comp_div_add (c d) :
-    (c⁻¹ • ∫ x in a..b, f (x / c + d)) = ∫ x in a / c + d..b / c + d, f x := by
+    c⁻¹ • ∫ x in a..b, f (x / c + d) = ∫ x in a / c + d..b / c + d, f x := by
   by_cases hc : c = 0 <;> simp [hc]
 #align interval_integral.inv_smul_integral_comp_div_add intervalIntegral.inv_smul_integral_comp_div_add
 
 @[simp]
 theorem integral_comp_add_div (hc : c ≠ 0) (d) :
-    (∫ x in a..b, f (d + x / c)) = c • ∫ x in d + a / c..d + b / c, f x := by
+    ∫ x in a..b, f (d + x / c) = c • ∫ x in d + a / c..d + b / c, f x := by
   simpa only [div_eq_inv_mul, inv_inv] using integral_comp_add_mul f (inv_ne_zero hc) d
 #align interval_integral.integral_comp_add_div intervalIntegral.integral_comp_add_div
 
 @[simp]
 theorem inv_smul_integral_comp_add_div (c d) :
-    (c⁻¹ • ∫ x in a..b, f (d + x / c)) = ∫ x in d + a / c..d + b / c, f x := by
+    c⁻¹ • ∫ x in a..b, f (d + x / c) = ∫ x in d + a / c..d + b / c, f x := by
   by_cases hc : c = 0 <;> simp [hc]
 #align interval_integral.inv_smul_integral_comp_add_div intervalIntegral.inv_smul_integral_comp_add_div
 
 @[simp]
 theorem integral_comp_mul_sub (hc : c ≠ 0) (d) :
-    (∫ x in a..b, f (c * x - d)) = c⁻¹ • ∫ x in c * a - d..c * b - d, f x := by
+    ∫ x in a..b, f (c * x - d) = c⁻¹ • ∫ x in c * a - d..c * b - d, f x := by
   simpa only [sub_eq_add_neg] using integral_comp_mul_add f hc (-d)
 #align interval_integral.integral_comp_mul_sub intervalIntegral.integral_comp_mul_sub
 
 @[simp]
 theorem smul_integral_comp_mul_sub (c d) :
-    (c • ∫ x in a..b, f (c * x - d)) = ∫ x in c * a - d..c * b - d, f x := by
+    c • ∫ x in a..b, f (c * x - d) = ∫ x in c * a - d..c * b - d, f x := by
   by_cases hc : c = 0 <;> simp [hc]
 #align interval_integral.smul_integral_comp_mul_sub intervalIntegral.smul_integral_comp_mul_sub
 
 @[simp]
 theorem integral_comp_sub_mul (hc : c ≠ 0) (d) :
-    (∫ x in a..b, f (d - c * x)) = c⁻¹ • ∫ x in d - c * b..d - c * a, f x :=
+    ∫ x in a..b, f (d - c * x) = c⁻¹ • ∫ x in d - c * b..d - c * a, f x :=
   by
   simp only [sub_eq_add_neg, neg_mul_eq_neg_mul]
   rw [integral_comp_add_mul f (neg_ne_zero.mpr hc) d, integral_symm]
@@ -933,46 +931,46 @@ theorem integral_comp_sub_mul (hc : c ≠ 0) (d) :
 
 @[simp]
 theorem smul_integral_comp_sub_mul (c d) :
-    (c • ∫ x in a..b, f (d - c * x)) = ∫ x in d - c * b..d - c * a, f x := by
+    c • ∫ x in a..b, f (d - c * x) = ∫ x in d - c * b..d - c * a, f x := by
   by_cases hc : c = 0 <;> simp [hc]
 #align interval_integral.smul_integral_comp_sub_mul intervalIntegral.smul_integral_comp_sub_mul
 
 @[simp]
 theorem integral_comp_div_sub (hc : c ≠ 0) (d) :
-    (∫ x in a..b, f (x / c - d)) = c • ∫ x in a / c - d..b / c - d, f x := by
+    ∫ x in a..b, f (x / c - d) = c • ∫ x in a / c - d..b / c - d, f x := by
   simpa only [div_eq_inv_mul, inv_inv] using integral_comp_mul_sub f (inv_ne_zero hc) d
 #align interval_integral.integral_comp_div_sub intervalIntegral.integral_comp_div_sub
 
 @[simp]
 theorem inv_smul_integral_comp_div_sub (c d) :
-    (c⁻¹ • ∫ x in a..b, f (x / c - d)) = ∫ x in a / c - d..b / c - d, f x := by
+    c⁻¹ • ∫ x in a..b, f (x / c - d) = ∫ x in a / c - d..b / c - d, f x := by
   by_cases hc : c = 0 <;> simp [hc]
 #align interval_integral.inv_smul_integral_comp_div_sub intervalIntegral.inv_smul_integral_comp_div_sub
 
 @[simp]
 theorem integral_comp_sub_div (hc : c ≠ 0) (d) :
-    (∫ x in a..b, f (d - x / c)) = c • ∫ x in d - b / c..d - a / c, f x := by
+    ∫ x in a..b, f (d - x / c) = c • ∫ x in d - b / c..d - a / c, f x := by
   simpa only [div_eq_inv_mul, inv_inv] using integral_comp_sub_mul f (inv_ne_zero hc) d
 #align interval_integral.integral_comp_sub_div intervalIntegral.integral_comp_sub_div
 
 @[simp]
 theorem inv_smul_integral_comp_sub_div (c d) :
-    (c⁻¹ • ∫ x in a..b, f (d - x / c)) = ∫ x in d - b / c..d - a / c, f x := by
+    c⁻¹ • ∫ x in a..b, f (d - x / c) = ∫ x in d - b / c..d - a / c, f x := by
   by_cases hc : c = 0 <;> simp [hc]
 #align interval_integral.inv_smul_integral_comp_sub_div intervalIntegral.inv_smul_integral_comp_sub_div
 
 @[simp]
-theorem integral_comp_sub_right (d) : (∫ x in a..b, f (x - d)) = ∫ x in a - d..b - d, f x := by
+theorem integral_comp_sub_right (d) : ∫ x in a..b, f (x - d) = ∫ x in a - d..b - d, f x := by
   simpa only [sub_eq_add_neg] using integral_comp_add_right f (-d)
 #align interval_integral.integral_comp_sub_right intervalIntegral.integral_comp_sub_right
 
 @[simp]
-theorem integral_comp_sub_left (d) : (∫ x in a..b, f (d - x)) = ∫ x in d - b..d - a, f x := by
+theorem integral_comp_sub_left (d) : ∫ x in a..b, f (d - x) = ∫ x in d - b..d - a, f x := by
   simpa only [one_mul, one_smul, inv_one] using integral_comp_sub_mul f one_ne_zero d
 #align interval_integral.integral_comp_sub_left intervalIntegral.integral_comp_sub_left
 
 @[simp]
-theorem integral_comp_neg : (∫ x in a..b, f (-x)) = ∫ x in -b..-a, f x := by
+theorem integral_comp_neg : ∫ x in a..b, f (-x) = ∫ x in -b..-a, f x := by
   simpa only [zero_sub] using integral_comp_sub_left f 0
 #align interval_integral.integral_comp_neg intervalIntegral.integral_comp_neg
 
@@ -994,7 +992,7 @@ variable {a b c d : ℝ} {f g : ℝ → E} {μ : Measure ℝ}
 #print intervalIntegral.integral_congr /-
 /-- If two functions are equal in the relevant interval, their interval integrals are also equal. -/
 theorem integral_congr {a b : ℝ} (h : EqOn f g [a, b]) :
-    (∫ x in a..b, f x ∂μ) = ∫ x in a..b, g x ∂μ := by
+    ∫ x in a..b, f x ∂μ = ∫ x in a..b, g x ∂μ := by
   cases' le_total a b with hab hab <;>
     simpa [hab, integral_of_le, integral_of_ge] using
       set_integral_congr measurableSet_Ioc (h.mono Ioc_subset_Icc_self)
@@ -1003,7 +1001,7 @@ theorem integral_congr {a b : ℝ} (h : EqOn f g [a, b]) :
 
 theorem integral_add_adjacent_intervals_cancel (hab : IntervalIntegrable f μ a b)
     (hbc : IntervalIntegrable f μ b c) :
-    (((∫ x in a..b, f x ∂μ) + ∫ x in b..c, f x ∂μ) + ∫ x in c..a, f x ∂μ) = 0 :=
+    ∫ x in a..b, f x ∂μ + ∫ x in b..c, f x ∂μ + ∫ x in c..a, f x ∂μ = 0 :=
   by
   have hac := hab.trans hbc
   simp only [intervalIntegral, sub_add_sub_comm, sub_eq_zero]
@@ -1018,13 +1016,13 @@ theorem integral_add_adjacent_intervals_cancel (hab : IntervalIntegrable f μ a
 
 theorem integral_add_adjacent_intervals (hab : IntervalIntegrable f μ a b)
     (hbc : IntervalIntegrable f μ b c) :
-    ((∫ x in a..b, f x ∂μ) + ∫ x in b..c, f x ∂μ) = ∫ x in a..c, f x ∂μ := by
+    ∫ x in a..b, f x ∂μ + ∫ x in b..c, f x ∂μ = ∫ x in a..c, f x ∂μ := by
   rw [← add_neg_eq_zero, ← integral_symm, integral_add_adjacent_intervals_cancel hab hbc]
 #align interval_integral.integral_add_adjacent_intervals intervalIntegral.integral_add_adjacent_intervals
 
 theorem sum_integral_adjacent_intervals_Ico {a : ℕ → ℝ} {m n : ℕ} (hmn : m ≤ n)
     (hint : ∀ k ∈ Ico m n, IntervalIntegrable f μ (a k) (a <| k + 1)) :
-    (∑ k : ℕ in Finset.Ico m n, ∫ x in a k..a <| k + 1, f x ∂μ) = ∫ x in a m..a n, f x ∂μ :=
+    ∑ k : ℕ in Finset.Ico m n, ∫ x in a k..a <| k + 1, f x ∂μ = ∫ x in a m..a n, f x ∂μ :=
   by
   revert hint
   refine' Nat.le_induction _ _ n hmn
@@ -1042,7 +1040,7 @@ theorem sum_integral_adjacent_intervals_Ico {a : ℕ → ℝ} {m n : ℕ} (hmn :
 #print intervalIntegral.sum_integral_adjacent_intervals /-
 theorem sum_integral_adjacent_intervals {a : ℕ → ℝ} {n : ℕ}
     (hint : ∀ k < n, IntervalIntegrable f μ (a k) (a <| k + 1)) :
-    (∑ k : ℕ in Finset.range n, ∫ x in a k..a <| k + 1, f x ∂μ) = ∫ x in a 0 ..a n, f x ∂μ :=
+    ∑ k : ℕ in Finset.range n, ∫ x in a k..a <| k + 1, f x ∂μ = ∫ x in a 0 ..a n, f x ∂μ :=
   by
   rw [← Nat.Ico_zero_eq_range]
   exact sum_integral_adjacent_intervals_Ico (zero_le n) fun k hk => hint k hk.2
@@ -1051,36 +1049,33 @@ theorem sum_integral_adjacent_intervals {a : ℕ → ℝ} {n : ℕ}
 
 theorem integral_interval_sub_left (hab : IntervalIntegrable f μ a b)
     (hac : IntervalIntegrable f μ a c) :
-    ((∫ x in a..b, f x ∂μ) - ∫ x in a..c, f x ∂μ) = ∫ x in c..b, f x ∂μ :=
+    ∫ x in a..b, f x ∂μ - ∫ x in a..c, f x ∂μ = ∫ x in c..b, f x ∂μ :=
   sub_eq_of_eq_add' <| Eq.symm <| integral_add_adjacent_intervals hac (hac.symm.trans hab)
 #align interval_integral.integral_interval_sub_left intervalIntegral.integral_interval_sub_left
 
 theorem integral_interval_add_interval_comm (hab : IntervalIntegrable f μ a b)
     (hcd : IntervalIntegrable f μ c d) (hac : IntervalIntegrable f μ a c) :
-    ((∫ x in a..b, f x ∂μ) + ∫ x in c..d, f x ∂μ) = (∫ x in a..d, f x ∂μ) + ∫ x in c..b, f x ∂μ :=
-  by
+    ∫ x in a..b, f x ∂μ + ∫ x in c..d, f x ∂μ = ∫ x in a..d, f x ∂μ + ∫ x in c..b, f x ∂μ := by
   rw [← integral_add_adjacent_intervals hac hcd, add_assoc, add_left_comm,
     integral_add_adjacent_intervals hac (hac.symm.trans hab), add_comm]
 #align interval_integral.integral_interval_add_interval_comm intervalIntegral.integral_interval_add_interval_comm
 
 theorem integral_interval_sub_interval_comm (hab : IntervalIntegrable f μ a b)
     (hcd : IntervalIntegrable f μ c d) (hac : IntervalIntegrable f μ a c) :
-    ((∫ x in a..b, f x ∂μ) - ∫ x in c..d, f x ∂μ) = (∫ x in a..c, f x ∂μ) - ∫ x in b..d, f x ∂μ :=
-  by
+    ∫ x in a..b, f x ∂μ - ∫ x in c..d, f x ∂μ = ∫ x in a..c, f x ∂μ - ∫ x in b..d, f x ∂μ := by
   simp only [sub_eq_add_neg, ← integral_symm,
     integral_interval_add_interval_comm hab hcd.symm (hac.trans hcd)]
 #align interval_integral.integral_interval_sub_interval_comm intervalIntegral.integral_interval_sub_interval_comm
 
 theorem integral_interval_sub_interval_comm' (hab : IntervalIntegrable f μ a b)
     (hcd : IntervalIntegrable f μ c d) (hac : IntervalIntegrable f μ a c) :
-    ((∫ x in a..b, f x ∂μ) - ∫ x in c..d, f x ∂μ) = (∫ x in d..b, f x ∂μ) - ∫ x in c..a, f x ∂μ :=
-  by
+    ∫ x in a..b, f x ∂μ - ∫ x in c..d, f x ∂μ = ∫ x in d..b, f x ∂μ - ∫ x in c..a, f x ∂μ := by
   rw [integral_interval_sub_interval_comm hab hcd hac, integral_symm b d, integral_symm a c,
     sub_neg_eq_add, sub_eq_neg_add]
 #align interval_integral.integral_interval_sub_interval_comm' intervalIntegral.integral_interval_sub_interval_comm'
 
 theorem integral_Iic_sub_Iic (ha : IntegrableOn f (Iic a) μ) (hb : IntegrableOn f (Iic b) μ) :
-    ((∫ x in Iic b, f x ∂μ) - ∫ x in Iic a, f x ∂μ) = ∫ x in a..b, f x ∂μ :=
+    ∫ x in Iic b, f x ∂μ - ∫ x in Iic a, f x ∂μ = ∫ x in a..b, f x ∂μ :=
   by
   wlog hab : a ≤ b generalizing a b
   · rw [integral_symm, ← this hb ha (le_of_not_le hab), neg_sub]
@@ -1091,7 +1086,7 @@ theorem integral_Iic_sub_Iic (ha : IntegrableOn f (Iic a) μ) (hb : IntegrableOn
 
 /-- If `μ` is a finite measure then `∫ x in a..b, c ∂μ = (μ (Iic b) - μ (Iic a)) • c`. -/
 theorem integral_const_of_cdf [IsFiniteMeasure μ] (c : E) :
-    (∫ x in a..b, c ∂μ) = ((μ (Iic b)).toReal - (μ (Iic a)).toReal) • c :=
+    ∫ x in a..b, c ∂μ = ((μ (Iic b)).toReal - (μ (Iic a)).toReal) • c :=
   by
   simp only [sub_smul, ← set_integral_const]
   refine' (integral_Iic_sub_Iic _ _).symm <;>
@@ -1099,7 +1094,7 @@ theorem integral_const_of_cdf [IsFiniteMeasure μ] (c : E) :
 #align interval_integral.integral_const_of_cdf intervalIntegral.integral_const_of_cdf
 
 theorem integral_eq_integral_of_support_subset {a b} (h : support f ⊆ Ioc a b) :
-    (∫ x in a..b, f x ∂μ) = ∫ x, f x ∂μ :=
+    ∫ x in a..b, f x ∂μ = ∫ x, f x ∂μ :=
   by
   cases' le_total a b with hab hab
   ·
@@ -1111,7 +1106,7 @@ theorem integral_eq_integral_of_support_subset {a b} (h : support f ⊆ Ioc a b)
 
 #print intervalIntegral.integral_congr_ae' /-
 theorem integral_congr_ae' (h : ∀ᵐ x ∂μ, x ∈ Ioc a b → f x = g x)
-    (h' : ∀ᵐ x ∂μ, x ∈ Ioc b a → f x = g x) : (∫ x in a..b, f x ∂μ) = ∫ x in a..b, g x ∂μ := by
+    (h' : ∀ᵐ x ∂μ, x ∈ Ioc b a → f x = g x) : ∫ x in a..b, f x ∂μ = ∫ x in a..b, g x ∂μ := by
   simp only [intervalIntegral, set_integral_congr_ae measurableSet_Ioc h,
     set_integral_congr_ae measurableSet_Ioc h']
 #align interval_integral.integral_congr_ae' intervalIntegral.integral_congr_ae'
@@ -1119,19 +1114,19 @@ theorem integral_congr_ae' (h : ∀ᵐ x ∂μ, x ∈ Ioc a b → f x = g x)
 
 #print intervalIntegral.integral_congr_ae /-
 theorem integral_congr_ae (h : ∀ᵐ x ∂μ, x ∈ Ι a b → f x = g x) :
-    (∫ x in a..b, f x ∂μ) = ∫ x in a..b, g x ∂μ :=
+    ∫ x in a..b, f x ∂μ = ∫ x in a..b, g x ∂μ :=
   integral_congr_ae' (ae_uIoc_iff.mp h).1 (ae_uIoc_iff.mp h).2
 #align interval_integral.integral_congr_ae intervalIntegral.integral_congr_ae
 -/
 
-theorem integral_zero_ae (h : ∀ᵐ x ∂μ, x ∈ Ι a b → f x = 0) : (∫ x in a..b, f x ∂μ) = 0 :=
+theorem integral_zero_ae (h : ∀ᵐ x ∂μ, x ∈ Ι a b → f x = 0) : ∫ x in a..b, f x ∂μ = 0 :=
   calc
-    (∫ x in a..b, f x ∂μ) = ∫ x in a..b, 0 ∂μ := integral_congr_ae h
+    ∫ x in a..b, f x ∂μ = ∫ x in a..b, 0 ∂μ := integral_congr_ae h
     _ = 0 := integral_zero
 #align interval_integral.integral_zero_ae intervalIntegral.integral_zero_ae
 
 theorem integral_indicator {a₁ a₂ a₃ : ℝ} (h : a₂ ∈ Icc a₁ a₃) :
-    (∫ x in a₁..a₃, indicator {x | x ≤ a₂} f x ∂μ) = ∫ x in a₁..a₂, f x ∂μ :=
+    ∫ x in a₁..a₃, indicator {x | x ≤ a₂} f x ∂μ = ∫ x in a₁..a₂, f x ∂μ :=
   by
   have : {x | x ≤ a₂} ∩ Ioc a₁ a₃ = Ioc a₁ a₂ := Iic_inter_Ioc_of_le h.2
   rw [integral_of_le h.1, integral_of_le (h.1.trans h.2), integral_indicator,
@@ -1198,7 +1193,7 @@ theorem hasSum_intervalIntegral_of_summable_norm [Countable ι] {f : ι → C(
 
 theorem tsum_intervalIntegral_eq_of_summable_norm [Countable ι] {f : ι → C(ℝ, E)}
     (hf_sum : Summable fun i : ι => ‖(f i).restrict (⟨uIcc a b, isCompact_uIcc⟩ : Compacts ℝ)‖) :
-    (∑' i : ι, ∫ x in a..b, f i x) = ∫ x in a..b, ∑' i : ι, f i x :=
+    ∑' i : ι, ∫ x in a..b, f i x = ∫ x in a..b, ∑' i : ι, f i x :=
   (hasSum_intervalIntegral_of_summable_norm hf_sum).tsum_eq
 #align interval_integral.tsum_interval_integral_eq_of_summable_norm intervalIntegral.tsum_intervalIntegral_eq_of_summable_norm
 
@@ -1279,7 +1274,7 @@ theorem continuousWithinAt_primitive (hb₀ : μ {b₀} = 0)
         exact
           ⟨min_le_of_left_le <| (min_le_right _ _).trans h₁,
             le_max_of_le_right <| h₂.trans <| le_max_right _ _⟩
-    have : ∀ b ∈ Icc b₁ b₂, (∫ x in a..b, f x ∂μ) = (∫ x in a..b₁, f x ∂μ) + ∫ x in b₁..b, f x ∂μ :=
+    have : ∀ b ∈ Icc b₁ b₂, ∫ x in a..b, f x ∂μ = ∫ x in a..b₁, f x ∂μ + ∫ x in b₁..b, f x ∂μ :=
       by
       rintro b ⟨h₁, h₂⟩
       rw [← integral_add_adjacent_intervals _ (h_int' ⟨h₁, h₂⟩)]
@@ -1344,7 +1339,7 @@ theorem continuousOn_primitive [NoAtoms μ] (h_int : IntegrableOn f (Icc a b) μ
     ContinuousOn (fun x => ∫ t in Ioc a x, f t ∂μ) (Icc a b) :=
   by
   by_cases h : a ≤ b
-  · have : ∀ x ∈ Icc a b, (∫ t in Ioc a x, f t ∂μ) = ∫ t in a..x, f t ∂μ :=
+  · have : ∀ x ∈ Icc a b, ∫ t in Ioc a x, f t ∂μ = ∫ t in a..x, f t ∂μ :=
       by
       intro x x_in
       simp_rw [← uIoc_of_le h, integral_of_le x_in.1]
@@ -1426,14 +1421,14 @@ section
 variable {f g : ℝ → ℝ} {a b : ℝ} {μ : Measure ℝ}
 
 theorem integral_eq_zero_iff_of_le_of_nonneg_ae (hab : a ≤ b) (hf : 0 ≤ᵐ[μ.restrict (Ioc a b)] f)
-    (hfi : IntervalIntegrable f μ a b) : (∫ x in a..b, f x ∂μ) = 0 ↔ f =ᵐ[μ.restrict (Ioc a b)] 0 :=
+    (hfi : IntervalIntegrable f μ a b) : ∫ x in a..b, f x ∂μ = 0 ↔ f =ᵐ[μ.restrict (Ioc a b)] 0 :=
   by rw [integral_of_le hab, integral_eq_zero_iff_of_nonneg_ae hf hfi.1]
 #align interval_integral.integral_eq_zero_iff_of_le_of_nonneg_ae intervalIntegral.integral_eq_zero_iff_of_le_of_nonneg_ae
 
 #print intervalIntegral.integral_eq_zero_iff_of_nonneg_ae /-
 theorem integral_eq_zero_iff_of_nonneg_ae (hf : 0 ≤ᵐ[μ.restrict (Ioc a b ∪ Ioc b a)] f)
     (hfi : IntervalIntegrable f μ a b) :
-    (∫ x in a..b, f x ∂μ) = 0 ↔ f =ᵐ[μ.restrict (Ioc a b ∪ Ioc b a)] 0 :=
+    ∫ x in a..b, f x ∂μ = 0 ↔ f =ᵐ[μ.restrict (Ioc a b ∪ Ioc b a)] 0 :=
   by
   cases' le_total a b with hab hab <;>
     simp only [Ioc_eq_empty hab.not_lt, empty_union, union_empty] at hf ⊢
@@ -1448,13 +1443,13 @@ integral over `a..b` is positive if and only if `a < b` and the measure of
 `function.support f ∩ set.Ioc a b` is positive. -/
 theorem integral_pos_iff_support_of_nonneg_ae' (hf : 0 ≤ᵐ[μ.restrict (Ι a b)] f)
     (hfi : IntervalIntegrable f μ a b) :
-    (0 < ∫ x in a..b, f x ∂μ) ↔ a < b ∧ 0 < μ (support f ∩ Ioc a b) :=
+    0 < ∫ x in a..b, f x ∂μ ↔ a < b ∧ 0 < μ (support f ∩ Ioc a b) :=
   by
   cases' lt_or_le a b with hab hba
   · rw [uIoc_of_le hab.le] at hf 
     simp only [hab, true_and_iff, integral_of_le hab.le,
       set_integral_pos_iff_support_of_nonneg_ae hf hfi.1]
-  · suffices (∫ x in a..b, f x ∂μ) ≤ 0 by simp only [this.not_lt, hba.not_lt, false_and_iff]
+  · suffices ∫ x in a..b, f x ∂μ ≤ 0 by simp only [this.not_lt, hba.not_lt, false_and_iff]
     rw [integral_of_ge hba, neg_nonpos]
     rw [uIoc_swap, uIoc_of_le hba] at hf 
     exact integral_nonneg_of_ae hf
@@ -1465,7 +1460,7 @@ theorem integral_pos_iff_support_of_nonneg_ae' (hf : 0 ≤ᵐ[μ.restrict (Ι a
 `set.uIoc a b`, then its integral over `a..b` is positive if and only if `a < b` and the
 measure of `function.support f ∩ set.Ioc a b` is positive. -/
 theorem integral_pos_iff_support_of_nonneg_ae (hf : 0 ≤ᵐ[μ] f) (hfi : IntervalIntegrable f μ a b) :
-    (0 < ∫ x in a..b, f x ∂μ) ↔ a < b ∧ 0 < μ (support f ∩ Ioc a b) :=
+    0 < ∫ x in a..b, f x ∂μ ↔ a < b ∧ 0 < μ (support f ∩ Ioc a b) :=
   integral_pos_iff_support_of_nonneg_ae' (ae_mono Measure.restrict_le_self hf) hfi
 #align interval_integral.integral_pos_iff_support_of_nonneg_ae intervalIntegral.integral_pos_iff_support_of_nonneg_ae
 
@@ -1500,7 +1495,7 @@ of nonzero measure, then `∫ x in a..b, f x ∂μ < ∫ x in a..b, g x ∂μ`.
 theorem integral_lt_integral_of_ae_le_of_measure_setOf_lt_ne_zero (hab : a ≤ b)
     (hfi : IntervalIntegrable f μ a b) (hgi : IntervalIntegrable g μ a b)
     (hle : f ≤ᵐ[μ.restrict (Ioc a b)] g) (hlt : μ.restrict (Ioc a b) {x | f x < g x} ≠ 0) :
-    (∫ x in a..b, f x ∂μ) < ∫ x in a..b, g x ∂μ :=
+    ∫ x in a..b, f x ∂μ < ∫ x in a..b, g x ∂μ :=
   by
   rw [← sub_pos, ← integral_sub hgi hfi, integral_of_le hab,
     MeasureTheory.integral_pos_iff_support_of_nonneg_ae]
@@ -1514,7 +1509,7 @@ theorem integral_lt_integral_of_ae_le_of_measure_setOf_lt_ne_zero (hab : a ≤ b
 theorem integral_lt_integral_of_continuousOn_of_le_of_exists_lt {f g : ℝ → ℝ} {a b : ℝ}
     (hab : a < b) (hfc : ContinuousOn f (Icc a b)) (hgc : ContinuousOn g (Icc a b))
     (hle : ∀ x ∈ Ioc a b, f x ≤ g x) (hlt : ∃ c ∈ Icc a b, f c < g c) :
-    (∫ x in a..b, f x) < ∫ x in a..b, g x :=
+    ∫ x in a..b, f x < ∫ x in a..b, g x :=
   by
   refine'
     integral_lt_integral_of_ae_le_of_measure_set_of_lt_ne_zero hab.le
@@ -1562,24 +1557,24 @@ variable (hab : a ≤ b) (hf : IntervalIntegrable f μ a b) (hg : IntervalIntegr
 include hab hf hg
 
 theorem integral_mono_ae_restrict (h : f ≤ᵐ[μ.restrict (Icc a b)] g) :
-    (∫ u in a..b, f u ∂μ) ≤ ∫ u in a..b, g u ∂μ :=
+    ∫ u in a..b, f u ∂μ ≤ ∫ u in a..b, g u ∂μ :=
   by
   let H := h.filter_mono <| ae_mono <| Measure.restrict_mono Ioc_subset_Icc_self <| le_refl μ
   simpa only [integral_of_le hab] using set_integral_mono_ae_restrict hf.1 hg.1 H
 #align interval_integral.integral_mono_ae_restrict intervalIntegral.integral_mono_ae_restrict
 
-theorem integral_mono_ae (h : f ≤ᵐ[μ] g) : (∫ u in a..b, f u ∂μ) ≤ ∫ u in a..b, g u ∂μ := by
+theorem integral_mono_ae (h : f ≤ᵐ[μ] g) : ∫ u in a..b, f u ∂μ ≤ ∫ u in a..b, g u ∂μ := by
   simpa only [integral_of_le hab] using set_integral_mono_ae hf.1 hg.1 h
 #align interval_integral.integral_mono_ae intervalIntegral.integral_mono_ae
 
 theorem integral_mono_on (h : ∀ x ∈ Icc a b, f x ≤ g x) :
-    (∫ u in a..b, f u ∂μ) ≤ ∫ u in a..b, g u ∂μ :=
+    ∫ u in a..b, f u ∂μ ≤ ∫ u in a..b, g u ∂μ :=
   by
   let H x hx := h x <| Ioc_subset_Icc_self hx
   simpa only [integral_of_le hab] using set_integral_mono_on hf.1 hg.1 measurableSet_Ioc H
 #align interval_integral.integral_mono_on intervalIntegral.integral_mono_on
 
-theorem integral_mono (h : f ≤ g) : (∫ u in a..b, f u ∂μ) ≤ ∫ u in a..b, g u ∂μ :=
+theorem integral_mono (h : f ≤ g) : ∫ u in a..b, f u ∂μ ≤ ∫ u in a..b, g u ∂μ :=
   integral_mono_ae hab hf hg <| ae_of_all _ h
 #align interval_integral.integral_mono intervalIntegral.integral_mono
 
@@ -1587,7 +1582,7 @@ omit hg hab
 
 theorem integral_mono_interval {c d} (hca : c ≤ a) (hab : a ≤ b) (hbd : b ≤ d)
     (hf : 0 ≤ᵐ[μ.restrict (Ioc c d)] f) (hfi : IntervalIntegrable f μ c d) :
-    (∫ x in a..b, f x ∂μ) ≤ ∫ x in c..d, f x ∂μ :=
+    ∫ x in a..b, f x ∂μ ≤ ∫ x in c..d, f x ∂μ :=
   by
   rw [integral_of_le hab, integral_of_le (hca.trans (hab.trans hbd))]
   exact set_integral_mono_set hfi.1 hf (Ioc_subset_Ioc hca hbd).EventuallyLE

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

@@ -657,7 +657,6 @@ theorem norm_integral_le_integral_norm_Ioc : ‖∫ x in a..b, f x ∂μ‖ ≤
   calc
     ‖∫ x in a..b, f x ∂μ‖ = ‖∫ x in Ι a b, f x ∂μ‖ := norm_integral_eq_norm_integral_Ioc f
     _ ≤ ∫ x in Ι a b, ‖f x‖ ∂μ := norm_integral_le_integral_norm f
-    
 #align interval_integral.norm_integral_le_integral_norm_Ioc intervalIntegral.norm_integral_le_integral_norm_Ioc
 
 theorem norm_integral_le_abs_integral_norm : ‖∫ x in a..b, f x ∂μ‖ ≤ |∫ x in a..b, ‖f x‖ ∂μ| :=
@@ -856,7 +855,6 @@ theorem integral_comp_add_right (d) : (∫ x in a..b, f (x + d)) = ∫ x in a +
     (∫ x in a..b, f (x + d)) = ∫ x in a + d..b + d, f x ∂Measure.map (fun x => x + d) volume := by
       simp [intervalIntegral, A.set_integral_map]
     _ = ∫ x in a + d..b + d, f x := by rw [map_add_right_eq_self]
-    
 #align interval_integral.integral_comp_add_right intervalIntegral.integral_comp_add_right
 
 @[simp]
@@ -1130,7 +1128,6 @@ theorem integral_zero_ae (h : ∀ᵐ x ∂μ, x ∈ Ι a b → f x = 0) : (∫ x
   calc
     (∫ x in a..b, f x ∂μ) = ∫ x in a..b, 0 ∂μ := integral_congr_ae h
     _ = 0 := integral_zero
-    
 #align interval_integral.integral_zero_ae intervalIntegral.integral_zero_ae
 
 theorem integral_indicator {a₁ a₂ a₃ : ℝ} (h : a₂ ∈ Icc a₁ a₃) :
@@ -1606,7 +1603,6 @@ theorem abs_integral_mono_interval {c d} (h : Ι a b ⊆ Ι c d) (hf : 0 ≤ᵐ[
     _ ≤ ∫ x in Ι c d, f x ∂μ := (set_integral_mono_set hfi.def hf h.EventuallyLE)
     _ ≤ |∫ x in Ι c d, f x ∂μ| := (le_abs_self _)
     _ = |∫ x in c..d, f x ∂μ| := (abs_integral_eq_abs_integral_uIoc f).symm
-    
 #align interval_integral.abs_integral_mono_interval intervalIntegral.abs_integral_mono_interval
 -/
 

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

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury G. Kudryashov, Patrick Massot, Sébastien Gouëzel
 
 ! This file was ported from Lean 3 source module measure_theory.integral.interval_integral
-! leanprover-community/mathlib commit fd5edc43dc4f10b85abfe544b88f82cf13c5f844
+! leanprover-community/mathlib commit 7e5137f579de09a059a5ce98f364a04e221aabf0
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -15,6 +15,9 @@ import Mathbin.MeasureTheory.Measure.Lebesgue.Basic
 /-!
 # Integral over an interval
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 In this file we define `∫ x in a..b, f x ∂μ` to be `∫ x in Ioc a b, f x ∂μ` if `a ≤ b` and
 `-∫ x in Ioc b a, f x ∂μ` if `b ≤ a`.
 

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

@@ -66,6 +66,7 @@ variable {ι 𝕜 E F A : Type _} [NormedAddCommGroup E]
 -/
 
 
+#print IntervalIntegrable /-
 /-- A function `f` is called *interval integrable* with respect to a measure `μ` on an unordered
 interval `a..b` if it is integrable on both intervals `(a, b]` and `(b, a]`. One of these
 intervals is always empty, so this property is equivalent to `f` being integrable on
@@ -73,62 +74,75 @@ intervals is always empty, so this property is equivalent to `f` being integrabl
 def IntervalIntegrable (f : ℝ → E) (μ : Measure ℝ) (a b : ℝ) : Prop :=
   IntegrableOn f (Ioc a b) μ ∧ IntegrableOn f (Ioc b a) μ
 #align interval_integrable IntervalIntegrable
+-/
 
 section
 
 variable {f : ℝ → E} {a b : ℝ} {μ : Measure ℝ}
 
+#print intervalIntegrable_iff /-
 /-- A function is interval integrable with respect to a given measure `μ` on `a..b` if and
   only if it is integrable on `uIoc a b` with respect to `μ`. This is an equivalent
   definition of `interval_integrable`. -/
 theorem intervalIntegrable_iff : IntervalIntegrable f μ a b ↔ IntegrableOn f (Ι a b) μ := by
   rw [uIoc_eq_union, integrable_on_union, IntervalIntegrable]
 #align interval_integrable_iff intervalIntegrable_iff
+-/
 
+#print IntervalIntegrable.def /-
 /-- If a function is interval integrable with respect to a given measure `μ` on `a..b` then
   it is integrable on `uIoc a b` with respect to `μ`. -/
 theorem IntervalIntegrable.def (h : IntervalIntegrable f μ a b) : IntegrableOn f (Ι a b) μ :=
   intervalIntegrable_iff.mp h
 #align interval_integrable.def IntervalIntegrable.def
+-/
 
 theorem intervalIntegrable_iff_integrable_Ioc_of_le (hab : a ≤ b) :
     IntervalIntegrable f μ a b ↔ IntegrableOn f (Ioc a b) μ := by
   rw [intervalIntegrable_iff, uIoc_of_le hab]
 #align interval_integrable_iff_integrable_Ioc_of_le intervalIntegrable_iff_integrable_Ioc_of_le
 
+#print intervalIntegrable_iff' /-
 theorem intervalIntegrable_iff' [NoAtoms μ] :
     IntervalIntegrable f μ a b ↔ IntegrableOn f (uIcc a b) μ := by
   rw [intervalIntegrable_iff, ← Icc_min_max, uIoc, integrableOn_Icc_iff_integrableOn_Ioc]
 #align interval_integrable_iff' intervalIntegrable_iff'
+-/
 
 theorem intervalIntegrable_iff_integrable_Icc_of_le {f : ℝ → E} {a b : ℝ} (hab : a ≤ b)
     {μ : Measure ℝ} [NoAtoms μ] : IntervalIntegrable f μ a b ↔ IntegrableOn f (Icc a b) μ := by
   rw [intervalIntegrable_iff_integrable_Ioc_of_le hab, integrableOn_Icc_iff_integrableOn_Ioc]
 #align interval_integrable_iff_integrable_Icc_of_le intervalIntegrable_iff_integrable_Icc_of_le
 
+#print MeasureTheory.Integrable.intervalIntegrable /-
 /-- If a function is integrable with respect to a given measure `μ` then it is interval integrable
   with respect to `μ` on `uIcc a b`. -/
 theorem MeasureTheory.Integrable.intervalIntegrable (hf : Integrable f μ) :
     IntervalIntegrable f μ a b :=
   ⟨hf.IntegrableOn, hf.IntegrableOn⟩
 #align measure_theory.integrable.interval_integrable MeasureTheory.Integrable.intervalIntegrable
+-/
 
+#print MeasureTheory.IntegrableOn.intervalIntegrable /-
 theorem MeasureTheory.IntegrableOn.intervalIntegrable (hf : IntegrableOn f [a, b] μ) :
     IntervalIntegrable f μ a b :=
   ⟨MeasureTheory.IntegrableOn.mono_set hf (Ioc_subset_Icc_self.trans Icc_subset_uIcc),
     MeasureTheory.IntegrableOn.mono_set hf (Ioc_subset_Icc_self.trans Icc_subset_uIcc')⟩
 #align measure_theory.integrable_on.interval_integrable MeasureTheory.IntegrableOn.intervalIntegrable
+-/
 
 theorem intervalIntegrable_const_iff {c : E} :
     IntervalIntegrable (fun _ => c) μ a b ↔ c = 0 ∨ μ (Ι a b) < ∞ := by
   simp only [intervalIntegrable_iff, integrable_on_const]
 #align interval_integrable_const_iff intervalIntegrable_const_iff
 
+#print intervalIntegrable_const /-
 @[simp]
 theorem intervalIntegrable_const [IsLocallyFiniteMeasure μ] {c : E} :
     IntervalIntegrable (fun _ => c) μ a b :=
   intervalIntegrable_const_iff.2 <| Or.inr measure_Ioc_lt_top
 #align interval_integrable_const intervalIntegrable_const
+-/
 
 end
 
@@ -138,22 +152,29 @@ section
 
 variable {f : ℝ → E} {a b c d : ℝ} {μ ν : Measure ℝ}
 
+#print IntervalIntegrable.symm /-
 @[symm]
 theorem symm (h : IntervalIntegrable f μ a b) : IntervalIntegrable f μ b a :=
   h.symm
 #align interval_integrable.symm IntervalIntegrable.symm
+-/
 
+#print IntervalIntegrable.refl /-
 @[refl]
 theorem refl : IntervalIntegrable f μ a a := by constructor <;> simp
 #align interval_integrable.refl IntervalIntegrable.refl
+-/
 
+#print IntervalIntegrable.trans /-
 @[trans]
 theorem trans {a b c : ℝ} (hab : IntervalIntegrable f μ a b) (hbc : IntervalIntegrable f μ b c) :
     IntervalIntegrable f μ a c :=
   ⟨(hab.1.union hbc.1).mono_set Ioc_subset_Ioc_union_Ioc,
     (hbc.2.union hab.2).mono_set Ioc_subset_Ioc_union_Ioc⟩
 #align interval_integrable.trans IntervalIntegrable.trans
+-/
 
+#print IntervalIntegrable.trans_iterate_Ico /-
 theorem trans_iterate_Ico {a : ℕ → ℝ} {m n : ℕ} (hmn : m ≤ n)
     (hint : ∀ k ∈ Ico m n, IntervalIntegrable f μ (a k) (a <| k + 1)) :
     IntervalIntegrable f μ (a m) (a n) := by
@@ -163,77 +184,106 @@ theorem trans_iterate_Ico {a : ℕ → ℝ} {m n : ℕ} (hmn : m ≤ n)
   · intro p hp IH h
     exact (IH fun k hk => h k (Ico_subset_Ico_right p.le_succ hk)).trans (h p (by simp [hp]))
 #align interval_integrable.trans_iterate_Ico IntervalIntegrable.trans_iterate_Ico
+-/
 
+#print IntervalIntegrable.trans_iterate /-
 theorem trans_iterate {a : ℕ → ℝ} {n : ℕ}
     (hint : ∀ k < n, IntervalIntegrable f μ (a k) (a <| k + 1)) :
     IntervalIntegrable f μ (a 0) (a n) :=
   trans_iterate_Ico bot_le fun k hk => hint k hk.2
 #align interval_integrable.trans_iterate IntervalIntegrable.trans_iterate
+-/
 
+#print IntervalIntegrable.neg /-
 theorem neg (h : IntervalIntegrable f μ a b) : IntervalIntegrable (-f) μ a b :=
   ⟨h.1.neg, h.2.neg⟩
 #align interval_integrable.neg IntervalIntegrable.neg
+-/
 
+#print IntervalIntegrable.norm /-
 theorem norm (h : IntervalIntegrable f μ a b) : IntervalIntegrable (fun x => ‖f x‖) μ a b :=
   ⟨h.1.norm, h.2.norm⟩
 #align interval_integrable.norm IntervalIntegrable.norm
+-/
 
+#print IntervalIntegrable.intervalIntegrable_norm_iff /-
 theorem intervalIntegrable_norm_iff {f : ℝ → E} {μ : Measure ℝ} {a b : ℝ}
     (hf : AEStronglyMeasurable f (μ.restrict (Ι a b))) :
     IntervalIntegrable (fun t => ‖f t‖) μ a b ↔ IntervalIntegrable f μ a b := by
   simp_rw [intervalIntegrable_iff, integrable_on]; exact integrable_norm_iff hf
 #align interval_integrable.interval_integrable_norm_iff IntervalIntegrable.intervalIntegrable_norm_iff
+-/
 
+#print IntervalIntegrable.abs /-
 theorem abs {f : ℝ → ℝ} (h : IntervalIntegrable f μ a b) :
     IntervalIntegrable (fun x => |f x|) μ a b :=
   h.norm
 #align interval_integrable.abs IntervalIntegrable.abs
+-/
 
+#print IntervalIntegrable.mono /-
 theorem mono (hf : IntervalIntegrable f ν a b) (h1 : [c, d] ⊆ [a, b]) (h2 : μ ≤ ν) :
     IntervalIntegrable f μ c d :=
   intervalIntegrable_iff.mpr <| hf.def.mono (uIoc_subset_uIoc_of_uIcc_subset_uIcc h1) h2
 #align interval_integrable.mono IntervalIntegrable.mono
+-/
 
+#print IntervalIntegrable.mono_measure /-
 theorem mono_measure (hf : IntervalIntegrable f ν a b) (h : μ ≤ ν) : IntervalIntegrable f μ a b :=
   hf.mono rfl.Subset h
 #align interval_integrable.mono_measure IntervalIntegrable.mono_measure
+-/
 
+#print IntervalIntegrable.mono_set /-
 theorem mono_set (hf : IntervalIntegrable f μ a b) (h : [c, d] ⊆ [a, b]) :
     IntervalIntegrable f μ c d :=
   hf.mono h rfl.le
 #align interval_integrable.mono_set IntervalIntegrable.mono_set
+-/
 
+#print IntervalIntegrable.mono_set_ae /-
 theorem mono_set_ae (hf : IntervalIntegrable f μ a b) (h : Ι c d ≤ᵐ[μ] Ι a b) :
     IntervalIntegrable f μ c d :=
   intervalIntegrable_iff.mpr <| hf.def.mono_set_ae h
 #align interval_integrable.mono_set_ae IntervalIntegrable.mono_set_ae
+-/
 
+#print IntervalIntegrable.mono_set' /-
 theorem mono_set' (hf : IntervalIntegrable f μ a b) (hsub : Ι c d ⊆ Ι a b) :
     IntervalIntegrable f μ c d :=
   hf.mono_set_ae <| eventually_of_forall hsub
 #align interval_integrable.mono_set' IntervalIntegrable.mono_set'
+-/
 
+#print IntervalIntegrable.mono_fun /-
 theorem mono_fun [NormedAddCommGroup F] {g : ℝ → F} (hf : IntervalIntegrable f μ a b)
     (hgm : AEStronglyMeasurable g (μ.restrict (Ι a b)))
     (hle : (fun x => ‖g x‖) ≤ᵐ[μ.restrict (Ι a b)] fun x => ‖f x‖) : IntervalIntegrable g μ a b :=
   intervalIntegrable_iff.2 <| hf.def.Integrable.mono hgm hle
 #align interval_integrable.mono_fun IntervalIntegrable.mono_fun
+-/
 
+#print IntervalIntegrable.mono_fun' /-
 theorem mono_fun' {g : ℝ → ℝ} (hg : IntervalIntegrable g μ a b)
     (hfm : AEStronglyMeasurable f (μ.restrict (Ι a b)))
     (hle : (fun x => ‖f x‖) ≤ᵐ[μ.restrict (Ι a b)] g) : IntervalIntegrable f μ a b :=
   intervalIntegrable_iff.2 <| hg.def.Integrable.mono' hfm hle
 #align interval_integrable.mono_fun' IntervalIntegrable.mono_fun'
+-/
 
-protected theorem aEStronglyMeasurable (h : IntervalIntegrable f μ a b) :
+#print IntervalIntegrable.aestronglyMeasurable /-
+protected theorem aestronglyMeasurable (h : IntervalIntegrable f μ a b) :
     AEStronglyMeasurable f (μ.restrict (Ioc a b)) :=
   h.1.AEStronglyMeasurable
-#align interval_integrable.ae_strongly_measurable IntervalIntegrable.aEStronglyMeasurable
+#align interval_integrable.ae_strongly_measurable IntervalIntegrable.aestronglyMeasurable
+-/
 
+#print IntervalIntegrable.ae_strongly_measurable' /-
 protected theorem ae_strongly_measurable' (h : IntervalIntegrable f μ a b) :
     AEStronglyMeasurable f (μ.restrict (Ioc b a)) :=
   h.2.AEStronglyMeasurable
 #align interval_integrable.ae_strongly_measurable' IntervalIntegrable.ae_strongly_measurable'
+-/
 
 end
 
@@ -244,55 +294,70 @@ theorem smul [NormedField 𝕜] [NormedSpace 𝕜 E] {f : ℝ → E} {a b : ℝ}
   ⟨h.1.smul r, h.2.smul r⟩
 #align interval_integrable.smul IntervalIntegrable.smul
 
+#print IntervalIntegrable.add /-
 @[simp]
 theorem add (hf : IntervalIntegrable f μ a b) (hg : IntervalIntegrable g μ a b) :
     IntervalIntegrable (fun x => f x + g x) μ a b :=
   ⟨hf.1.add hg.1, hf.2.add hg.2⟩
 #align interval_integrable.add IntervalIntegrable.add
+-/
 
+#print IntervalIntegrable.sub /-
 @[simp]
 theorem sub (hf : IntervalIntegrable f μ a b) (hg : IntervalIntegrable g μ a b) :
     IntervalIntegrable (fun x => f x - g x) μ a b :=
   ⟨hf.1.sub hg.1, hf.2.sub hg.2⟩
 #align interval_integrable.sub IntervalIntegrable.sub
+-/
 
 theorem sum (s : Finset ι) {f : ι → ℝ → E} (h : ∀ i ∈ s, IntervalIntegrable (f i) μ a b) :
     IntervalIntegrable (∑ i in s, f i) μ a b :=
   ⟨integrable_finset_sum' s fun i hi => (h i hi).1, integrable_finset_sum' s fun i hi => (h i hi).2⟩
 #align interval_integrable.sum IntervalIntegrable.sum
 
+#print IntervalIntegrable.mul_continuousOn /-
 theorem mul_continuousOn {f g : ℝ → A} (hf : IntervalIntegrable f μ a b)
     (hg : ContinuousOn g [a, b]) : IntervalIntegrable (fun x => f x * g x) μ a b :=
   by
   rw [intervalIntegrable_iff] at hf ⊢
   exact hf.mul_continuous_on_of_subset hg measurableSet_Ioc isCompact_uIcc Ioc_subset_Icc_self
 #align interval_integrable.mul_continuous_on IntervalIntegrable.mul_continuousOn
+-/
 
+#print IntervalIntegrable.continuousOn_mul /-
 theorem continuousOn_mul {f g : ℝ → A} (hf : IntervalIntegrable f μ a b)
     (hg : ContinuousOn g [a, b]) : IntervalIntegrable (fun x => g x * f x) μ a b :=
   by
   rw [intervalIntegrable_iff] at hf ⊢
   exact hf.continuous_on_mul_of_subset hg isCompact_uIcc measurableSet_Ioc Ioc_subset_Icc_self
 #align interval_integrable.continuous_on_mul IntervalIntegrable.continuousOn_mul
+-/
 
+#print IntervalIntegrable.const_mul /-
 @[simp]
 theorem const_mul {f : ℝ → A} (hf : IntervalIntegrable f μ a b) (c : A) :
     IntervalIntegrable (fun x => c * f x) μ a b :=
   hf.continuousOn_mul continuousOn_const
 #align interval_integrable.const_mul IntervalIntegrable.const_mul
+-/
 
+#print IntervalIntegrable.mul_const /-
 @[simp]
 theorem mul_const {f : ℝ → A} (hf : IntervalIntegrable f μ a b) (c : A) :
     IntervalIntegrable (fun x => f x * c) μ a b :=
   hf.mul_continuousOn continuousOn_const
 #align interval_integrable.mul_const IntervalIntegrable.mul_const
+-/
 
+#print IntervalIntegrable.div_const /-
 @[simp]
 theorem div_const {𝕜 : Type _} {f : ℝ → 𝕜} [NormedField 𝕜] (h : IntervalIntegrable f μ a b)
     (c : 𝕜) : IntervalIntegrable (fun x => f x / c) μ a b := by
   simpa only [div_eq_mul_inv] using mul_const h c⁻¹
 #align interval_integrable.div_const IntervalIntegrable.div_const
+-/
 
+#print IntervalIntegrable.comp_mul_left /-
 theorem comp_mul_left (hf : IntervalIntegrable f volume a b) (c : ℝ) :
     IntervalIntegrable (fun x => f (c * x)) volume (a / c) (b / c) :=
   by
@@ -307,12 +372,16 @@ theorem comp_mul_left (hf : IntervalIntegrable f volume a b) (c : ℝ) :
   · ext; simp only [comp_app]; congr 1; field_simp; ring
   · rw [preimage_mul_const_uIcc (inv_ne_zero hc)]; field_simp [hc]
 #align interval_integrable.comp_mul_left IntervalIntegrable.comp_mul_left
+-/
 
+#print IntervalIntegrable.comp_mul_right /-
 theorem comp_mul_right (hf : IntervalIntegrable f volume a b) (c : ℝ) :
     IntervalIntegrable (fun x => f (x * c)) volume (a / c) (b / c) := by
   simpa only [mul_comm] using comp_mul_left hf c
 #align interval_integrable.comp_mul_right IntervalIntegrable.comp_mul_right
+-/
 
+#print IntervalIntegrable.comp_add_right /-
 theorem comp_add_right (hf : IntervalIntegrable f volume a b) (c : ℝ) :
     IntervalIntegrable (fun x => f (x + c)) volume (a - c) (b - c) :=
   by
@@ -327,26 +396,35 @@ theorem comp_add_right (hf : IntervalIntegrable f volume a b) (c : ℝ) :
   convert (MeasurableEmbedding.integrableOn_map_iff A).mp hf
   rw [preimage_add_const_uIcc]
 #align interval_integrable.comp_add_right IntervalIntegrable.comp_add_right
+-/
 
+#print IntervalIntegrable.comp_add_left /-
 theorem comp_add_left (hf : IntervalIntegrable f volume a b) (c : ℝ) :
     IntervalIntegrable (fun x => f (c + x)) volume (a - c) (b - c) := by
   simpa only [add_comm] using IntervalIntegrable.comp_add_right hf c
 #align interval_integrable.comp_add_left IntervalIntegrable.comp_add_left
+-/
 
+#print IntervalIntegrable.comp_sub_right /-
 theorem comp_sub_right (hf : IntervalIntegrable f volume a b) (c : ℝ) :
     IntervalIntegrable (fun x => f (x - c)) volume (a + c) (b + c) := by
   simpa only [sub_neg_eq_add] using IntervalIntegrable.comp_add_right hf (-c)
 #align interval_integrable.comp_sub_right IntervalIntegrable.comp_sub_right
+-/
 
+#print IntervalIntegrable.iff_comp_neg /-
 theorem iff_comp_neg :
     IntervalIntegrable f volume a b ↔ IntervalIntegrable (fun x => f (-x)) volume (-a) (-b) := by
   constructor; all_goals intro hf; convert comp_mul_left hf (-1); simp; field_simp; field_simp
 #align interval_integrable.iff_comp_neg IntervalIntegrable.iff_comp_neg
+-/
 
+#print IntervalIntegrable.comp_sub_left /-
 theorem comp_sub_left (hf : IntervalIntegrable f volume a b) (c : ℝ) :
     IntervalIntegrable (fun x => f (c - x)) volume (c - a) (c - b) := by
   simpa only [neg_sub, ← sub_eq_add_neg] using iff_comp_neg.mp (hf.comp_add_left c)
 #align interval_integrable.comp_sub_left IntervalIntegrable.comp_sub_left
+-/
 
 end IntervalIntegrable
 
@@ -354,22 +432,26 @@ section
 
 variable {μ : Measure ℝ} [IsLocallyFiniteMeasure μ]
 
+#print ContinuousOn.intervalIntegrable /-
 theorem ContinuousOn.intervalIntegrable {u : ℝ → E} {a b : ℝ} (hu : ContinuousOn u (uIcc a b)) :
     IntervalIntegrable u μ a b :=
   (ContinuousOn.integrableOn_Icc hu).IntervalIntegrable
 #align continuous_on.interval_integrable ContinuousOn.intervalIntegrable
+-/
 
 theorem ContinuousOn.intervalIntegrable_of_Icc {u : ℝ → E} {a b : ℝ} (h : a ≤ b)
     (hu : ContinuousOn u (Icc a b)) : IntervalIntegrable u μ a b :=
   ContinuousOn.intervalIntegrable ((uIcc_of_le h).symm ▸ hu)
 #align continuous_on.interval_integrable_of_Icc ContinuousOn.intervalIntegrable_of_Icc
 
+#print Continuous.intervalIntegrable /-
 /-- A continuous function on `ℝ` is `interval_integrable` with respect to any locally finite measure
 `ν` on ℝ. -/
 theorem Continuous.intervalIntegrable {u : ℝ → E} (hu : Continuous u) (a b : ℝ) :
     IntervalIntegrable u μ a b :=
   hu.ContinuousOn.IntervalIntegrable
 #align continuous.interval_integrable Continuous.intervalIntegrable
+-/
 
 end
 
@@ -378,29 +460,38 @@ section
 variable {μ : Measure ℝ} [IsLocallyFiniteMeasure μ] [ConditionallyCompleteLinearOrder E]
   [OrderTopology E] [SecondCountableTopology E]
 
+#print MonotoneOn.intervalIntegrable /-
 theorem MonotoneOn.intervalIntegrable {u : ℝ → E} {a b : ℝ} (hu : MonotoneOn u (uIcc a b)) :
     IntervalIntegrable u μ a b := by
   rw [intervalIntegrable_iff]
   exact (hu.integrable_on_is_compact isCompact_uIcc).mono_set Ioc_subset_Icc_self
 #align monotone_on.interval_integrable MonotoneOn.intervalIntegrable
+-/
 
+#print AntitoneOn.intervalIntegrable /-
 theorem AntitoneOn.intervalIntegrable {u : ℝ → E} {a b : ℝ} (hu : AntitoneOn u (uIcc a b)) :
     IntervalIntegrable u μ a b :=
   hu.dual_right.IntervalIntegrable
 #align antitone_on.interval_integrable AntitoneOn.intervalIntegrable
+-/
 
+#print Monotone.intervalIntegrable /-
 theorem Monotone.intervalIntegrable {u : ℝ → E} {a b : ℝ} (hu : Monotone u) :
     IntervalIntegrable u μ a b :=
   (hu.MonotoneOn _).IntervalIntegrable
 #align monotone.interval_integrable Monotone.intervalIntegrable
+-/
 
+#print Antitone.intervalIntegrable /-
 theorem Antitone.intervalIntegrable {u : ℝ → E} {a b : ℝ} (hu : Antitone u) :
     IntervalIntegrable u μ a b :=
   (hu.AntitoneOn _).IntervalIntegrable
 #align antitone.interval_integrable Antitone.intervalIntegrable
+-/
 
 end
 
+#print Filter.Tendsto.eventually_intervalIntegrable_ae /-
 /-- Let `l'` be a measurably generated filter; let `l` be a of filter such that each `s ∈ l'`
 eventually includes `Ioc u v` as both `u` and `v` tend to `l`. Let `μ` be a measure finite at `l'`.
 
@@ -418,7 +509,9 @@ theorem Filter.Tendsto.eventually_intervalIntegrable_ae {f : ℝ → E} {μ : Me
   have := (hf.integrableAtFilter_ae hfm hμ).Eventually
   ((hu.Ioc hv).Eventually this).And <| (hv.Ioc hu).Eventually this
 #align filter.tendsto.eventually_interval_integrable_ae Filter.Tendsto.eventually_intervalIntegrable_ae
+-/
 
+#print Filter.Tendsto.eventually_intervalIntegrable /-
 /-- Let `l'` be a measurably generated filter; let `l` be a of filter such that each `s ∈ l'`
 eventually includes `Ioc u v` as both `u` and `v` tend to `l`. Let `μ` be a measure finite at `l'`.
 
@@ -434,6 +527,7 @@ theorem Filter.Tendsto.eventually_intervalIntegrable {f : ℝ → E} {μ : Measu
     (hu : Tendsto u lt l) (hv : Tendsto v lt l) : ∀ᶠ t in lt, IntervalIntegrable f μ (u t) (v t) :=
   (hf.mono_left inf_le_left).eventually_intervalIntegrable_ae hfm hμ hu hv
 #align filter.tendsto.eventually_interval_integrable Filter.Tendsto.eventually_intervalIntegrable
+-/
 
 /-!
 ### Interval integral: definition and basic properties
@@ -445,12 +539,14 @@ and prove some basic properties.
 
 variable [CompleteSpace E] [NormedSpace ℝ E]
 
+#print intervalIntegral /-
 /-- The interval integral `∫ x in a..b, f x ∂μ` is defined
 as `∫ x in Ioc a b, f x ∂μ - ∫ x in Ioc b a, f x ∂μ`. If `a ≤ b`, then it equals
 `∫ x in Ioc a b, f x ∂μ`, otherwise it equals `-∫ x in Ioc b a, f x ∂μ`. -/
 def intervalIntegral (f : ℝ → E) (a b : ℝ) (μ : Measure ℝ) : E :=
   (∫ x in Ioc a b, f x ∂μ) - ∫ x in Ioc b a, f x ∂μ
 #align interval_integral intervalIntegral
+-/
 
 -- mathport name: «expr∫ in .. , ∂ »
 notation3"∫ "(...)" in "a".."b", "r:(scoped f => f)" ∂"μ => intervalIntegral r a b μ
@@ -493,12 +589,14 @@ theorem intervalIntegral_eq_integral_uIoc (f : ℝ → E) (a b : ℝ) (μ : Meas
   · simp only [integral_of_ge (not_le.1 h).le, uIoc_of_lt (not_le.1 h), neg_one_smul]
 #align interval_integral.interval_integral_eq_integral_uIoc intervalIntegral.intervalIntegral_eq_integral_uIoc
 
+#print intervalIntegral.norm_intervalIntegral_eq /-
 theorem norm_intervalIntegral_eq (f : ℝ → E) (a b : ℝ) (μ : Measure ℝ) :
     ‖∫ x in a..b, f x ∂μ‖ = ‖∫ x in Ι a b, f x ∂μ‖ :=
   by
   simp_rw [interval_integral_eq_integral_uIoc, norm_smul]
   split_ifs <;> simp only [norm_neg, norm_one, one_mul]
 #align interval_integral.norm_interval_integral_eq intervalIntegral.norm_intervalIntegral_eq
+-/
 
 theorem abs_intervalIntegral_eq (f : ℝ → ℝ) (a b : ℝ) (μ : Measure ℝ) :
     |∫ x in a..b, f x ∂μ| = |∫ x in Ι a b, f x ∂μ| :=
@@ -523,25 +621,29 @@ theorem intervalIntegrable_of_integral_ne_zero {a b : ℝ} {f : ℝ → E} {μ :
   exact intervalIntegral.integral_undef h
 #align interval_integral.interval_integrable_of_integral_ne_zero intervalIntegral.intervalIntegrable_of_integral_ne_zero
 
-theorem integral_non_aEStronglyMeasurable (hf : ¬AEStronglyMeasurable f (μ.restrict (Ι a b))) :
+theorem integral_non_aestronglyMeasurable (hf : ¬AEStronglyMeasurable f (μ.restrict (Ι a b))) :
     (∫ x in a..b, f x ∂μ) = 0 := by
   rw [interval_integral_eq_integral_uIoc, integral_non_ae_strongly_measurable hf, smul_zero]
-#align interval_integral.integral_non_ae_strongly_measurable intervalIntegral.integral_non_aEStronglyMeasurable
+#align interval_integral.integral_non_ae_strongly_measurable intervalIntegral.integral_non_aestronglyMeasurable
 
-theorem integral_non_aEStronglyMeasurable_of_le (h : a ≤ b)
+theorem integral_non_aestronglyMeasurable_of_le (h : a ≤ b)
     (hf : ¬AEStronglyMeasurable f (μ.restrict (Ioc a b))) : (∫ x in a..b, f x ∂μ) = 0 :=
-  integral_non_aEStronglyMeasurable <| by rwa [uIoc_of_le h]
-#align interval_integral.integral_non_ae_strongly_measurable_of_le intervalIntegral.integral_non_aEStronglyMeasurable_of_le
+  integral_non_aestronglyMeasurable <| by rwa [uIoc_of_le h]
+#align interval_integral.integral_non_ae_strongly_measurable_of_le intervalIntegral.integral_non_aestronglyMeasurable_of_le
 
+#print intervalIntegral.norm_integral_min_max /-
 theorem norm_integral_min_max (f : ℝ → E) :
     ‖∫ x in min a b..max a b, f x ∂μ‖ = ‖∫ x in a..b, f x ∂μ‖ := by
   cases le_total a b <;> simp [*, integral_symm a b]
 #align interval_integral.norm_integral_min_max intervalIntegral.norm_integral_min_max
+-/
 
+#print intervalIntegral.norm_integral_eq_norm_integral_Ioc /-
 theorem norm_integral_eq_norm_integral_Ioc (f : ℝ → E) :
     ‖∫ x in a..b, f x ∂μ‖ = ‖∫ x in Ι a b, f x ∂μ‖ := by
   rw [← norm_integral_min_max, integral_of_le min_le_max, uIoc]
 #align interval_integral.norm_integral_eq_norm_integral_Ioc intervalIntegral.norm_integral_eq_norm_integral_Ioc
+-/
 
 theorem abs_integral_eq_abs_integral_uIoc (f : ℝ → ℝ) :
     |∫ x in a..b, f x ∂μ| = |∫ x in Ι a b, f x ∂μ| :=
@@ -566,12 +668,14 @@ theorem norm_integral_le_integral_norm (h : a ≤ b) :
   norm_integral_le_integral_norm_Ioc.trans_eq <| by rw [uIoc_of_le h, integral_of_le h]
 #align interval_integral.norm_integral_le_integral_norm intervalIntegral.norm_integral_le_integral_norm
 
+#print intervalIntegral.norm_integral_le_of_norm_le /-
 theorem norm_integral_le_of_norm_le {g : ℝ → ℝ} (h : ∀ᵐ t ∂μ.restrict <| Ι a b, ‖f t‖ ≤ g t)
     (hbound : IntervalIntegrable g μ a b) : ‖∫ t in a..b, f t ∂μ‖ ≤ |∫ t in a..b, g t ∂μ| := by
   simp_rw [norm_interval_integral_eq, abs_interval_integral_eq,
     abs_eq_self.mpr (integral_nonneg_of_ae <| h.mono fun t ht => (norm_nonneg _).trans ht),
     norm_integral_le_of_norm_le hbound.def h]
 #align interval_integral.norm_integral_le_of_norm_le intervalIntegral.norm_integral_le_of_norm_le
+-/
 
 theorem norm_integral_le_of_norm_le_const_ae {a b C : ℝ} {f : ℝ → E}
     (h : ∀ᵐ x, x ∈ Ι a b → ‖f x‖ ≤ C) : ‖∫ x in a..b, f x‖ ≤ C * |b - a| :=
@@ -593,12 +697,14 @@ theorem integral_add (hf : IntervalIntegrable f μ a b) (hg : IntervalIntegrable
   simp only [interval_integral_eq_integral_uIoc, integral_add hf.def hg.def, smul_add]
 #align interval_integral.integral_add intervalIntegral.integral_add
 
+#print intervalIntegral.integral_finset_sum /-
 theorem integral_finset_sum {ι} {s : Finset ι} {f : ι → ℝ → E}
     (h : ∀ i ∈ s, IntervalIntegrable (f i) μ a b) :
     (∫ x in a..b, ∑ i in s, f i x ∂μ) = ∑ i in s, ∫ x in a..b, f i x ∂μ := by
   simp only [interval_integral_eq_integral_uIoc, integral_finset_sum s fun i hi => (h i hi).def,
     Finset.smul_sum]
 #align interval_integral.integral_finset_sum intervalIntegral.integral_finset_sum
+-/
 
 @[simp]
 theorem integral_neg : (∫ x in a..b, -f x ∂μ) = -∫ x in a..b, f x ∂μ := by
@@ -611,18 +717,22 @@ theorem integral_sub (hf : IntervalIntegrable f μ a b) (hg : IntervalIntegrable
   simpa only [sub_eq_add_neg] using (integral_add hf hg.neg).trans (congr_arg _ integral_neg)
 #align interval_integral.integral_sub intervalIntegral.integral_sub
 
+#print intervalIntegral.integral_smul /-
 @[simp]
 theorem integral_smul {𝕜 : Type _} [NontriviallyNormedField 𝕜] [NormedSpace 𝕜 E]
     [SMulCommClass ℝ 𝕜 E] (r : 𝕜) (f : ℝ → E) :
     (∫ x in a..b, r • f x ∂μ) = r • ∫ x in a..b, f x ∂μ := by
   simp only [intervalIntegral, integral_smul, smul_sub]
 #align interval_integral.integral_smul intervalIntegral.integral_smul
+-/
 
+#print intervalIntegral.integral_smul_const /-
 @[simp]
 theorem integral_smul_const {𝕜 : Type _} [IsROrC 𝕜] [NormedSpace 𝕜 E] (f : ℝ → 𝕜) (c : E) :
     (∫ x in a..b, f x • c ∂μ) = (∫ x in a..b, f x ∂μ) • c := by
   simp only [interval_integral_eq_integral_uIoc, integral_smul_const, smul_assoc]
 #align interval_integral.integral_smul_const intervalIntegral.integral_smul_const
+-/
 
 @[simp]
 theorem integral_const_mul {𝕜 : Type _} [IsROrC 𝕜] (r : 𝕜) (f : ℝ → 𝕜) :
@@ -653,17 +763,19 @@ theorem integral_const (c : E) : (∫ x in a..b, c) = (b - a) • c := by
     max_zero_sub_eq_self]
 #align interval_integral.integral_const intervalIntegral.integral_const
 
+#print intervalIntegral.integral_smul_measure /-
 theorem integral_smul_measure (c : ℝ≥0∞) :
     (∫ x in a..b, f x ∂c • μ) = c.toReal • ∫ x in a..b, f x ∂μ := by
   simp only [intervalIntegral, measure.restrict_smul, integral_smul_measure, smul_sub]
 #align interval_integral.integral_smul_measure intervalIntegral.integral_smul_measure
+-/
 
 end Basic
 
-theorem integral_of_real {a b : ℝ} {μ : Measure ℝ} {f : ℝ → ℝ} :
+theorem integral_ofReal {a b : ℝ} {μ : Measure ℝ} {f : ℝ → ℝ} :
     (∫ x in a..b, (f x : ℂ) ∂μ) = ↑(∫ x in a..b, f x ∂μ) := by
-  simp only [intervalIntegral, integral_of_real, Complex.ofReal_sub]
-#align interval_integral.integral_of_real intervalIntegral.integral_of_real
+  simp only [intervalIntegral, integral_ofReal, Complex.ofReal_sub]
+#align interval_integral.integral_of_real intervalIntegral.integral_ofReal
 
 section ContinuousLinearMap
 
@@ -878,6 +990,7 @@ section OrderClosedTopology
 
 variable {a b c d : ℝ} {f g : ℝ → E} {μ : Measure ℝ}
 
+#print intervalIntegral.integral_congr /-
 /-- If two functions are equal in the relevant interval, their interval integrals are also equal. -/
 theorem integral_congr {a b : ℝ} (h : EqOn f g [a, b]) :
     (∫ x in a..b, f x ∂μ) = ∫ x in a..b, g x ∂μ := by
@@ -885,6 +998,7 @@ theorem integral_congr {a b : ℝ} (h : EqOn f g [a, b]) :
     simpa [hab, integral_of_le, integral_of_ge] using
       set_integral_congr measurableSet_Ioc (h.mono Ioc_subset_Icc_self)
 #align interval_integral.integral_congr intervalIntegral.integral_congr
+-/
 
 theorem integral_add_adjacent_intervals_cancel (hab : IntervalIntegrable f μ a b)
     (hbc : IntervalIntegrable f μ b c) :
@@ -924,6 +1038,7 @@ theorem sum_integral_adjacent_intervals_Ico {a : ℕ → ℝ} {m n : ℕ} (hmn :
       exact h _ (Ico_subset_Ico_right p.le_succ hk)
 #align interval_integral.sum_integral_adjacent_intervals_Ico intervalIntegral.sum_integral_adjacent_intervals_Ico
 
+#print intervalIntegral.sum_integral_adjacent_intervals /-
 theorem sum_integral_adjacent_intervals {a : ℕ → ℝ} {n : ℕ}
     (hint : ∀ k < n, IntervalIntegrable f μ (a k) (a <| k + 1)) :
     (∑ k : ℕ in Finset.range n, ∫ x in a k..a <| k + 1, f x ∂μ) = ∫ x in a 0 ..a n, f x ∂μ :=
@@ -931,6 +1046,7 @@ theorem sum_integral_adjacent_intervals {a : ℕ → ℝ} {n : ℕ}
   rw [← Nat.Ico_zero_eq_range]
   exact sum_integral_adjacent_intervals_Ico (zero_le n) fun k hk => hint k hk.2
 #align interval_integral.sum_integral_adjacent_intervals intervalIntegral.sum_integral_adjacent_intervals
+-/
 
 theorem integral_interval_sub_left (hab : IntervalIntegrable f μ a b)
     (hac : IntervalIntegrable f μ a c) :
@@ -992,16 +1108,20 @@ theorem integral_eq_integral_of_support_subset {a b} (h : support f ⊆ Ioc a b)
     simp [h]
 #align interval_integral.integral_eq_integral_of_support_subset intervalIntegral.integral_eq_integral_of_support_subset
 
+#print intervalIntegral.integral_congr_ae' /-
 theorem integral_congr_ae' (h : ∀ᵐ x ∂μ, x ∈ Ioc a b → f x = g x)
     (h' : ∀ᵐ x ∂μ, x ∈ Ioc b a → f x = g x) : (∫ x in a..b, f x ∂μ) = ∫ x in a..b, g x ∂μ := by
   simp only [intervalIntegral, set_integral_congr_ae measurableSet_Ioc h,
     set_integral_congr_ae measurableSet_Ioc h']
 #align interval_integral.integral_congr_ae' intervalIntegral.integral_congr_ae'
+-/
 
+#print intervalIntegral.integral_congr_ae /-
 theorem integral_congr_ae (h : ∀ᵐ x ∂μ, x ∈ Ι a b → f x = g x) :
     (∫ x in a..b, f x ∂μ) = ∫ x in a..b, g x ∂μ :=
   integral_congr_ae' (ae_uIoc_iff.mp h).1 (ae_uIoc_iff.mp h).2
 #align interval_integral.integral_congr_ae intervalIntegral.integral_congr_ae
+-/
 
 theorem integral_zero_ae (h : ∀ᵐ x ∂μ, x ∈ Ι a b → f x = 0) : (∫ x in a..b, f x ∂μ) = 0 :=
   calc
@@ -1219,6 +1339,7 @@ theorem continuousWithinAt_primitive (hb₀ : μ {b₀} = 0)
     rwa [closure_Icc]
 #align interval_integral.continuous_within_at_primitive intervalIntegral.continuousWithinAt_primitive
 
+#print intervalIntegral.continuousOn_primitive /-
 theorem continuousOn_primitive [NoAtoms μ] (h_int : IntegrableOn f (Icc a b) μ) :
     ContinuousOn (fun x => ∫ t in Ioc a x, f t ∂μ) (Icc a b) :=
   by
@@ -1235,7 +1356,9 @@ theorem continuousOn_primitive [NoAtoms μ] (h_int : IntegrableOn f (Icc a b) μ
   · rw [Icc_eq_empty h]
     exact continuousOn_empty _
 #align interval_integral.continuous_on_primitive intervalIntegral.continuousOn_primitive
+-/
 
+#print intervalIntegral.continuousOn_primitive_Icc /-
 theorem continuousOn_primitive_Icc [NoAtoms μ] (h_int : IntegrableOn f (Icc a b) μ) :
     ContinuousOn (fun x => ∫ t in Icc a x, f t ∂μ) (Icc a b) :=
   by
@@ -1243,7 +1366,9 @@ theorem continuousOn_primitive_Icc [NoAtoms μ] (h_int : IntegrableOn f (Icc a b
       exact integral_Icc_eq_integral_Ioc]
   exact continuous_on_primitive h_int
 #align interval_integral.continuous_on_primitive_Icc intervalIntegral.continuousOn_primitive_Icc
+-/
 
+#print intervalIntegral.continuousOn_primitive_interval' /-
 /-- Note: this assumes that `f` is `interval_integrable`, in contrast to some other lemmas here. -/
 theorem continuousOn_primitive_interval' [NoAtoms μ] (h_int : IntervalIntegrable f μ b₁ b₂)
     (ha : a ∈ [b₁, b₂]) : ContinuousOn (fun b => ∫ x in a..b, f x ∂μ) [b₁, b₂] :=
@@ -1253,12 +1378,16 @@ theorem continuousOn_primitive_interval' [NoAtoms μ] (h_int : IntervalIntegrabl
   rw [min_eq_right ha.1, max_eq_right ha.2]
   simpa [intervalIntegrable_iff, uIoc] using h_int
 #align interval_integral.continuous_on_primitive_interval' intervalIntegral.continuousOn_primitive_interval'
+-/
 
+#print intervalIntegral.continuousOn_primitive_interval /-
 theorem continuousOn_primitive_interval [NoAtoms μ] (h_int : IntegrableOn f (uIcc a b) μ) :
     ContinuousOn (fun x => ∫ t in a..x, f t ∂μ) (uIcc a b) :=
   continuousOn_primitive_interval' h_int.IntervalIntegrable left_mem_uIcc
 #align interval_integral.continuous_on_primitive_interval intervalIntegral.continuousOn_primitive_interval
+-/
 
+#print intervalIntegral.continuousOn_primitive_interval_left /-
 theorem continuousOn_primitive_interval_left [NoAtoms μ] (h_int : IntegrableOn f (uIcc a b) μ) :
     ContinuousOn (fun x => ∫ t in x..b, f t ∂μ) (uIcc a b) :=
   by
@@ -1266,9 +1395,11 @@ theorem continuousOn_primitive_interval_left [NoAtoms μ] (h_int : IntegrableOn
   simp only [integral_symm b]
   exact (continuous_on_primitive_interval h_int).neg
 #align interval_integral.continuous_on_primitive_interval_left intervalIntegral.continuousOn_primitive_interval_left
+-/
 
 variable [NoAtoms μ]
 
+#print intervalIntegral.continuous_primitive /-
 theorem continuous_primitive (h_int : ∀ a b, IntervalIntegrable f μ a b) (a : ℝ) :
     Continuous fun b => ∫ x in a..b, f x ∂μ :=
   by
@@ -1279,11 +1410,14 @@ theorem continuous_primitive (h_int : ∀ a b, IntervalIntegrable f μ a b) (a :
   apply ContinuousWithinAt.continuousAt _ (Icc_mem_nhds hb₁ hb₂)
   exact continuous_within_at_primitive (measure_singleton b₀) (h_int _ _)
 #align interval_integral.continuous_primitive intervalIntegral.continuous_primitive
+-/
 
+#print MeasureTheory.Integrable.continuous_primitive /-
 theorem MeasureTheory.Integrable.continuous_primitive (h_int : Integrable f μ) (a : ℝ) :
     Continuous fun b => ∫ x in a..b, f x ∂μ :=
   continuous_primitive (fun _ _ => h_int.IntervalIntegrable) a
 #align measure_theory.integrable.continuous_primitive MeasureTheory.Integrable.continuous_primitive
+-/
 
 end ContinuousPrimitive
 
@@ -1296,6 +1430,7 @@ theorem integral_eq_zero_iff_of_le_of_nonneg_ae (hab : a ≤ b) (hf : 0 ≤ᵐ[
   by rw [integral_of_le hab, integral_eq_zero_iff_of_nonneg_ae hf hfi.1]
 #align interval_integral.integral_eq_zero_iff_of_le_of_nonneg_ae intervalIntegral.integral_eq_zero_iff_of_le_of_nonneg_ae
 
+#print intervalIntegral.integral_eq_zero_iff_of_nonneg_ae /-
 theorem integral_eq_zero_iff_of_nonneg_ae (hf : 0 ≤ᵐ[μ.restrict (Ioc a b ∪ Ioc b a)] f)
     (hfi : IntervalIntegrable f μ a b) :
     (∫ x in a..b, f x ∂μ) = 0 ↔ f =ᵐ[μ.restrict (Ioc a b ∪ Ioc b a)] 0 :=
@@ -1305,7 +1440,9 @@ theorem integral_eq_zero_iff_of_nonneg_ae (hf : 0 ≤ᵐ[μ.restrict (Ioc a b 
   · exact integral_eq_zero_iff_of_le_of_nonneg_ae hab hf hfi
   · rw [integral_symm, neg_eq_zero, integral_eq_zero_iff_of_le_of_nonneg_ae hab hf hfi.symm]
 #align interval_integral.integral_eq_zero_iff_of_nonneg_ae intervalIntegral.integral_eq_zero_iff_of_nonneg_ae
+-/
 
+#print intervalIntegral.integral_pos_iff_support_of_nonneg_ae' /-
 /-- If `f` is nonnegative and integrable on the unordered interval `set.uIoc a b`, then its
 integral over `a..b` is positive if and only if `a < b` and the measure of
 `function.support f ∩ set.Ioc a b` is positive. -/
@@ -1322,6 +1459,7 @@ theorem integral_pos_iff_support_of_nonneg_ae' (hf : 0 ≤ᵐ[μ.restrict (Ι a
     rw [uIoc_swap, uIoc_of_le hba] at hf 
     exact integral_nonneg_of_ae hf
 #align interval_integral.integral_pos_iff_support_of_nonneg_ae' intervalIntegral.integral_pos_iff_support_of_nonneg_ae'
+-/
 
 /-- If `f` is nonnegative a.e.-everywhere and it is integrable on the unordered interval
 `set.uIoc a b`, then its integral over `a..b` is positive if and only if `a < b` and the
@@ -1455,6 +1593,7 @@ theorem integral_mono_interval {c d} (hca : c ≤ a) (hab : a ≤ b) (hbd : b 
   exact set_integral_mono_set hfi.1 hf (Ioc_subset_Ioc hca hbd).EventuallyLE
 #align interval_integral.integral_mono_interval intervalIntegral.integral_mono_interval
 
+#print intervalIntegral.abs_integral_mono_interval /-
 theorem abs_integral_mono_interval {c d} (h : Ι a b ⊆ Ι c d) (hf : 0 ≤ᵐ[μ.restrict (Ι c d)] f)
     (hfi : IntervalIntegrable f μ c d) : |∫ x in a..b, f x ∂μ| ≤ |∫ x in c..d, f x ∂μ| :=
   have hf' : 0 ≤ᵐ[μ.restrict (Ι a b)] f := ae_mono (Measure.restrict_mono h le_rfl) hf
@@ -1466,6 +1605,7 @@ theorem abs_integral_mono_interval {c d} (h : Ι a b ⊆ Ι c d) (hf : 0 ≤ᵐ[
     _ = |∫ x in c..d, f x ∂μ| := (abs_integral_eq_abs_integral_uIoc f).symm
     
 #align interval_integral.abs_integral_mono_interval intervalIntegral.abs_integral_mono_interval
+-/
 
 end Mono
 
@@ -1475,6 +1615,7 @@ section HasSum
 
 variable {μ : Measure ℝ} {f : ℝ → E}
 
+#print MeasureTheory.Integrable.hasSum_intervalIntegral /-
 theorem MeasureTheory.Integrable.hasSum_intervalIntegral (hfi : Integrable f μ) (y : ℝ) :
     HasSum (fun n : ℤ => ∫ x in y + n..y + n + 1, f x ∂μ) (∫ x, f x ∂μ) :=
   by
@@ -1484,7 +1625,9 @@ theorem MeasureTheory.Integrable.hasSum_intervalIntegral (hfi : Integrable f μ)
     has_sum_integral_Union (fun i => measurableSet_Ioc) (pairwise_disjoint_Ioc_add_int_cast y)
       hfi.integrable_on
 #align measure_theory.integrable.has_sum_interval_integral MeasureTheory.Integrable.hasSum_intervalIntegral
+-/
 
+#print MeasureTheory.Integrable.hasSum_intervalIntegral_comp_add_int /-
 theorem MeasureTheory.Integrable.hasSum_intervalIntegral_comp_add_int (hfi : Integrable f) :
     HasSum (fun n : ℤ => ∫ x in 0 ..1, f (x + n)) (∫ x, f x) :=
   by
@@ -1492,6 +1635,7 @@ theorem MeasureTheory.Integrable.hasSum_intervalIntegral_comp_add_int (hfi : Int
   ext1 n
   rw [integral_comp_add_right, zero_add, add_comm]
 #align measure_theory.integrable.has_sum_interval_integral_comp_add_int MeasureTheory.Integrable.hasSum_intervalIntegral_comp_add_int
+-/
 
 end HasSum
 

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

@@ -125,7 +125,7 @@ theorem intervalIntegrable_const_iff {c : E} :
 #align interval_integrable_const_iff intervalIntegrable_const_iff
 
 @[simp]
-theorem intervalIntegrable_const [LocallyFiniteMeasure μ] {c : E} :
+theorem intervalIntegrable_const [IsLocallyFiniteMeasure μ] {c : E} :
     IntervalIntegrable (fun _ => c) μ a b :=
   intervalIntegrable_const_iff.2 <| Or.inr measure_Ioc_lt_top
 #align interval_integrable_const intervalIntegrable_const
@@ -324,7 +324,7 @@ theorem comp_add_right (hf : IntervalIntegrable f volume a b) (c : ℝ) :
   have Am : measure.map (fun x => x + c) volume = volume :=
     is_add_left_invariant.is_add_right_invariant.map_add_right_eq_self _
   rw [← Am] at hf 
-  convert(MeasurableEmbedding.integrableOn_map_iff A).mp hf
+  convert (MeasurableEmbedding.integrableOn_map_iff A).mp hf
   rw [preimage_add_const_uIcc]
 #align interval_integrable.comp_add_right IntervalIntegrable.comp_add_right
 
@@ -352,7 +352,7 @@ end IntervalIntegrable
 
 section
 
-variable {μ : Measure ℝ} [LocallyFiniteMeasure μ]
+variable {μ : Measure ℝ} [IsLocallyFiniteMeasure μ]
 
 theorem ContinuousOn.intervalIntegrable {u : ℝ → E} {a b : ℝ} (hu : ContinuousOn u (uIcc a b)) :
     IntervalIntegrable u μ a b :=
@@ -375,7 +375,7 @@ end
 
 section
 
-variable {μ : Measure ℝ} [LocallyFiniteMeasure μ] [ConditionallyCompleteLinearOrder E]
+variable {μ : Measure ℝ} [IsLocallyFiniteMeasure μ] [ConditionallyCompleteLinearOrder E]
   [OrderTopology E] [SecondCountableTopology E]
 
 theorem MonotoneOn.intervalIntegrable {u : ℝ → E} {a b : ℝ} (hu : MonotoneOn u (uIcc a b)) :
@@ -973,7 +973,7 @@ theorem integral_Iic_sub_Iic (ha : IntegrableOn f (Iic a) μ) (hb : IntegrableOn
 #align interval_integral.integral_Iic_sub_Iic intervalIntegral.integral_Iic_sub_Iic
 
 /-- If `μ` is a finite measure then `∫ x in a..b, c ∂μ = (μ (Iic b) - μ (Iic a)) • c`. -/
-theorem integral_const_of_cdf [FiniteMeasure μ] (c : E) :
+theorem integral_const_of_cdf [IsFiniteMeasure μ] (c : E) :
     (∫ x in a..b, c ∂μ) = ((μ (Iic b)).toReal - (μ (Iic a)).toReal) • c :=
   by
   simp only [sub_smul, ← set_integral_const]
@@ -1011,9 +1011,9 @@ theorem integral_zero_ae (h : ∀ᵐ x ∂μ, x ∈ Ι a b → f x = 0) : (∫ x
 #align interval_integral.integral_zero_ae intervalIntegral.integral_zero_ae
 
 theorem integral_indicator {a₁ a₂ a₃ : ℝ} (h : a₂ ∈ Icc a₁ a₃) :
-    (∫ x in a₁..a₃, indicator { x | x ≤ a₂ } f x ∂μ) = ∫ x in a₁..a₂, f x ∂μ :=
+    (∫ x in a₁..a₃, indicator {x | x ≤ a₂} f x ∂μ) = ∫ x in a₁..a₂, f x ∂μ :=
   by
-  have : { x | x ≤ a₂ } ∩ Ioc a₁ a₃ = Ioc a₁ a₂ := Iic_inter_Ioc_of_le h.2
+  have : {x | x ≤ a₂} ∩ Ioc a₁ a₃ = Ioc a₁ a₂ := Iic_inter_Ioc_of_le h.2
   rw [integral_of_le h.1, integral_of_le (h.1.trans h.2), integral_indicator,
     measure.restrict_restrict, this]
   exact measurableSet_Iic
@@ -1174,7 +1174,7 @@ theorem continuousWithinAt_primitive (hb₀ : μ {b₀} = 0)
     refine' continuous_within_at_const.add _
     have :
       (fun b => ∫ x in b₁..b, f x ∂μ) =ᶠ[𝓝[Icc b₁ b₂] b₀] fun b =>
-        ∫ x in b₁..b₂, indicator { x | x ≤ b } f x ∂μ :=
+        ∫ x in b₁..b₂, indicator {x | x ≤ b} f x ∂μ :=
       by
       apply eventually_eq_of_mem self_mem_nhdsWithin
       exact fun b b_in => (integral_indicator b_in).symm
@@ -1199,7 +1199,7 @@ theorem continuousWithinAt_primitive (hb₀ : μ {b₀} = 0)
         exact Ne.lt_or_lt hx
       apply this.mono
       rintro x₀ (hx₀ | hx₀) -
-      · have : ∀ᶠ x in 𝓝[Icc b₁ b₂] b₀, { t : ℝ | t ≤ x }.indicator f x₀ = f x₀ :=
+      · have : ∀ᶠ x in 𝓝[Icc b₁ b₂] b₀, {t : ℝ | t ≤ x}.indicator f x₀ = f x₀ :=
           by
           apply mem_nhdsWithin_of_mem_nhds
           apply eventually.mono (Ioi_mem_nhds hx₀)
@@ -1207,7 +1207,7 @@ theorem continuousWithinAt_primitive (hb₀ : μ {b₀} = 0)
           simp [hx.le]
         apply continuous_within_at_const.congr_of_eventually_eq this
         simp [hx₀.le]
-      · have : ∀ᶠ x in 𝓝[Icc b₁ b₂] b₀, { t : ℝ | t ≤ x }.indicator f x₀ = 0 :=
+      · have : ∀ᶠ x in 𝓝[Icc b₁ b₂] b₀, {t : ℝ | t ≤ x}.indicator f x₀ = 0 :=
           by
           apply mem_nhdsWithin_of_mem_nhds
           apply eventually.mono (Iio_mem_nhds hx₀)
@@ -1361,7 +1361,7 @@ theorem intervalIntegral_pos_of_pos {f : ℝ → ℝ} {a b : ℝ}
 of nonzero measure, then `∫ x in a..b, f x ∂μ < ∫ x in a..b, g x ∂μ`. -/
 theorem integral_lt_integral_of_ae_le_of_measure_setOf_lt_ne_zero (hab : a ≤ b)
     (hfi : IntervalIntegrable f μ a b) (hgi : IntervalIntegrable g μ a b)
-    (hle : f ≤ᵐ[μ.restrict (Ioc a b)] g) (hlt : μ.restrict (Ioc a b) { x | f x < g x } ≠ 0) :
+    (hle : f ≤ᵐ[μ.restrict (Ioc a b)] g) (hlt : μ.restrict (Ioc a b) {x | f x < g x} ≠ 0) :
     (∫ x in a..b, f x ∂μ) < ∫ x in a..b, g x ∂μ :=
   by
   rw [← sub_pos, ← integral_sub hgi hfi, integral_of_le hab,

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

@@ -264,14 +264,14 @@ theorem sum (s : Finset ι) {f : ι → ℝ → E} (h : ∀ i ∈ s, IntervalInt
 theorem mul_continuousOn {f g : ℝ → A} (hf : IntervalIntegrable f μ a b)
     (hg : ContinuousOn g [a, b]) : IntervalIntegrable (fun x => f x * g x) μ a b :=
   by
-  rw [intervalIntegrable_iff] at hf⊢
+  rw [intervalIntegrable_iff] at hf ⊢
   exact hf.mul_continuous_on_of_subset hg measurableSet_Ioc isCompact_uIcc Ioc_subset_Icc_self
 #align interval_integrable.mul_continuous_on IntervalIntegrable.mul_continuousOn
 
 theorem continuousOn_mul {f g : ℝ → A} (hf : IntervalIntegrable f μ a b)
     (hg : ContinuousOn g [a, b]) : IntervalIntegrable (fun x => g x * f x) μ a b :=
   by
-  rw [intervalIntegrable_iff] at hf⊢
+  rw [intervalIntegrable_iff] at hf ⊢
   exact hf.continuous_on_mul_of_subset hg isCompact_uIcc measurableSet_Ioc Ioc_subset_Icc_self
 #align interval_integrable.continuous_on_mul IntervalIntegrable.continuousOn_mul
 
@@ -297,7 +297,7 @@ theorem comp_mul_left (hf : IntervalIntegrable f volume a b) (c : ℝ) :
     IntervalIntegrable (fun x => f (c * x)) volume (a / c) (b / c) :=
   by
   rcases eq_or_ne c 0 with (hc | hc); · rw [hc]; simp
-  rw [intervalIntegrable_iff'] at hf⊢
+  rw [intervalIntegrable_iff'] at hf ⊢
   have A : MeasurableEmbedding fun x => x * c⁻¹ :=
     (Homeomorph.mulRight₀ _ (inv_ne_zero hc)).ClosedEmbedding.MeasurableEmbedding
   rw [← Real.smul_map_volume_mul_right (inv_ne_zero hc), integrable_on, measure.restrict_smul,
@@ -318,12 +318,12 @@ theorem comp_add_right (hf : IntervalIntegrable f volume a b) (c : ℝ) :
   by
   wlog h : a ≤ b
   · exact IntervalIntegrable.symm (this hf.symm _ (le_of_not_le h))
-  rw [intervalIntegrable_iff'] at hf⊢
+  rw [intervalIntegrable_iff'] at hf ⊢
   have A : MeasurableEmbedding fun x => x + c :=
     (Homeomorph.addRight c).ClosedEmbedding.MeasurableEmbedding
   have Am : measure.map (fun x => x + c) volume = volume :=
     is_add_left_invariant.is_add_right_invariant.map_add_right_eq_self _
-  rw [← Am] at hf
+  rw [← Am] at hf 
   convert(MeasurableEmbedding.integrableOn_map_iff A).mp hf
   rw [preimage_add_const_uIcc]
 #align interval_integrable.comp_add_right IntervalIntegrable.comp_add_right
@@ -969,7 +969,7 @@ theorem integral_Iic_sub_Iic (ha : IntegrableOn f (Iic a) μ) (hb : IntegrableOn
   · rw [integral_symm, ← this hb ha (le_of_not_le hab), neg_sub]
   rw [sub_eq_iff_eq_add', integral_of_le hab, ← integral_union (Iic_disjoint_Ioc le_rfl),
     Iic_union_Ioc_eq_Iic hab]
-  exacts[measurableSet_Ioc, ha, hb.mono_set fun _ => And.right]
+  exacts [measurableSet_Ioc, ha, hb.mono_set fun _ => And.right]
 #align interval_integral.integral_Iic_sub_Iic intervalIntegral.integral_Iic_sub_Iic
 
 /-- If `μ` is a finite measure then `∫ x in a..b, c ∂μ = (μ (Iic b) - μ (Iic a)) • c`. -/
@@ -988,7 +988,7 @@ theorem integral_eq_integral_of_support_subset {a b} (h : support f ⊆ Ioc a b)
   ·
     rw [integral_of_le hab, ← integral_indicator measurableSet_Ioc, indicator_eq_self.2 h] <;>
       infer_instance
-  · rw [Ioc_eq_empty hab.not_lt, subset_empty_iff, support_eq_empty_iff] at h
+  · rw [Ioc_eq_empty hab.not_lt, subset_empty_iff, support_eq_empty_iff] at h 
     simp [h]
 #align interval_integral.integral_eq_integral_of_support_subset intervalIntegral.integral_eq_integral_of_support_subset
 
@@ -1188,7 +1188,7 @@ theorem continuousWithinAt_primitive (hb₀ : μ {b₀} = 0)
       · rw [min₁₂]
         exact (h_int' hx).1.AEStronglyMeasurable
       · exact le_max_of_le_right hx.2
-      exacts[measurableSet_Iic, measurableSet_Iic]
+      exacts [measurableSet_Iic, measurableSet_Iic]
     · refine' eventually_of_forall fun x => eventually_of_forall fun t => _
       dsimp [indicator]
       split_ifs <;> simp
@@ -1262,7 +1262,7 @@ theorem continuousOn_primitive_interval [NoAtoms μ] (h_int : IntegrableOn f (uI
 theorem continuousOn_primitive_interval_left [NoAtoms μ] (h_int : IntegrableOn f (uIcc a b) μ) :
     ContinuousOn (fun x => ∫ t in x..b, f t ∂μ) (uIcc a b) :=
   by
-  rw [uIcc_comm a b] at h_int⊢
+  rw [uIcc_comm a b] at h_int ⊢
   simp only [integral_symm b]
   exact (continuous_on_primitive_interval h_int).neg
 #align interval_integral.continuous_on_primitive_interval_left intervalIntegral.continuousOn_primitive_interval_left
@@ -1301,7 +1301,7 @@ theorem integral_eq_zero_iff_of_nonneg_ae (hf : 0 ≤ᵐ[μ.restrict (Ioc a b 
     (∫ x in a..b, f x ∂μ) = 0 ↔ f =ᵐ[μ.restrict (Ioc a b ∪ Ioc b a)] 0 :=
   by
   cases' le_total a b with hab hab <;>
-    simp only [Ioc_eq_empty hab.not_lt, empty_union, union_empty] at hf⊢
+    simp only [Ioc_eq_empty hab.not_lt, empty_union, union_empty] at hf ⊢
   · exact integral_eq_zero_iff_of_le_of_nonneg_ae hab hf hfi
   · rw [integral_symm, neg_eq_zero, integral_eq_zero_iff_of_le_of_nonneg_ae hab hf hfi.symm]
 #align interval_integral.integral_eq_zero_iff_of_nonneg_ae intervalIntegral.integral_eq_zero_iff_of_nonneg_ae
@@ -1314,12 +1314,12 @@ theorem integral_pos_iff_support_of_nonneg_ae' (hf : 0 ≤ᵐ[μ.restrict (Ι a
     (0 < ∫ x in a..b, f x ∂μ) ↔ a < b ∧ 0 < μ (support f ∩ Ioc a b) :=
   by
   cases' lt_or_le a b with hab hba
-  · rw [uIoc_of_le hab.le] at hf
+  · rw [uIoc_of_le hab.le] at hf 
     simp only [hab, true_and_iff, integral_of_le hab.le,
       set_integral_pos_iff_support_of_nonneg_ae hf hfi.1]
   · suffices (∫ x in a..b, f x ∂μ) ≤ 0 by simp only [this.not_lt, hba.not_lt, false_and_iff]
     rw [integral_of_ge hba, neg_nonpos]
-    rw [uIoc_swap, uIoc_of_le hba] at hf
+    rw [uIoc_swap, uIoc_of_le hba] at hf 
     exact integral_nonneg_of_ae hf
 #align interval_integral.integral_pos_iff_support_of_nonneg_ae' intervalIntegral.integral_pos_iff_support_of_nonneg_ae'
 
@@ -1368,7 +1368,7 @@ theorem integral_lt_integral_of_ae_le_of_measure_setOf_lt_ne_zero (hab : a ≤ b
     MeasureTheory.integral_pos_iff_support_of_nonneg_ae]
   · refine' pos_iff_ne_zero.2 (mt (measure_mono_null _) hlt)
     exact fun x hx => (sub_pos.2 hx).ne'
-  exacts[hle.mono fun x => sub_nonneg.2, hgi.1.sub hfi.1]
+  exacts [hle.mono fun x => sub_nonneg.2, hgi.1.sub hfi.1]
 #align interval_integral.integral_lt_integral_of_ae_le_of_measure_set_of_lt_ne_zero intervalIntegral.integral_lt_integral_of_ae_le_of_measure_setOf_lt_ne_zero
 
 /-- If `f` and `g` are continuous on `[a, b]`, `a < b`, `f x ≤ g x` on this interval, and
@@ -1385,11 +1385,11 @@ theorem integral_lt_integral_of_continuousOn_of_le_of_exists_lt {f g : ℝ → 
   contrapose! hlt
   have h_eq : f =ᵐ[volume.restrict (Ioc a b)] g :=
     by
-    simp only [← not_le, ← ae_iff] at hlt
+    simp only [← not_le, ← ae_iff] at hlt 
     exact
       eventually_le.antisymm ((ae_restrict_iff' measurableSet_Ioc).2 <| eventually_of_forall hle)
         hlt
-  simp only [measure.restrict_congr_set Ioc_ae_eq_Icc] at h_eq
+  simp only [measure.restrict_congr_set Ioc_ae_eq_Icc] at h_eq 
   exact fun c hc => (measure.eq_on_Icc_of_ae_eq volume hab.ne h_eq hfc hgc hc).ge
 #align interval_integral.integral_lt_integral_of_continuous_on_of_le_of_exists_lt intervalIntegral.integral_lt_integral_of_continuousOn_of_le_of_exists_lt
 

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

@@ -57,7 +57,7 @@ open TopologicalSpace (SecondCountableTopology)
 
 open MeasureTheory Set Classical Filter Function
 
-open Classical Topology Filter ENNReal BigOperators Interval NNReal
+open scoped Classical Topology Filter ENNReal BigOperators Interval NNReal
 
 variable {ι 𝕜 E F A : Type _} [NormedAddCommGroup E]
 

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

@@ -180,10 +180,8 @@ theorem norm (h : IntervalIntegrable f μ a b) : IntervalIntegrable (fun x => 
 
 theorem intervalIntegrable_norm_iff {f : ℝ → E} {μ : Measure ℝ} {a b : ℝ}
     (hf : AEStronglyMeasurable f (μ.restrict (Ι a b))) :
-    IntervalIntegrable (fun t => ‖f t‖) μ a b ↔ IntervalIntegrable f μ a b :=
-  by
-  simp_rw [intervalIntegrable_iff, integrable_on]
-  exact integrable_norm_iff hf
+    IntervalIntegrable (fun t => ‖f t‖) μ a b ↔ IntervalIntegrable f μ a b := by
+  simp_rw [intervalIntegrable_iff, integrable_on]; exact integrable_norm_iff hf
 #align interval_integrable.interval_integrable_norm_iff IntervalIntegrable.intervalIntegrable_norm_iff
 
 theorem abs {f : ℝ → ℝ} (h : IntervalIntegrable f μ a b) :
@@ -298,9 +296,7 @@ theorem div_const {𝕜 : Type _} {f : ℝ → 𝕜} [NormedField 𝕜] (h : Int
 theorem comp_mul_left (hf : IntervalIntegrable f volume a b) (c : ℝ) :
     IntervalIntegrable (fun x => f (c * x)) volume (a / c) (b / c) :=
   by
-  rcases eq_or_ne c 0 with (hc | hc);
-  · rw [hc]
-    simp
+  rcases eq_or_ne c 0 with (hc | hc); · rw [hc]; simp
   rw [intervalIntegrable_iff'] at hf⊢
   have A : MeasurableEmbedding fun x => x * c⁻¹ :=
     (Homeomorph.mulRight₀ _ (inv_ne_zero hc)).ClosedEmbedding.MeasurableEmbedding
@@ -308,13 +304,8 @@ theorem comp_mul_left (hf : IntervalIntegrable f volume a b) (c : ℝ) :
     integrable_smul_measure (by simpa : ENNReal.ofReal (|c⁻¹|) ≠ 0) ENNReal.ofReal_ne_top, ←
     integrable_on, MeasurableEmbedding.integrableOn_map_iff A]
   convert hf using 1
-  · ext
-    simp only [comp_app]
-    congr 1
-    field_simp
-    ring
-  · rw [preimage_mul_const_uIcc (inv_ne_zero hc)]
-    field_simp [hc]
+  · ext; simp only [comp_app]; congr 1; field_simp; ring
+  · rw [preimage_mul_const_uIcc (inv_ne_zero hc)]; field_simp [hc]
 #align interval_integrable.comp_mul_left IntervalIntegrable.comp_mul_left
 
 theorem comp_mul_right (hf : IntervalIntegrable f volume a b) (c : ℝ) :
@@ -515,10 +506,8 @@ theorem abs_intervalIntegral_eq (f : ℝ → ℝ) (a b : ℝ) (μ : Measure ℝ)
 #align interval_integral.abs_interval_integral_eq intervalIntegral.abs_intervalIntegral_eq
 
 theorem integral_cases (f : ℝ → E) (a b) :
-    (∫ x in a..b, f x ∂μ) ∈ ({∫ x in Ι a b, f x ∂μ, -∫ x in Ι a b, f x ∂μ} : Set E) :=
-  by
-  rw [interval_integral_eq_integral_uIoc]
-  split_ifs <;> simp
+    (∫ x in a..b, f x ∂μ) ∈ ({∫ x in Ι a b, f x ∂μ, -∫ x in Ι a b, f x ∂μ} : Set E) := by
+  rw [interval_integral_eq_integral_uIoc]; split_ifs <;> simp
 #align interval_integral.integral_cases intervalIntegral.integral_cases
 
 theorem integral_undef (h : ¬IntervalIntegrable f μ a b) : (∫ x in a..b, f x ∂μ) = 0 := by
@@ -530,9 +519,7 @@ theorem integral_undef (h : ¬IntervalIntegrable f μ a b) : (∫ x in a..b, f x
 #align interval_integral.integral_undef intervalIntegral.integral_undef
 
 theorem intervalIntegrable_of_integral_ne_zero {a b : ℝ} {f : ℝ → E} {μ : Measure ℝ}
-    (h : (∫ x in a..b, f x ∂μ) ≠ 0) : IntervalIntegrable f μ a b :=
-  by
-  contrapose! h
+    (h : (∫ x in a..b, f x ∂μ) ≠ 0) : IntervalIntegrable f μ a b := by contrapose! h;
   exact intervalIntegral.integral_undef h
 #align interval_integral.interval_integrable_of_integral_ne_zero intervalIntegral.intervalIntegrable_of_integral_ne_zero
 
@@ -614,10 +601,8 @@ theorem integral_finset_sum {ι} {s : Finset ι} {f : ι → ℝ → E}
 #align interval_integral.integral_finset_sum intervalIntegral.integral_finset_sum
 
 @[simp]
-theorem integral_neg : (∫ x in a..b, -f x ∂μ) = -∫ x in a..b, f x ∂μ :=
-  by
-  simp only [intervalIntegral, integral_neg]
-  abel
+theorem integral_neg : (∫ x in a..b, -f x ∂μ) = -∫ x in a..b, f x ∂μ := by
+  simp only [intervalIntegral, integral_neg]; abel
 #align interval_integral.integral_neg intervalIntegral.integral_neg
 
 @[simp]
@@ -1185,8 +1170,7 @@ theorem continuousWithinAt_primitive (hb₀ : μ {b₀} = 0)
         exact
           ⟨min_le_of_left_le (min_le_right _ _),
             le_max_of_le_right (h₁.trans <| h₂.trans (le_max_right a b₂))⟩
-    apply ContinuousWithinAt.congr _ this (this _ h₀)
-    clear this
+    apply ContinuousWithinAt.congr _ this (this _ h₀); clear this
     refine' continuous_within_at_const.add _
     have :
       (fun b => ∫ x in b₁..b, f x ∂μ) =ᶠ[𝓝[Icc b₁ b₂] b₀] fun b =>
@@ -1255,9 +1239,7 @@ theorem continuousOn_primitive [NoAtoms μ] (h_int : IntegrableOn f (Icc a b) μ
 theorem continuousOn_primitive_Icc [NoAtoms μ] (h_int : IntegrableOn f (Icc a b) μ) :
     ContinuousOn (fun x => ∫ t in Icc a x, f t ∂μ) (Icc a b) :=
   by
-  rw [show (fun x => ∫ t in Icc a x, f t ∂μ) = fun x => ∫ t in Ioc a x, f t ∂μ
-      by
-      ext x
+  rw [show (fun x => ∫ t in Icc a x, f t ∂μ) = fun x => ∫ t in Ioc a x, f t ∂μ by ext x;
       exact integral_Icc_eq_integral_Ioc]
   exact continuous_on_primitive h_int
 #align interval_integral.continuous_on_primitive_Icc intervalIntegral.continuousOn_primitive_Icc

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

@@ -179,7 +179,7 @@ theorem norm (h : IntervalIntegrable f μ a b) : IntervalIntegrable (fun x => 
 #align interval_integrable.norm IntervalIntegrable.norm
 
 theorem intervalIntegrable_norm_iff {f : ℝ → E} {μ : Measure ℝ} {a b : ℝ}
-    (hf : AeStronglyMeasurable f (μ.restrict (Ι a b))) :
+    (hf : AEStronglyMeasurable f (μ.restrict (Ι a b))) :
     IntervalIntegrable (fun t => ‖f t‖) μ a b ↔ IntervalIntegrable f μ a b :=
   by
   simp_rw [intervalIntegrable_iff, integrable_on]
@@ -216,25 +216,25 @@ theorem mono_set' (hf : IntervalIntegrable f μ a b) (hsub : Ι c d ⊆ Ι a b)
 #align interval_integrable.mono_set' IntervalIntegrable.mono_set'
 
 theorem mono_fun [NormedAddCommGroup F] {g : ℝ → F} (hf : IntervalIntegrable f μ a b)
-    (hgm : AeStronglyMeasurable g (μ.restrict (Ι a b)))
+    (hgm : AEStronglyMeasurable g (μ.restrict (Ι a b)))
     (hle : (fun x => ‖g x‖) ≤ᵐ[μ.restrict (Ι a b)] fun x => ‖f x‖) : IntervalIntegrable g μ a b :=
   intervalIntegrable_iff.2 <| hf.def.Integrable.mono hgm hle
 #align interval_integrable.mono_fun IntervalIntegrable.mono_fun
 
 theorem mono_fun' {g : ℝ → ℝ} (hg : IntervalIntegrable g μ a b)
-    (hfm : AeStronglyMeasurable f (μ.restrict (Ι a b)))
+    (hfm : AEStronglyMeasurable f (μ.restrict (Ι a b)))
     (hle : (fun x => ‖f x‖) ≤ᵐ[μ.restrict (Ι a b)] g) : IntervalIntegrable f μ a b :=
   intervalIntegrable_iff.2 <| hg.def.Integrable.mono' hfm hle
 #align interval_integrable.mono_fun' IntervalIntegrable.mono_fun'
 
-protected theorem aeStronglyMeasurable (h : IntervalIntegrable f μ a b) :
-    AeStronglyMeasurable f (μ.restrict (Ioc a b)) :=
-  h.1.AeStronglyMeasurable
-#align interval_integrable.ae_strongly_measurable IntervalIntegrable.aeStronglyMeasurable
+protected theorem aEStronglyMeasurable (h : IntervalIntegrable f μ a b) :
+    AEStronglyMeasurable f (μ.restrict (Ioc a b)) :=
+  h.1.AEStronglyMeasurable
+#align interval_integrable.ae_strongly_measurable IntervalIntegrable.aEStronglyMeasurable
 
 protected theorem ae_strongly_measurable' (h : IntervalIntegrable f μ a b) :
-    AeStronglyMeasurable f (μ.restrict (Ioc b a)) :=
-  h.2.AeStronglyMeasurable
+    AEStronglyMeasurable f (μ.restrict (Ioc b a)) :=
+  h.2.AEStronglyMeasurable
 #align interval_integrable.ae_strongly_measurable' IntervalIntegrable.ae_strongly_measurable'
 
 end
@@ -536,15 +536,15 @@ theorem intervalIntegrable_of_integral_ne_zero {a b : ℝ} {f : ℝ → E} {μ :
   exact intervalIntegral.integral_undef h
 #align interval_integral.interval_integrable_of_integral_ne_zero intervalIntegral.intervalIntegrable_of_integral_ne_zero
 
-theorem integral_non_aeStronglyMeasurable (hf : ¬AeStronglyMeasurable f (μ.restrict (Ι a b))) :
+theorem integral_non_aEStronglyMeasurable (hf : ¬AEStronglyMeasurable f (μ.restrict (Ι a b))) :
     (∫ x in a..b, f x ∂μ) = 0 := by
   rw [interval_integral_eq_integral_uIoc, integral_non_ae_strongly_measurable hf, smul_zero]
-#align interval_integral.integral_non_ae_strongly_measurable intervalIntegral.integral_non_aeStronglyMeasurable
+#align interval_integral.integral_non_ae_strongly_measurable intervalIntegral.integral_non_aEStronglyMeasurable
 
-theorem integral_non_aeStronglyMeasurable_of_le (h : a ≤ b)
-    (hf : ¬AeStronglyMeasurable f (μ.restrict (Ioc a b))) : (∫ x in a..b, f x ∂μ) = 0 :=
-  integral_non_aeStronglyMeasurable <| by rwa [uIoc_of_le h]
-#align interval_integral.integral_non_ae_strongly_measurable_of_le intervalIntegral.integral_non_aeStronglyMeasurable_of_le
+theorem integral_non_aEStronglyMeasurable_of_le (h : a ≤ b)
+    (hf : ¬AEStronglyMeasurable f (μ.restrict (Ioc a b))) : (∫ x in a..b, f x ∂μ) = 0 :=
+  integral_non_aEStronglyMeasurable <| by rwa [uIoc_of_le h]
+#align interval_integral.integral_non_ae_strongly_measurable_of_le intervalIntegral.integral_non_aEStronglyMeasurable_of_le
 
 theorem norm_integral_min_max (f : ℝ → E) :
     ‖∫ x in min a b..max a b, f x ∂μ‖ = ‖∫ x in a..b, f x ∂μ‖ := by
@@ -1038,7 +1038,7 @@ theorem integral_indicator {a₁ a₂ a₃ : ℝ} (h : a₂ ∈ Icc a₁ a₃) :
 /-- Lebesgue dominated convergence theorem for filters with a countable basis -/
 theorem tendsto_integral_filter_of_dominated_convergence {ι} {l : Filter ι} [l.IsCountablyGenerated]
     {F : ι → ℝ → E} (bound : ℝ → ℝ)
-    (hF_meas : ∀ᶠ n in l, AeStronglyMeasurable (F n) (μ.restrict (Ι a b)))
+    (hF_meas : ∀ᶠ n in l, AEStronglyMeasurable (F n) (μ.restrict (Ι a b)))
     (h_bound : ∀ᶠ n in l, ∀ᵐ x ∂μ, x ∈ Ι a b → ‖F n x‖ ≤ bound x)
     (bound_integrable : IntervalIntegrable bound μ a b)
     (h_lim : ∀ᵐ x ∂μ, x ∈ Ι a b → Tendsto (fun n => F n x) l (𝓝 (f x))) :
@@ -1054,7 +1054,7 @@ theorem tendsto_integral_filter_of_dominated_convergence {ι} {l : Filter ι} [l
 
 /-- Lebesgue dominated convergence theorem for series. -/
 theorem hasSum_integral_of_dominated_convergence {ι} [Countable ι] {F : ι → ℝ → E}
-    (bound : ι → ℝ → ℝ) (hF_meas : ∀ n, AeStronglyMeasurable (F n) (μ.restrict (Ι a b)))
+    (bound : ι → ℝ → ℝ) (hF_meas : ∀ n, AEStronglyMeasurable (F n) (μ.restrict (Ι a b)))
     (h_bound : ∀ n, ∀ᵐ t ∂μ, t ∈ Ι a b → ‖F n t‖ ≤ bound n t)
     (bound_summable : ∀ᵐ t ∂μ, t ∈ Ι a b → Summable fun n => bound n t)
     (bound_integrable : IntervalIntegrable (fun t => ∑' n, bound n t) μ a b)
@@ -1080,7 +1080,7 @@ theorem hasSum_intervalIntegral_of_summable_norm [Countable ι] {f : ι → C(
   refine'
     has_sum_integral_of_dominated_convergence
       (fun i (x : ℝ) => ‖(f i).restrict ↑(⟨uIcc a b, isCompact_uIcc⟩ : compacts ℝ)‖)
-      (fun i => (map_continuous <| f i).AeStronglyMeasurable)
+      (fun i => (map_continuous <| f i).AEStronglyMeasurable)
       (fun i =>
         ae_of_all _ fun x hx =>
           ((f i).restrict ↑(⟨uIcc a b, isCompact_uIcc⟩ : compacts ℝ)).norm_coe_le_norm
@@ -1106,7 +1106,7 @@ variable {X : Type _} [TopologicalSpace X] [FirstCountableTopology X]
   is continuous at `x₀` within `s` for almost every `t` in `[a, b]`
   then the same holds for `(λ x, ∫ t in a..b, F x t ∂μ) s x₀`. -/
 theorem continuousWithinAt_of_dominated_interval {F : X → ℝ → E} {x₀ : X} {bound : ℝ → ℝ} {a b : ℝ}
-    {s : Set X} (hF_meas : ∀ᶠ x in 𝓝[s] x₀, AeStronglyMeasurable (F x) (μ.restrict <| Ι a b))
+    {s : Set X} (hF_meas : ∀ᶠ x in 𝓝[s] x₀, AEStronglyMeasurable (F x) (μ.restrict <| Ι a b))
     (h_bound : ∀ᶠ x in 𝓝[s] x₀, ∀ᵐ t ∂μ, t ∈ Ι a b → ‖F x t‖ ≤ bound t)
     (bound_integrable : IntervalIntegrable bound μ a b)
     (h_cont : ∀ᵐ t ∂μ, t ∈ Ι a b → ContinuousWithinAt (fun x => F x t) s x₀) :
@@ -1121,7 +1121,7 @@ theorem continuousWithinAt_of_dominated_interval {F : X → ℝ → E} {x₀ : X
   is continuous at `x₀` for almost every `t` in `[a, b]`
   then the same holds for `(λ x, ∫ t in a..b, F x t ∂μ) s x₀`. -/
 theorem continuousAt_of_dominated_interval {F : X → ℝ → E} {x₀ : X} {bound : ℝ → ℝ} {a b : ℝ}
-    (hF_meas : ∀ᶠ x in 𝓝 x₀, AeStronglyMeasurable (F x) (μ.restrict <| Ι a b))
+    (hF_meas : ∀ᶠ x in 𝓝 x₀, AEStronglyMeasurable (F x) (μ.restrict <| Ι a b))
     (h_bound : ∀ᶠ x in 𝓝 x₀, ∀ᵐ t ∂μ, t ∈ Ι a b → ‖F x t‖ ≤ bound t)
     (bound_integrable : IntervalIntegrable bound μ a b)
     (h_cont : ∀ᵐ t ∂μ, t ∈ Ι a b → ContinuousAt (fun x => F x t) x₀) :
@@ -1135,7 +1135,7 @@ theorem continuousAt_of_dominated_interval {F : X → ℝ → E} {x₀ : X} {bou
   If `(λ x, F x t)` is continuous for almost every `t` in `[a, b]`
   then the same holds for `(λ x, ∫ t in a..b, F x t ∂μ) s x₀`. -/
 theorem continuous_of_dominated_interval {F : X → ℝ → E} {bound : ℝ → ℝ} {a b : ℝ}
-    (hF_meas : ∀ x, AeStronglyMeasurable (F x) <| μ.restrict <| Ι a b)
+    (hF_meas : ∀ x, AEStronglyMeasurable (F x) <| μ.restrict <| Ι a b)
     (h_bound : ∀ x, ∀ᵐ t ∂μ, t ∈ Ι a b → ‖F x t‖ ≤ bound t)
     (bound_integrable : IntervalIntegrable bound μ a b)
     (h_cont : ∀ᵐ t ∂μ, t ∈ Ι a b → Continuous fun x => F x t) :
@@ -1200,9 +1200,9 @@ theorem continuousWithinAt_primitive (hb₀ : μ {b₀} = 0)
     refine' continuous_within_at_of_dominated_interval _ _ this _ <;> clear this
     · apply eventually.mono self_mem_nhdsWithin
       intro x hx
-      erw [aeStronglyMeasurable_indicator_iff, measure.restrict_restrict, Iic_inter_Ioc_of_le]
+      erw [aestronglyMeasurable_indicator_iff, measure.restrict_restrict, Iic_inter_Ioc_of_le]
       · rw [min₁₂]
-        exact (h_int' hx).1.AeStronglyMeasurable
+        exact (h_int' hx).1.AEStronglyMeasurable
       · exact le_max_of_le_right hx.2
       exacts[measurableSet_Iic, measurableSet_Iic]
     · refine' eventually_of_forall fun x => eventually_of_forall fun t => _

mathlib commit https://github.com/leanprover-community/mathlib/commit/f51de8769c34652d82d1c8e5f8f18f8374782bed

@@ -4,13 +4,13 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury G. Kudryashov, Patrick Massot, Sébastien Gouëzel
 
 ! This file was ported from Lean 3 source module measure_theory.integral.interval_integral
-! leanprover-community/mathlib commit f0c8bf9245297a541f468be517f1bde6195105e9
+! leanprover-community/mathlib commit fd5edc43dc4f10b85abfe544b88f82cf13c5f844
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
 import Mathbin.Data.Set.Intervals.Disjoint
 import Mathbin.MeasureTheory.Integral.SetIntegral
-import Mathbin.MeasureTheory.Measure.Lebesgue
+import Mathbin.MeasureTheory.Measure.Lebesgue.Basic
 
 /-!
 # Integral over an interval

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

@@ -1497,7 +1497,7 @@ theorem MeasureTheory.Integrable.hasSum_intervalIntegral (hfi : Integrable f μ)
     HasSum (fun n : ℤ => ∫ x in y + n..y + n + 1, f x ∂μ) (∫ x, f x ∂μ) :=
   by
   simp_rw [integral_of_le (le_add_of_nonneg_right zero_le_one)]
-  rw [← integral_univ, ← unionᵢ_Ioc_add_int_cast y]
+  rw [← integral_univ, ← iUnion_Ioc_add_int_cast y]
   exact
     has_sum_integral_Union (fun i => measurableSet_Ioc) (pairwise_disjoint_Ioc_add_int_cast y)
       hfi.integrable_on

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

@@ -96,13 +96,13 @@ theorem intervalIntegrable_iff_integrable_Ioc_of_le (hab : a ≤ b) :
   rw [intervalIntegrable_iff, uIoc_of_le hab]
 #align interval_integrable_iff_integrable_Ioc_of_le intervalIntegrable_iff_integrable_Ioc_of_le
 
-theorem intervalIntegrable_iff' [HasNoAtoms μ] :
+theorem intervalIntegrable_iff' [NoAtoms μ] :
     IntervalIntegrable f μ a b ↔ IntegrableOn f (uIcc a b) μ := by
   rw [intervalIntegrable_iff, ← Icc_min_max, uIoc, integrableOn_Icc_iff_integrableOn_Ioc]
 #align interval_integrable_iff' intervalIntegrable_iff'
 
 theorem intervalIntegrable_iff_integrable_Icc_of_le {f : ℝ → E} {a b : ℝ} (hab : a ≤ b)
-    {μ : Measure ℝ} [HasNoAtoms μ] : IntervalIntegrable f μ a b ↔ IntegrableOn f (Icc a b) μ := by
+    {μ : Measure ℝ} [NoAtoms μ] : IntervalIntegrable f μ a b ↔ IntegrableOn f (Icc a b) μ := by
   rw [intervalIntegrable_iff_integrable_Ioc_of_le hab, integrableOn_Icc_iff_integrableOn_Ioc]
 #align interval_integrable_iff_integrable_Icc_of_le intervalIntegrable_iff_integrable_Icc_of_le
 
@@ -125,7 +125,7 @@ theorem intervalIntegrable_const_iff {c : E} :
 #align interval_integrable_const_iff intervalIntegrable_const_iff
 
 @[simp]
-theorem intervalIntegrable_const [IsLocallyFiniteMeasure μ] {c : E} :
+theorem intervalIntegrable_const [LocallyFiniteMeasure μ] {c : E} :
     IntervalIntegrable (fun _ => c) μ a b :=
   intervalIntegrable_const_iff.2 <| Or.inr measure_Ioc_lt_top
 #align interval_integrable_const intervalIntegrable_const
@@ -361,7 +361,7 @@ end IntervalIntegrable
 
 section
 
-variable {μ : Measure ℝ} [IsLocallyFiniteMeasure μ]
+variable {μ : Measure ℝ} [LocallyFiniteMeasure μ]
 
 theorem ContinuousOn.intervalIntegrable {u : ℝ → E} {a b : ℝ} (hu : ContinuousOn u (uIcc a b)) :
     IntervalIntegrable u μ a b :=
@@ -384,7 +384,7 @@ end
 
 section
 
-variable {μ : Measure ℝ} [IsLocallyFiniteMeasure μ] [ConditionallyCompleteLinearOrder E]
+variable {μ : Measure ℝ} [LocallyFiniteMeasure μ] [ConditionallyCompleteLinearOrder E]
   [OrderTopology E] [SecondCountableTopology E]
 
 theorem MonotoneOn.intervalIntegrable {u : ℝ → E} {a b : ℝ} (hu : MonotoneOn u (uIcc a b)) :
@@ -988,7 +988,7 @@ theorem integral_Iic_sub_Iic (ha : IntegrableOn f (Iic a) μ) (hb : IntegrableOn
 #align interval_integral.integral_Iic_sub_Iic intervalIntegral.integral_Iic_sub_Iic
 
 /-- If `μ` is a finite measure then `∫ x in a..b, c ∂μ = (μ (Iic b) - μ (Iic a)) • c`. -/
-theorem integral_const_of_cdf [IsFiniteMeasure μ] (c : E) :
+theorem integral_const_of_cdf [FiniteMeasure μ] (c : E) :
     (∫ x in a..b, c ∂μ) = ((μ (Iic b)).toReal - (μ (Iic a)).toReal) • c :=
   by
   simp only [sub_smul, ← set_integral_const]
@@ -1235,7 +1235,7 @@ theorem continuousWithinAt_primitive (hb₀ : μ {b₀} = 0)
     rwa [closure_Icc]
 #align interval_integral.continuous_within_at_primitive intervalIntegral.continuousWithinAt_primitive
 
-theorem continuousOn_primitive [HasNoAtoms μ] (h_int : IntegrableOn f (Icc a b) μ) :
+theorem continuousOn_primitive [NoAtoms μ] (h_int : IntegrableOn f (Icc a b) μ) :
     ContinuousOn (fun x => ∫ t in Ioc a x, f t ∂μ) (Icc a b) :=
   by
   by_cases h : a ≤ b
@@ -1252,7 +1252,7 @@ theorem continuousOn_primitive [HasNoAtoms μ] (h_int : IntegrableOn f (Icc a b)
     exact continuousOn_empty _
 #align interval_integral.continuous_on_primitive intervalIntegral.continuousOn_primitive
 
-theorem continuousOn_primitive_Icc [HasNoAtoms μ] (h_int : IntegrableOn f (Icc a b) μ) :
+theorem continuousOn_primitive_Icc [NoAtoms μ] (h_int : IntegrableOn f (Icc a b) μ) :
     ContinuousOn (fun x => ∫ t in Icc a x, f t ∂μ) (Icc a b) :=
   by
   rw [show (fun x => ∫ t in Icc a x, f t ∂μ) = fun x => ∫ t in Ioc a x, f t ∂μ
@@ -1263,7 +1263,7 @@ theorem continuousOn_primitive_Icc [HasNoAtoms μ] (h_int : IntegrableOn f (Icc
 #align interval_integral.continuous_on_primitive_Icc intervalIntegral.continuousOn_primitive_Icc
 
 /-- Note: this assumes that `f` is `interval_integrable`, in contrast to some other lemmas here. -/
-theorem continuousOn_primitive_interval' [HasNoAtoms μ] (h_int : IntervalIntegrable f μ b₁ b₂)
+theorem continuousOn_primitive_interval' [NoAtoms μ] (h_int : IntervalIntegrable f μ b₁ b₂)
     (ha : a ∈ [b₁, b₂]) : ContinuousOn (fun b => ∫ x in a..b, f x ∂μ) [b₁, b₂] :=
   by
   intro b₀ hb₀
@@ -1272,12 +1272,12 @@ theorem continuousOn_primitive_interval' [HasNoAtoms μ] (h_int : IntervalIntegr
   simpa [intervalIntegrable_iff, uIoc] using h_int
 #align interval_integral.continuous_on_primitive_interval' intervalIntegral.continuousOn_primitive_interval'
 
-theorem continuousOn_primitive_interval [HasNoAtoms μ] (h_int : IntegrableOn f (uIcc a b) μ) :
+theorem continuousOn_primitive_interval [NoAtoms μ] (h_int : IntegrableOn f (uIcc a b) μ) :
     ContinuousOn (fun x => ∫ t in a..x, f t ∂μ) (uIcc a b) :=
   continuousOn_primitive_interval' h_int.IntervalIntegrable left_mem_uIcc
 #align interval_integral.continuous_on_primitive_interval intervalIntegral.continuousOn_primitive_interval
 
-theorem continuousOn_primitive_interval_left [HasNoAtoms μ] (h_int : IntegrableOn f (uIcc a b) μ) :
+theorem continuousOn_primitive_interval_left [NoAtoms μ] (h_int : IntegrableOn f (uIcc a b) μ) :
     ContinuousOn (fun x => ∫ t in x..b, f t ∂μ) (uIcc a b) :=
   by
   rw [uIcc_comm a b] at h_int⊢
@@ -1285,7 +1285,7 @@ theorem continuousOn_primitive_interval_left [HasNoAtoms μ] (h_int : Integrable
   exact (continuous_on_primitive_interval h_int).neg
 #align interval_integral.continuous_on_primitive_interval_left intervalIntegral.continuousOn_primitive_interval_left
 
-variable [HasNoAtoms μ]
+variable [NoAtoms μ]
 
 theorem continuous_primitive (h_int : ∀ a b, IntervalIntegrable f μ a b) (a : ℝ) :
     Continuous fun b => ∫ x in a..b, f x ∂μ :=

mathlib commit https://github.com/leanprover-community/mathlib/commit/738054fa93d43512da144ec45ce799d18fd44248

@@ -4,13 +4,13 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury G. Kudryashov, Patrick Massot, Sébastien Gouëzel
 
 ! This file was ported from Lean 3 source module measure_theory.integral.interval_integral
-! leanprover-community/mathlib commit 8b8ba04e2f326f3f7cf24ad129beda58531ada61
+! leanprover-community/mathlib commit f0c8bf9245297a541f468be517f1bde6195105e9
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
 import Mathbin.Data.Set.Intervals.Disjoint
 import Mathbin.MeasureTheory.Integral.SetIntegral
-import Mathbin.MeasureTheory.Measure.HaarLebesgue
+import Mathbin.MeasureTheory.Measure.Lebesgue
 
 /-!
 # Integral over an interval

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

@@ -115,8 +115,8 @@ theorem MeasureTheory.Integrable.intervalIntegrable (hf : Integrable f μ) :
 
 theorem MeasureTheory.IntegrableOn.intervalIntegrable (hf : IntegrableOn f [a, b] μ) :
     IntervalIntegrable f μ a b :=
-  ⟨MeasureTheory.IntegrableOn.monoSet hf (Ioc_subset_Icc_self.trans Icc_subset_uIcc),
-    MeasureTheory.IntegrableOn.monoSet hf (Ioc_subset_Icc_self.trans Icc_subset_uIcc')⟩
+  ⟨MeasureTheory.IntegrableOn.mono_set hf (Ioc_subset_Icc_self.trans Icc_subset_uIcc),
+    MeasureTheory.IntegrableOn.mono_set hf (Ioc_subset_Icc_self.trans Icc_subset_uIcc')⟩
 #align measure_theory.integrable_on.interval_integrable MeasureTheory.IntegrableOn.intervalIntegrable
 
 theorem intervalIntegrable_const_iff {c : E} :
@@ -125,10 +125,10 @@ theorem intervalIntegrable_const_iff {c : E} :
 #align interval_integrable_const_iff intervalIntegrable_const_iff
 
 @[simp]
-theorem intervalIntegrableConst [IsLocallyFiniteMeasure μ] {c : E} :
+theorem intervalIntegrable_const [IsLocallyFiniteMeasure μ] {c : E} :
     IntervalIntegrable (fun _ => c) μ a b :=
   intervalIntegrable_const_iff.2 <| Or.inr measure_Ioc_lt_top
-#align interval_integrable_const intervalIntegrableConst
+#align interval_integrable_const intervalIntegrable_const
 
 end
 
@@ -150,11 +150,11 @@ theorem refl : IntervalIntegrable f μ a a := by constructor <;> simp
 @[trans]
 theorem trans {a b c : ℝ} (hab : IntervalIntegrable f μ a b) (hbc : IntervalIntegrable f μ b c) :
     IntervalIntegrable f μ a c :=
-  ⟨(hab.1.union hbc.1).monoSet Ioc_subset_Ioc_union_Ioc,
-    (hbc.2.union hab.2).monoSet Ioc_subset_Ioc_union_Ioc⟩
+  ⟨(hab.1.union hbc.1).mono_set Ioc_subset_Ioc_union_Ioc,
+    (hbc.2.union hab.2).mono_set Ioc_subset_Ioc_union_Ioc⟩
 #align interval_integrable.trans IntervalIntegrable.trans
 
-theorem transIterateIco {a : ℕ → ℝ} {m n : ℕ} (hmn : m ≤ n)
+theorem trans_iterate_Ico {a : ℕ → ℝ} {m n : ℕ} (hmn : m ≤ n)
     (hint : ∀ k ∈ Ico m n, IntervalIntegrable f μ (a k) (a <| k + 1)) :
     IntervalIntegrable f μ (a m) (a n) := by
   revert hint
@@ -162,13 +162,13 @@ theorem transIterateIco {a : ℕ → ℝ} {m n : ℕ} (hmn : m ≤ n)
   · simp
   · intro p hp IH h
     exact (IH fun k hk => h k (Ico_subset_Ico_right p.le_succ hk)).trans (h p (by simp [hp]))
-#align interval_integrable.trans_iterate_Ico IntervalIntegrable.transIterateIco
+#align interval_integrable.trans_iterate_Ico IntervalIntegrable.trans_iterate_Ico
 
-theorem transIterate {a : ℕ → ℝ} {n : ℕ}
+theorem trans_iterate {a : ℕ → ℝ} {n : ℕ}
     (hint : ∀ k < n, IntervalIntegrable f μ (a k) (a <| k + 1)) :
     IntervalIntegrable f μ (a 0) (a n) :=
-  transIterateIco bot_le fun k hk => hint k hk.2
-#align interval_integrable.trans_iterate IntervalIntegrable.transIterate
+  trans_iterate_Ico bot_le fun k hk => hint k hk.2
+#align interval_integrable.trans_iterate IntervalIntegrable.trans_iterate
 
 theorem neg (h : IntervalIntegrable f μ a b) : IntervalIntegrable (-f) μ a b :=
   ⟨h.1.neg, h.2.neg⟩
@@ -196,46 +196,46 @@ theorem mono (hf : IntervalIntegrable f ν a b) (h1 : [c, d] ⊆ [a, b]) (h2 : 
   intervalIntegrable_iff.mpr <| hf.def.mono (uIoc_subset_uIoc_of_uIcc_subset_uIcc h1) h2
 #align interval_integrable.mono IntervalIntegrable.mono
 
-theorem monoMeasure (hf : IntervalIntegrable f ν a b) (h : μ ≤ ν) : IntervalIntegrable f μ a b :=
+theorem mono_measure (hf : IntervalIntegrable f ν a b) (h : μ ≤ ν) : IntervalIntegrable f μ a b :=
   hf.mono rfl.Subset h
-#align interval_integrable.mono_measure IntervalIntegrable.monoMeasure
+#align interval_integrable.mono_measure IntervalIntegrable.mono_measure
 
-theorem monoSet (hf : IntervalIntegrable f μ a b) (h : [c, d] ⊆ [a, b]) :
+theorem mono_set (hf : IntervalIntegrable f μ a b) (h : [c, d] ⊆ [a, b]) :
     IntervalIntegrable f μ c d :=
   hf.mono h rfl.le
-#align interval_integrable.mono_set IntervalIntegrable.monoSet
+#align interval_integrable.mono_set IntervalIntegrable.mono_set
 
-theorem monoSetAe (hf : IntervalIntegrable f μ a b) (h : Ι c d ≤ᵐ[μ] Ι a b) :
+theorem mono_set_ae (hf : IntervalIntegrable f μ a b) (h : Ι c d ≤ᵐ[μ] Ι a b) :
     IntervalIntegrable f μ c d :=
-  intervalIntegrable_iff.mpr <| hf.def.monoSetAe h
-#align interval_integrable.mono_set_ae IntervalIntegrable.monoSetAe
+  intervalIntegrable_iff.mpr <| hf.def.mono_set_ae h
+#align interval_integrable.mono_set_ae IntervalIntegrable.mono_set_ae
 
-theorem monoSet' (hf : IntervalIntegrable f μ a b) (hsub : Ι c d ⊆ Ι a b) :
+theorem mono_set' (hf : IntervalIntegrable f μ a b) (hsub : Ι c d ⊆ Ι a b) :
     IntervalIntegrable f μ c d :=
-  hf.monoSetAe <| eventually_of_forall hsub
-#align interval_integrable.mono_set' IntervalIntegrable.monoSet'
+  hf.mono_set_ae <| eventually_of_forall hsub
+#align interval_integrable.mono_set' IntervalIntegrable.mono_set'
 
-theorem monoFun [NormedAddCommGroup F] {g : ℝ → F} (hf : IntervalIntegrable f μ a b)
+theorem mono_fun [NormedAddCommGroup F] {g : ℝ → F} (hf : IntervalIntegrable f μ a b)
     (hgm : AeStronglyMeasurable g (μ.restrict (Ι a b)))
     (hle : (fun x => ‖g x‖) ≤ᵐ[μ.restrict (Ι a b)] fun x => ‖f x‖) : IntervalIntegrable g μ a b :=
   intervalIntegrable_iff.2 <| hf.def.Integrable.mono hgm hle
-#align interval_integrable.mono_fun IntervalIntegrable.monoFun
+#align interval_integrable.mono_fun IntervalIntegrable.mono_fun
 
-theorem monoFun' {g : ℝ → ℝ} (hg : IntervalIntegrable g μ a b)
+theorem mono_fun' {g : ℝ → ℝ} (hg : IntervalIntegrable g μ a b)
     (hfm : AeStronglyMeasurable f (μ.restrict (Ι a b)))
     (hle : (fun x => ‖f x‖) ≤ᵐ[μ.restrict (Ι a b)] g) : IntervalIntegrable f μ a b :=
   intervalIntegrable_iff.2 <| hg.def.Integrable.mono' hfm hle
-#align interval_integrable.mono_fun' IntervalIntegrable.monoFun'
+#align interval_integrable.mono_fun' IntervalIntegrable.mono_fun'
 
 protected theorem aeStronglyMeasurable (h : IntervalIntegrable f μ a b) :
     AeStronglyMeasurable f (μ.restrict (Ioc a b)) :=
   h.1.AeStronglyMeasurable
 #align interval_integrable.ae_strongly_measurable IntervalIntegrable.aeStronglyMeasurable
 
-protected theorem aeStronglyMeasurable' (h : IntervalIntegrable f μ a b) :
+protected theorem ae_strongly_measurable' (h : IntervalIntegrable f μ a b) :
     AeStronglyMeasurable f (μ.restrict (Ioc b a)) :=
   h.2.AeStronglyMeasurable
-#align interval_integrable.ae_strongly_measurable' IntervalIntegrable.aeStronglyMeasurable'
+#align interval_integrable.ae_strongly_measurable' IntervalIntegrable.ae_strongly_measurable'
 
 end
 
@@ -260,42 +260,42 @@ theorem sub (hf : IntervalIntegrable f μ a b) (hg : IntervalIntegrable g μ a b
 
 theorem sum (s : Finset ι) {f : ι → ℝ → E} (h : ∀ i ∈ s, IntervalIntegrable (f i) μ a b) :
     IntervalIntegrable (∑ i in s, f i) μ a b :=
-  ⟨integrableFinsetSum' s fun i hi => (h i hi).1, integrableFinsetSum' s fun i hi => (h i hi).2⟩
+  ⟨integrable_finset_sum' s fun i hi => (h i hi).1, integrable_finset_sum' s fun i hi => (h i hi).2⟩
 #align interval_integrable.sum IntervalIntegrable.sum
 
-theorem mulContinuousOn {f g : ℝ → A} (hf : IntervalIntegrable f μ a b)
+theorem mul_continuousOn {f g : ℝ → A} (hf : IntervalIntegrable f μ a b)
     (hg : ContinuousOn g [a, b]) : IntervalIntegrable (fun x => f x * g x) μ a b :=
   by
   rw [intervalIntegrable_iff] at hf⊢
   exact hf.mul_continuous_on_of_subset hg measurableSet_Ioc isCompact_uIcc Ioc_subset_Icc_self
-#align interval_integrable.mul_continuous_on IntervalIntegrable.mulContinuousOn
+#align interval_integrable.mul_continuous_on IntervalIntegrable.mul_continuousOn
 
-theorem continuousOnMul {f g : ℝ → A} (hf : IntervalIntegrable f μ a b)
+theorem continuousOn_mul {f g : ℝ → A} (hf : IntervalIntegrable f μ a b)
     (hg : ContinuousOn g [a, b]) : IntervalIntegrable (fun x => g x * f x) μ a b :=
   by
   rw [intervalIntegrable_iff] at hf⊢
   exact hf.continuous_on_mul_of_subset hg isCompact_uIcc measurableSet_Ioc Ioc_subset_Icc_self
-#align interval_integrable.continuous_on_mul IntervalIntegrable.continuousOnMul
+#align interval_integrable.continuous_on_mul IntervalIntegrable.continuousOn_mul
 
 @[simp]
-theorem constMul {f : ℝ → A} (hf : IntervalIntegrable f μ a b) (c : A) :
+theorem const_mul {f : ℝ → A} (hf : IntervalIntegrable f μ a b) (c : A) :
     IntervalIntegrable (fun x => c * f x) μ a b :=
-  hf.continuousOnMul continuousOn_const
-#align interval_integrable.const_mul IntervalIntegrable.constMul
+  hf.continuousOn_mul continuousOn_const
+#align interval_integrable.const_mul IntervalIntegrable.const_mul
 
 @[simp]
-theorem mulConst {f : ℝ → A} (hf : IntervalIntegrable f μ a b) (c : A) :
+theorem mul_const {f : ℝ → A} (hf : IntervalIntegrable f μ a b) (c : A) :
     IntervalIntegrable (fun x => f x * c) μ a b :=
-  hf.mulContinuousOn continuousOn_const
-#align interval_integrable.mul_const IntervalIntegrable.mulConst
+  hf.mul_continuousOn continuousOn_const
+#align interval_integrable.mul_const IntervalIntegrable.mul_const
 
 @[simp]
-theorem divConst {𝕜 : Type _} {f : ℝ → 𝕜} [NormedField 𝕜] (h : IntervalIntegrable f μ a b) (c : 𝕜) :
-    IntervalIntegrable (fun x => f x / c) μ a b := by
+theorem div_const {𝕜 : Type _} {f : ℝ → 𝕜} [NormedField 𝕜] (h : IntervalIntegrable f μ a b)
+    (c : 𝕜) : IntervalIntegrable (fun x => f x / c) μ a b := by
   simpa only [div_eq_mul_inv] using mul_const h c⁻¹
-#align interval_integrable.div_const IntervalIntegrable.divConst
+#align interval_integrable.div_const IntervalIntegrable.div_const
 
-theorem compMulLeft (hf : IntervalIntegrable f volume a b) (c : ℝ) :
+theorem comp_mul_left (hf : IntervalIntegrable f volume a b) (c : ℝ) :
     IntervalIntegrable (fun x => f (c * x)) volume (a / c) (b / c) :=
   by
   rcases eq_or_ne c 0 with (hc | hc);
@@ -315,14 +315,14 @@ theorem compMulLeft (hf : IntervalIntegrable f volume a b) (c : ℝ) :
     ring
   · rw [preimage_mul_const_uIcc (inv_ne_zero hc)]
     field_simp [hc]
-#align interval_integrable.comp_mul_left IntervalIntegrable.compMulLeft
+#align interval_integrable.comp_mul_left IntervalIntegrable.comp_mul_left
 
-theorem compMulRight (hf : IntervalIntegrable f volume a b) (c : ℝ) :
+theorem comp_mul_right (hf : IntervalIntegrable f volume a b) (c : ℝ) :
     IntervalIntegrable (fun x => f (x * c)) volume (a / c) (b / c) := by
   simpa only [mul_comm] using comp_mul_left hf c
-#align interval_integrable.comp_mul_right IntervalIntegrable.compMulRight
+#align interval_integrable.comp_mul_right IntervalIntegrable.comp_mul_right
 
-theorem compAddRight (hf : IntervalIntegrable f volume a b) (c : ℝ) :
+theorem comp_add_right (hf : IntervalIntegrable f volume a b) (c : ℝ) :
     IntervalIntegrable (fun x => f (x + c)) volume (a - c) (b - c) :=
   by
   wlog h : a ≤ b
@@ -335,27 +335,27 @@ theorem compAddRight (hf : IntervalIntegrable f volume a b) (c : ℝ) :
   rw [← Am] at hf
   convert(MeasurableEmbedding.integrableOn_map_iff A).mp hf
   rw [preimage_add_const_uIcc]
-#align interval_integrable.comp_add_right IntervalIntegrable.compAddRight
+#align interval_integrable.comp_add_right IntervalIntegrable.comp_add_right
 
-theorem compAddLeft (hf : IntervalIntegrable f volume a b) (c : ℝ) :
+theorem comp_add_left (hf : IntervalIntegrable f volume a b) (c : ℝ) :
     IntervalIntegrable (fun x => f (c + x)) volume (a - c) (b - c) := by
-  simpa only [add_comm] using IntervalIntegrable.compAddRight hf c
-#align interval_integrable.comp_add_left IntervalIntegrable.compAddLeft
+  simpa only [add_comm] using IntervalIntegrable.comp_add_right hf c
+#align interval_integrable.comp_add_left IntervalIntegrable.comp_add_left
 
-theorem compSubRight (hf : IntervalIntegrable f volume a b) (c : ℝ) :
+theorem comp_sub_right (hf : IntervalIntegrable f volume a b) (c : ℝ) :
     IntervalIntegrable (fun x => f (x - c)) volume (a + c) (b + c) := by
-  simpa only [sub_neg_eq_add] using IntervalIntegrable.compAddRight hf (-c)
-#align interval_integrable.comp_sub_right IntervalIntegrable.compSubRight
+  simpa only [sub_neg_eq_add] using IntervalIntegrable.comp_add_right hf (-c)
+#align interval_integrable.comp_sub_right IntervalIntegrable.comp_sub_right
 
 theorem iff_comp_neg :
     IntervalIntegrable f volume a b ↔ IntervalIntegrable (fun x => f (-x)) volume (-a) (-b) := by
   constructor; all_goals intro hf; convert comp_mul_left hf (-1); simp; field_simp; field_simp
 #align interval_integrable.iff_comp_neg IntervalIntegrable.iff_comp_neg
 
-theorem compSubLeft (hf : IntervalIntegrable f volume a b) (c : ℝ) :
+theorem comp_sub_left (hf : IntervalIntegrable f volume a b) (c : ℝ) :
     IntervalIntegrable (fun x => f (c - x)) volume (c - a) (c - b) := by
   simpa only [neg_sub, ← sub_eq_add_neg] using iff_comp_neg.mp (hf.comp_add_left c)
-#align interval_integrable.comp_sub_left IntervalIntegrable.compSubLeft
+#align interval_integrable.comp_sub_left IntervalIntegrable.comp_sub_left
 
 end IntervalIntegrable
 
@@ -365,13 +365,13 @@ variable {μ : Measure ℝ} [IsLocallyFiniteMeasure μ]
 
 theorem ContinuousOn.intervalIntegrable {u : ℝ → E} {a b : ℝ} (hu : ContinuousOn u (uIcc a b)) :
     IntervalIntegrable u μ a b :=
-  (ContinuousOn.integrableOnIcc hu).IntervalIntegrable
+  (ContinuousOn.integrableOn_Icc hu).IntervalIntegrable
 #align continuous_on.interval_integrable ContinuousOn.intervalIntegrable
 
-theorem ContinuousOn.intervalIntegrableOfIcc {u : ℝ → E} {a b : ℝ} (h : a ≤ b)
+theorem ContinuousOn.intervalIntegrable_of_Icc {u : ℝ → E} {a b : ℝ} (h : a ≤ b)
     (hu : ContinuousOn u (Icc a b)) : IntervalIntegrable u μ a b :=
   ContinuousOn.intervalIntegrable ((uIcc_of_le h).symm ▸ hu)
-#align continuous_on.interval_integrable_of_Icc ContinuousOn.intervalIntegrableOfIcc
+#align continuous_on.interval_integrable_of_Icc ContinuousOn.intervalIntegrable_of_Icc
 
 /-- A continuous function on `ℝ` is `interval_integrable` with respect to any locally finite measure
 `ν` on ℝ. -/
@@ -390,7 +390,7 @@ variable {μ : Measure ℝ} [IsLocallyFiniteMeasure μ] [ConditionallyCompleteLi
 theorem MonotoneOn.intervalIntegrable {u : ℝ → E} {a b : ℝ} (hu : MonotoneOn u (uIcc a b)) :
     IntervalIntegrable u μ a b := by
   rw [intervalIntegrable_iff]
-  exact (hu.integrable_on_is_compact isCompact_uIcc).monoSet Ioc_subset_Icc_self
+  exact (hu.integrable_on_is_compact isCompact_uIcc).mono_set Ioc_subset_Icc_self
 #align monotone_on.interval_integrable MonotoneOn.intervalIntegrable
 
 theorem AntitoneOn.intervalIntegrable {u : ℝ → E} {a b : ℝ} (hu : AntitoneOn u (uIcc a b)) :
@@ -424,7 +424,7 @@ theorem Filter.Tendsto.eventually_intervalIntegrable_ae {f : ℝ → E} {μ : Me
     [IsMeasurablyGenerated l'] (hμ : μ.FiniteAtFilter l') {c : E} (hf : Tendsto f (l' ⊓ μ.ae) (𝓝 c))
     {u v : ι → ℝ} {lt : Filter ι} (hu : Tendsto u lt l) (hv : Tendsto v lt l) :
     ∀ᶠ t in lt, IntervalIntegrable f μ (u t) (v t) :=
-  have := (hf.integrableAtFilterAe hfm hμ).Eventually
+  have := (hf.integrableAtFilter_ae hfm hμ).Eventually
   ((hu.Ioc hv).Eventually this).And <| (hv.Ioc hu).Eventually this
 #align filter.tendsto.eventually_interval_integrable_ae Filter.Tendsto.eventually_intervalIntegrable_ae
 
@@ -529,12 +529,12 @@ theorem integral_undef (h : ¬IntervalIntegrable f μ a b) : (∫ x in a..b, f x
       or_false_iff] using not_and_distrib.mp h
 #align interval_integral.integral_undef intervalIntegral.integral_undef
 
-theorem intervalIntegrableOfIntegralNeZero {a b : ℝ} {f : ℝ → E} {μ : Measure ℝ}
+theorem intervalIntegrable_of_integral_ne_zero {a b : ℝ} {f : ℝ → E} {μ : Measure ℝ}
     (h : (∫ x in a..b, f x ∂μ) ≠ 0) : IntervalIntegrable f μ a b :=
   by
   contrapose! h
   exact intervalIntegral.integral_undef h
-#align interval_integral.interval_integrable_of_integral_ne_zero intervalIntegral.intervalIntegrableOfIntegralNeZero
+#align interval_integral.interval_integrable_of_integral_ne_zero intervalIntegral.intervalIntegrable_of_integral_ne_zero
 
 theorem integral_non_aeStronglyMeasurable (hf : ¬AeStronglyMeasurable f (μ.restrict (Ι a b))) :
     (∫ x in a..b, f x ∂μ) = 0 := by
@@ -931,7 +931,7 @@ theorem sum_integral_adjacent_intervals_Ico {a : ℕ → ℝ} {m n : ℕ} (hmn :
   · simp
   · intro p hmp IH h
     rw [Finset.sum_Ico_succ_top hmp, IH, integral_add_adjacent_intervals]
-    · apply IntervalIntegrable.transIterateIco hmp fun k hk => h k _
+    · apply IntervalIntegrable.trans_iterate_Ico hmp fun k hk => h k _
       exact (Ico_subset_Ico le_rfl (Nat.le_succ _)) hk
     · apply h
       simp [hmp]
@@ -1085,7 +1085,7 @@ theorem hasSum_intervalIntegral_of_summable_norm [Countable ι] {f : ι → C(
         ae_of_all _ fun x hx =>
           ((f i).restrict ↑(⟨uIcc a b, isCompact_uIcc⟩ : compacts ℝ)).norm_coe_le_norm
             ⟨x, ⟨hx.1.le, hx.2⟩⟩)
-      (ae_of_all _ fun x hx => hf_sum) intervalIntegrableConst
+      (ae_of_all _ fun x hx => hf_sum) intervalIntegrable_const
       (ae_of_all _ fun x hx => Summable.hasSum _)
   -- next line is slow, & doesn't work with "exact" in place of "apply" -- ?
   apply ContinuousMap.summable_apply (summable_of_summable_norm hf_sum) ⟨x, ⟨hx.1.le, hx.2⟩⟩

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

@@ -4,106 +4,19 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury G. Kudryashov, Patrick Massot, Sébastien Gouëzel
 
 ! This file was ported from Lean 3 source module measure_theory.integral.interval_integral
-! leanprover-community/mathlib commit d4817f8867c368d6c5571f7379b3888aaec1d95a
+! leanprover-community/mathlib commit 8b8ba04e2f326f3f7cf24ad129beda58531ada61
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
-import Mathbin.Analysis.NormedSpace.Dual
 import Mathbin.Data.Set.Intervals.Disjoint
-import Mathbin.MeasureTheory.Measure.HaarLebesgue
-import Mathbin.MeasureTheory.Function.LocallyIntegrable
 import Mathbin.MeasureTheory.Integral.SetIntegral
-import Mathbin.MeasureTheory.Integral.VitaliCaratheodory
-import Mathbin.Analysis.Calculus.FderivMeasurable
+import Mathbin.MeasureTheory.Measure.HaarLebesgue
 
 /-!
 # Integral over an interval
 
 In this file we define `∫ x in a..b, f x ∂μ` to be `∫ x in Ioc a b, f x ∂μ` if `a ≤ b` and
-`-∫ x in Ioc b a, f x ∂μ` if `b ≤ a`. We prove a few simple properties and several versions of the
-[fundamental theorem of calculus](https://en.wikipedia.org/wiki/Fundamental_theorem_of_calculus).
-
-Recall that its first version states that the function `(u, v) ↦ ∫ x in u..v, f x` has derivative
-`(δu, δv) ↦ δv • f b - δu • f a` at `(a, b)` provided that `f` is continuous at `a` and `b`,
-and its second version states that, if `f` has an integrable derivative on `[a, b]`, then
-`∫ x in a..b, f' x = f b - f a`.
-
-## Main statements
-
-### FTC-1 for Lebesgue measure
-
-We prove several versions of FTC-1, all in the `interval_integral` namespace. Many of them follow
-the naming scheme `integral_has(_strict?)_(f?)deriv(_within?)_at(_of_tendsto_ae?)(_right|_left?)`.
-They formulate FTC in terms of `has(_strict?)_(f?)deriv(_within?)_at`.
-Let us explain the meaning of each part of the name:
-
-* `_strict` means that the theorem is about strict differentiability;
-* `f` means that the theorem is about differentiability in both endpoints; incompatible with
-  `_right|_left`;
-* `_within` means that the theorem is about one-sided derivatives, see below for details;
-* `_of_tendsto_ae` means that instead of continuity the theorem assumes that `f` has a finite limit
-  almost surely as `x` tends to `a` and/or `b`;
-* `_right` or `_left` mean that the theorem is about differentiability in the right (resp., left)
-  endpoint.
-
-We also reformulate these theorems in terms of `(f?)deriv(_within?)`. These theorems are named
-`(f?)deriv(_within?)_integral(_of_tendsto_ae?)(_right|_left?)` with the same meaning of parts of the
-name.
-
-### One-sided derivatives
-
-Theorem `integral_has_fderiv_within_at_of_tendsto_ae` states that `(u, v) ↦ ∫ x in u..v, f x` has a
-derivative `(δu, δv) ↦ δv • cb - δu • ca` within the set `s × t` at `(a, b)` provided that `f` tends
-to `ca` (resp., `cb`) almost surely at `la` (resp., `lb`), where possible values of `s`, `t`, and
-corresponding filters `la`, `lb` are given in the following table.
-
-| `s`     | `la`     | `t`     | `lb`     |
-| ------- | ----     | ---     | ----     |
-| `Iic a` | `𝓝[≤] a` | `Iic b` | `𝓝[≤] b` |
-| `Ici a` | `𝓝[>] a` | `Ici b` | `𝓝[>] b` |
-| `{a}`   | `⊥`      | `{b}`   | `⊥`      |
-| `univ`  | `𝓝 a`    | `univ`  | `𝓝 b`    |
-
-We use a typeclass `FTC_filter` to make Lean automatically find `la`/`lb` based on `s`/`t`. This way
-we can formulate one theorem instead of `16` (or `8` if we leave only non-trivial ones not covered
-by `integral_has_deriv_within_at_of_tendsto_ae_(left|right)` and
-`integral_has_fderiv_at_of_tendsto_ae`). Similarly,
-`integral_has_deriv_within_at_of_tendsto_ae_right` works for both one-sided derivatives using the
-same typeclass to find an appropriate filter.
-
-### FTC for a locally finite measure
-
-Before proving FTC for the Lebesgue measure, we prove a few statements that can be seen as FTC for
-any measure. The most general of them,
-`measure_integral_sub_integral_sub_linear_is_o_of_tendsto_ae`, states the following. Let `(la, la')`
-be an `FTC_filter` pair of filters around `a` (i.e., `FTC_filter a la la'`) and let `(lb, lb')` be
-an `FTC_filter` pair of filters around `b`. If `f` has finite limits `ca` and `cb` almost surely at
-`la'` and `lb'`, respectively, then
-`∫ x in va..vb, f x ∂μ - ∫ x in ua..ub, f x ∂μ = ∫ x in ub..vb, cb ∂μ - ∫ x in ua..va, ca ∂μ +
-  o(‖∫ x in ua..va, (1:ℝ) ∂μ‖ + ‖∫ x in ub..vb, (1:ℝ) ∂μ‖)` as `ua` and `va` tend to `la` while
-`ub` and `vb` tend to `lb`.
-
-### FTC-2 and corollaries
-
-We use FTC-1 to prove several versions of FTC-2 for the Lebesgue measure, using a similar naming
-scheme as for the versions of FTC-1. They include:
-* `interval_integral.integral_eq_sub_of_has_deriv_right_of_le` - most general version, for functions
-  with a right derivative
-* `interval_integral.integral_eq_sub_of_has_deriv_at'` - version for functions with a derivative on
-  an open set
-* `interval_integral.integral_deriv_eq_sub'` - version that is easiest to use when computing the
-  integral of a specific function
-
-We then derive additional integration techniques from FTC-2:
-* `interval_integral.integral_mul_deriv_eq_deriv_mul` - integration by parts
-* `interval_integral.integral_comp_mul_deriv''` - integration by substitution
-
-Many applications of these theorems can be found in the file `analysis.special_functions.integrals`.
-
-Note that the assumptions of FTC-2 are formulated in the form that `f'` is integrable. To use it in
-a context with the stronger assumption that `f'` is continuous, one can use
-`continuous_on.interval_integrable` or `continuous_on.integrable_on_Icc` or
-`continuous_on.integrable_on_interval`.
+`-∫ x in Ioc b a, f x ∂μ` if `b ≤ a`.
 
 ## Implementation notes
 
@@ -132,39 +45,9 @@ three possible intervals with the same endpoints for two reasons:
   [cumulative distribution function](https://en.wikipedia.org/wiki/Cumulative_distribution_function)
   of `μ`.
 
-### `FTC_filter` class
-
-As explained above, many theorems in this file rely on the typeclass
-`FTC_filter (a : ℝ) (l l' : filter ℝ)` to avoid code duplication. This typeclass combines four
-assumptions:
-
-- `pure a ≤ l`;
-- `l' ≤ 𝓝 a`;
-- `l'` has a basis of measurable sets;
-- if `u n` and `v n` tend to `l`, then for any `s ∈ l'`, `Ioc (u n) (v n)` is eventually included
-  in `s`.
-
-This typeclass has the following “real” instances: `(a, pure a, ⊥)`, `(a, 𝓝[≥] a, 𝓝[>] a)`,
-`(a, 𝓝[≤] a, 𝓝[≤] a)`, `(a, 𝓝 a, 𝓝 a)`.
-Furthermore, we have the following instances that are equal to the previously mentioned instances:
-`(a, 𝓝[{a}] a, ⊥)` and `(a, 𝓝[univ] a, 𝓝[univ] a)`.
-While the difference between `Ici a` and `Ioi a` doesn't matter for theorems about Lebesgue measure,
-it becomes important in the versions of FTC about any locally finite measure if this measure has an
-atom at one of the endpoints.
-
-### Combining one-sided and two-sided derivatives
-
-There are some `FTC_filter` instances where the fact that it is one-sided or
-two-sided depends on the point, namely `(x, 𝓝[Icc a b] x, 𝓝[Icc a b] x)`
-(resp. `(x, 𝓝[[a, b]] x, 𝓝[[a, b]] x)`, where `[a, b] = set.uIcc a b`),
-with `x ∈ Icc a b` (resp. `x ∈ [a, b]`).
-This results in a two-sided derivatives for `x ∈ Ioo a b` and one-sided derivatives for
-`x ∈ {a, b}`. Other instances could be added when needed (in that case, one also needs to add
-instances for `filter.is_measurably_generated` and `filter.tendsto_Ixx_class`).
-
 ## Tags
 
-integral, fundamental theorem of calculus, FTC-1, FTC-2, change of variables in integrals
+integral
 -/
 
 
@@ -179,7 +62,7 @@ open Classical Topology Filter ENNReal BigOperators Interval NNReal
 variable {ι 𝕜 E F A : Type _} [NormedAddCommGroup E]
 
 /-!
-### Integrability at an interval
+### Integrability on an interval
 -/
 
 
@@ -213,41 +96,6 @@ theorem intervalIntegrable_iff_integrable_Ioc_of_le (hab : a ≤ b) :
   rw [intervalIntegrable_iff, uIoc_of_le hab]
 #align interval_integrable_iff_integrable_Ioc_of_le intervalIntegrable_iff_integrable_Ioc_of_le
 
-theorem integrableOn_Icc_iff_integrableOn_Ioc' {f : ℝ → E} (ha : μ {a} ≠ ∞) :
-    IntegrableOn f (Icc a b) μ ↔ IntegrableOn f (Ioc a b) μ :=
-  by
-  cases' le_or_lt a b with hab hab
-  · have : Icc a b = Icc a a ∪ Ioc a b := (Icc_union_Ioc_eq_Icc le_rfl hab).symm
-    rw [this, integrable_on_union]
-    simp [ha.lt_top]
-  · simp [hab, hab.le]
-#align integrable_on_Icc_iff_integrable_on_Ioc' integrableOn_Icc_iff_integrableOn_Ioc'
-
-theorem integrableOn_Icc_iff_integrableOn_Ioc [HasNoAtoms μ] {f : ℝ → E} {a b : ℝ} :
-    IntegrableOn f (Icc a b) μ ↔ IntegrableOn f (Ioc a b) μ :=
-  integrableOn_Icc_iff_integrableOn_Ioc' (by simp)
-#align integrable_on_Icc_iff_integrable_on_Ioc integrableOn_Icc_iff_integrableOn_Ioc
-
-theorem integrableOn_Ioc_iff_integrableOn_Ioo' {f : ℝ → E} {a b : ℝ} (hb : μ {b} ≠ ∞) :
-    IntegrableOn f (Ioc a b) μ ↔ IntegrableOn f (Ioo a b) μ :=
-  by
-  cases' lt_or_le a b with hab hab
-  · have : Ioc a b = Ioo a b ∪ Icc b b := (Ioo_union_Icc_eq_Ioc hab le_rfl).symm
-    rw [this, integrable_on_union]
-    simp [hb.lt_top]
-  · simp [hab]
-#align integrable_on_Ioc_iff_integrable_on_Ioo' integrableOn_Ioc_iff_integrableOn_Ioo'
-
-theorem integrableOn_Ioc_iff_integrableOn_Ioo [HasNoAtoms μ] {f : ℝ → E} {a b : ℝ} :
-    IntegrableOn f (Ioc a b) μ ↔ IntegrableOn f (Ioo a b) μ :=
-  integrableOn_Ioc_iff_integrableOn_Ioo' (by simp)
-#align integrable_on_Ioc_iff_integrable_on_Ioo integrableOn_Ioc_iff_integrableOn_Ioo
-
-theorem integrableOn_Icc_iff_integrableOn_Ioo [HasNoAtoms μ] {f : ℝ → E} {a b : ℝ} :
-    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 intervalIntegrable_iff' [HasNoAtoms μ] :
     IntervalIntegrable f μ a b ↔ IntegrableOn f (uIcc a b) μ := by
   rw [intervalIntegrable_iff, ← Icc_min_max, uIoc, integrableOn_Icc_iff_integrableOn_Ioc]
@@ -258,19 +106,6 @@ theorem intervalIntegrable_iff_integrable_Icc_of_le {f : ℝ → E} {a b : ℝ}
   rw [intervalIntegrable_iff_integrable_Ioc_of_le hab, integrableOn_Icc_iff_integrableOn_Ioc]
 #align interval_integrable_iff_integrable_Icc_of_le intervalIntegrable_iff_integrable_Icc_of_le
 
-theorem integrableOn_Ici_iff_integrableOn_Ioi' {f : ℝ → E} (ha : μ {a} ≠ ∞) :
-    IntegrableOn f (Ici a) μ ↔ IntegrableOn f (Ioi a) μ :=
-  by
-  have : Ici a = Icc a a ∪ Ioi a := (Icc_union_Ioi_eq_Ici le_rfl).symm
-  rw [this, integrable_on_union]
-  simp [ha.lt_top]
-#align integrable_on_Ici_iff_integrable_on_Ioi' integrableOn_Ici_iff_integrableOn_Ioi'
-
-theorem integrableOn_Ici_iff_integrableOn_Ioi [HasNoAtoms μ] {f : ℝ → E} :
-    IntegrableOn f (Ici a) μ ↔ IntegrableOn f (Ioi a) μ :=
-  integrableOn_Ici_iff_integrableOn_Ioi' (by simp)
-#align integrable_on_Ici_iff_integrable_on_Ioi integrableOn_Ici_iff_integrableOn_Ioi
-
 /-- If a function is integrable with respect to a given measure `μ` then it is interval integrable
   with respect to `μ` on `uIcc a b`. -/
 theorem MeasureTheory.Integrable.intervalIntegrable (hf : Integrable f μ) :
@@ -1678,1419 +1513,5 @@ theorem MeasureTheory.Integrable.hasSum_intervalIntegral_comp_add_int (hfi : Int
 
 end HasSum
 
-/-!
-### Fundamental theorem of calculus, part 1, for any measure
-
-In this section we prove a few lemmas that can be seen as versions of FTC-1 for interval integrals
-w.r.t. any measure. Many theorems are formulated for one or two pairs of filters related by
-`FTC_filter a l l'`. This typeclass has exactly four “real” instances: `(a, pure a, ⊥)`,
-`(a, 𝓝[≥] a, 𝓝[>] a)`, `(a, 𝓝[≤] a, 𝓝[≤] a)`, `(a, 𝓝 a, 𝓝 a)`, and two instances
-that are equal to the first and last “real” instances: `(a, 𝓝[{a}] a, ⊥)` and
-`(a, 𝓝[univ] a, 𝓝[univ] a)`.  We use this approach to avoid repeating arguments in many very similar
-cases.  Lean can automatically find both `a` and `l'` based on `l`.
-
-The most general theorem `measure_integral_sub_integral_sub_linear_is_o_of_tendsto_ae` can be seen
-as a generalization of lemma `integral_has_strict_fderiv_at` below which states strict
-differentiability of `∫ x in u..v, f x` in `(u, v)` at `(a, b)` for a measurable function `f` that
-is integrable on `a..b` and is continuous at `a` and `b`. The lemma is generalized in three
-directions: first, `measure_integral_sub_integral_sub_linear_is_o_of_tendsto_ae` deals with any
-locally finite measure `μ`; second, it works for one-sided limits/derivatives; third, it assumes
-only that `f` has finite limits almost surely at `a` and `b`.
-
-Namely, let `f` be a measurable function integrable on `a..b`. Let `(la, la')` be a pair of
-`FTC_filter`s around `a`; let `(lb, lb')` be a pair of `FTC_filter`s around `b`. Suppose that `f`
-has finite limits `ca` and `cb` at `la' ⊓ μ.ae` and `lb' ⊓ μ.ae`, respectively.  Then
-`∫ x in va..vb, f x ∂μ - ∫ x in ua..ub, f x ∂μ = ∫ x in ub..vb, cb ∂μ - ∫ x in ua..va, ca ∂μ +
-  o(‖∫ x in ua..va, (1:ℝ) ∂μ‖ + ‖∫ x in ub..vb, (1:ℝ) ∂μ‖)`
-as `ua` and `va` tend to `la` while `ub` and `vb` tend to `lb`.
-
-This theorem is formulated with integral of constants instead of measures in the right hand sides
-for two reasons: first, this way we avoid `min`/`max` in the statements; second, often it is
-possible to write better `simp` lemmas for these integrals, see `integral_const` and
-`integral_const_of_cdf`.
-
-In the next subsection we apply this theorem to prove various theorems about differentiability
-of the integral w.r.t. Lebesgue measure. -/
-
-
-/-- An auxiliary typeclass for the Fundamental theorem of calculus, part 1. It is used to formulate
-theorems that work simultaneously for left and right one-sided derivatives of `∫ x in u..v, f x`. -/
-class FTCFilter (a : outParam ℝ) (outer : Filter ℝ) (inner : outParam <| Filter ℝ) extends
-  TendstoIxxClass Ioc outer inner : Prop where
-  pure_le : pure a ≤ outer
-  le_nhds : inner ≤ 𝓝 a
-  [meas_gen : IsMeasurablyGenerated inner]
-#align interval_integral.FTC_filter intervalIntegral.FTCFilter
-
-/- The `dangerous_instance` linter doesn't take `out_param`s into account, so it thinks that
-`FTC_filter.to_tendsto_Ixx_class` is dangerous. Disable this linter using `nolint`.
--/
-attribute [nolint dangerous_instance] FTC_filter.to_tendsto_Ixx_class
-
-namespace FTCFilter
-
-instance pure (a : ℝ) : FTCFilter a (pure a) ⊥
-    where
-  pure_le := le_rfl
-  le_nhds := bot_le
-#align interval_integral.FTC_filter.pure intervalIntegral.FTCFilter.pure
-
-instance nhdsWithinSingleton (a : ℝ) : FTCFilter a (𝓝[{a}] a) ⊥ :=
-  by
-  rw [nhdsWithin, principal_singleton, inf_eq_right.2 (pure_le_nhds a)]
-  infer_instance
-#align interval_integral.FTC_filter.nhds_within_singleton intervalIntegral.FTCFilter.nhdsWithinSingleton
-
-theorem finiteAtInner {a : ℝ} (l : Filter ℝ) {l'} [h : FTCFilter a l l'] {μ : Measure ℝ}
-    [IsLocallyFiniteMeasure μ] : μ.FiniteAtFilter l' :=
-  (μ.finiteAtNhds a).filter_mono h.le_nhds
-#align interval_integral.FTC_filter.finite_at_inner intervalIntegral.FTCFilter.finiteAtInner
-
-instance nhds (a : ℝ) : FTCFilter a (𝓝 a) (𝓝 a)
-    where
-  pure_le := pure_le_nhds a
-  le_nhds := le_rfl
-#align interval_integral.FTC_filter.nhds intervalIntegral.FTCFilter.nhds
-
-instance nhdsUniv (a : ℝ) : FTCFilter a (𝓝[univ] a) (𝓝 a) :=
-  by
-  rw [nhdsWithin_univ]
-  infer_instance
-#align interval_integral.FTC_filter.nhds_univ intervalIntegral.FTCFilter.nhdsUniv
-
-instance nhdsLeft (a : ℝ) : FTCFilter a (𝓝[≤] a) (𝓝[≤] a)
-    where
-  pure_le := pure_le_nhdsWithin right_mem_Iic
-  le_nhds := inf_le_left
-#align interval_integral.FTC_filter.nhds_left intervalIntegral.FTCFilter.nhdsLeft
-
-instance nhdsRight (a : ℝ) : FTCFilter a (𝓝[≥] a) (𝓝[>] a)
-    where
-  pure_le := pure_le_nhdsWithin left_mem_Ici
-  le_nhds := inf_le_left
-#align interval_integral.FTC_filter.nhds_right intervalIntegral.FTCFilter.nhdsRight
-
-instance nhdsIcc {x a b : ℝ} [h : Fact (x ∈ Icc a b)] : FTCFilter x (𝓝[Icc a b] x) (𝓝[Icc a b] x)
-    where
-  pure_le := pure_le_nhdsWithin h.out
-  le_nhds := inf_le_left
-#align interval_integral.FTC_filter.nhds_Icc intervalIntegral.FTCFilter.nhdsIcc
-
-instance nhdsUIcc {x a b : ℝ} [h : Fact (x ∈ [a, b])] : FTCFilter x (𝓝[[a, b]] x) (𝓝[[a, b]] x) :=
-  haveI : Fact (x ∈ Set.Icc (min a b) (max a b)) := h
-  FTC_filter.nhds_Icc
-#align interval_integral.FTC_filter.nhds_uIcc intervalIntegral.FTCFilter.nhdsUIcc
-
-end FTCFilter
-
-open Asymptotics
-
-section
-
-variable {f : ℝ → E} {a b : ℝ} {c ca cb : E} {l l' la la' lb lb' : Filter ℝ} {lt : Filter ι}
-  {μ : Measure ℝ} {u v ua va ub vb : ι → ℝ}
-
-/-- Fundamental theorem of calculus-1, local version for any measure.
-Let filters `l` and `l'` be related by `tendsto_Ixx_class Ioc`.
-If `f` has a finite limit `c` at `l' ⊓ μ.ae`, where `μ` is a measure
-finite at `l'`, then `∫ x in u..v, f x ∂μ = ∫ x in u..v, c ∂μ + o(∫ x in u..v, 1 ∂μ)` as both
-`u` and `v` tend to `l`.
-
-See also `measure_integral_sub_linear_is_o_of_tendsto_ae` for a version assuming
-`[FTC_filter a l l']` and `[is_locally_finite_measure μ]`. If `l` is one of `𝓝[≥] a`,
-`𝓝[≤] a`, `𝓝 a`, then it's easier to apply the non-primed version.
-The primed version also works, e.g., for `l = l' = at_top`.
-
-We use integrals of constants instead of measures because this way it is easier to formulate
-a statement that works in both cases `u ≤ v` and `v ≤ u`. -/
-theorem measure_integral_sub_linear_isLittleO_of_tendsto_ae' [IsMeasurablyGenerated l']
-    [TendstoIxxClass Ioc l l'] (hfm : StronglyMeasurableAtFilter f l' μ)
-    (hf : Tendsto f (l' ⊓ μ.ae) (𝓝 c)) (hl : μ.FiniteAtFilter l') (hu : Tendsto u lt l)
-    (hv : Tendsto v lt l) :
-    (fun t => (∫ x in u t..v t, f x ∂μ) - ∫ x in u t..v t, c ∂μ) =o[lt] fun t =>
-      ∫ x in u t..v t, (1 : ℝ) ∂μ :=
-  by
-  have A := hf.integral_sub_linear_is_o_ae hfm hl (hu.Ioc hv)
-  have B := hf.integral_sub_linear_is_o_ae hfm hl (hv.Ioc hu)
-  simp only [integral_const']
-  convert(A.trans_le _).sub (B.trans_le _)
-  · ext t
-    simp_rw [intervalIntegral, sub_smul]
-    abel
-  all_goals intro t; cases' le_total (u t) (v t) with huv huv <;> simp [huv]
-#align interval_integral.measure_integral_sub_linear_is_o_of_tendsto_ae' intervalIntegral.measure_integral_sub_linear_isLittleO_of_tendsto_ae'
-
-/-- Fundamental theorem of calculus-1, local version for any measure.
-Let filters `l` and `l'` be related by `tendsto_Ixx_class Ioc`.
-If `f` has a finite limit `c` at `l ⊓ μ.ae`, where `μ` is a measure
-finite at `l`, then `∫ x in u..v, f x ∂μ = μ (Ioc u v) • c + o(μ(Ioc u v))` as both
-`u` and `v` tend to `l` so that `u ≤ v`.
-
-See also `measure_integral_sub_linear_is_o_of_tendsto_ae_of_le` for a version assuming
-`[FTC_filter a l l']` and `[is_locally_finite_measure μ]`. If `l` is one of `𝓝[≥] a`,
-`𝓝[≤] a`, `𝓝 a`, then it's easier to apply the non-primed version.
-The primed version also works, e.g., for `l = l' = at_top`. -/
-theorem measure_integral_sub_linear_isLittleO_of_tendsto_ae_of_le' [IsMeasurablyGenerated l']
-    [TendstoIxxClass Ioc l l'] (hfm : StronglyMeasurableAtFilter f l' μ)
-    (hf : Tendsto f (l' ⊓ μ.ae) (𝓝 c)) (hl : μ.FiniteAtFilter l') (hu : Tendsto u lt l)
-    (hv : Tendsto v lt l) (huv : u ≤ᶠ[lt] v) :
-    (fun t => (∫ x in u t..v t, f x ∂μ) - (μ (Ioc (u t) (v t))).toReal • c) =o[lt] fun t =>
-      (μ <| Ioc (u t) (v t)).toReal :=
-  (measure_integral_sub_linear_isLittleO_of_tendsto_ae' hfm hf hl hu hv).congr'
-    (huv.mono fun x hx => by simp [integral_const', hx])
-    (huv.mono fun x hx => by simp [integral_const', hx])
-#align interval_integral.measure_integral_sub_linear_is_o_of_tendsto_ae_of_le' intervalIntegral.measure_integral_sub_linear_isLittleO_of_tendsto_ae_of_le'
-
-/-- Fundamental theorem of calculus-1, local version for any measure.
-Let filters `l` and `l'` be related by `tendsto_Ixx_class Ioc`.
-If `f` has a finite limit `c` at `l ⊓ μ.ae`, where `μ` is a measure
-finite at `l`, then `∫ x in u..v, f x ∂μ = -μ (Ioc v u) • c + o(μ(Ioc v u))` as both
-`u` and `v` tend to `l` so that `v ≤ u`.
-
-See also `measure_integral_sub_linear_is_o_of_tendsto_ae_of_ge` for a version assuming
-`[FTC_filter a l l']` and `[is_locally_finite_measure μ]`. If `l` is one of `𝓝[≥] a`,
-`𝓝[≤] a`, `𝓝 a`, then it's easier to apply the non-primed version.
-The primed version also works, e.g., for `l = l' = at_top`. -/
-theorem measure_integral_sub_linear_isLittleO_of_tendsto_ae_of_ge' [IsMeasurablyGenerated l']
-    [TendstoIxxClass Ioc l l'] (hfm : StronglyMeasurableAtFilter f l' μ)
-    (hf : Tendsto f (l' ⊓ μ.ae) (𝓝 c)) (hl : μ.FiniteAtFilter l') (hu : Tendsto u lt l)
-    (hv : Tendsto v lt l) (huv : v ≤ᶠ[lt] u) :
-    (fun t => (∫ x in u t..v t, f x ∂μ) + (μ (Ioc (v t) (u t))).toReal • c) =o[lt] fun t =>
-      (μ <| Ioc (v t) (u t)).toReal :=
-  (measure_integral_sub_linear_isLittleO_of_tendsto_ae_of_le' hfm hf hl hv hu
-          huv).neg_left.congr_left
-    fun t => by simp [integral_symm (u t), add_comm]
-#align interval_integral.measure_integral_sub_linear_is_o_of_tendsto_ae_of_ge' intervalIntegral.measure_integral_sub_linear_isLittleO_of_tendsto_ae_of_ge'
-
-section
-
-variable [IsLocallyFiniteMeasure μ] [FTCFilter a l l']
-
-include a
-
-attribute [local instance] FTC_filter.meas_gen
-
-/-- Fundamental theorem of calculus-1, local version for any measure.
-Let filters `l` and `l'` be related by `[FTC_filter a l l']`; let `μ` be a locally finite measure.
-If `f` has a finite limit `c` at `l' ⊓ μ.ae`, then
-`∫ x in u..v, f x ∂μ = ∫ x in u..v, c ∂μ + o(∫ x in u..v, 1 ∂μ)` as both `u` and `v` tend to `l`.
-
-See also `measure_integral_sub_linear_is_o_of_tendsto_ae'` for a version that also works, e.g., for
-`l = l' = at_top`.
-
-We use integrals of constants instead of measures because this way it is easier to formulate
-a statement that works in both cases `u ≤ v` and `v ≤ u`. -/
-theorem measure_integral_sub_linear_isLittleO_of_tendsto_ae
-    (hfm : StronglyMeasurableAtFilter f l' μ) (hf : Tendsto f (l' ⊓ μ.ae) (𝓝 c))
-    (hu : Tendsto u lt l) (hv : Tendsto v lt l) :
-    (fun t => (∫ x in u t..v t, f x ∂μ) - ∫ x in u t..v t, c ∂μ) =o[lt] fun t =>
-      ∫ x in u t..v t, (1 : ℝ) ∂μ :=
-  measure_integral_sub_linear_isLittleO_of_tendsto_ae' hfm hf (FTCFilter.finiteAtInner l) hu hv
-#align interval_integral.measure_integral_sub_linear_is_o_of_tendsto_ae intervalIntegral.measure_integral_sub_linear_isLittleO_of_tendsto_ae
-
-/-- Fundamental theorem of calculus-1, local version for any measure.
-Let filters `l` and `l'` be related by `[FTC_filter a l l']`; let `μ` be a locally finite measure.
-If `f` has a finite limit `c` at `l' ⊓ μ.ae`, then
-`∫ x in u..v, f x ∂μ = μ (Ioc u v) • c + o(μ(Ioc u v))` as both `u` and `v` tend to `l`.
-
-See also `measure_integral_sub_linear_is_o_of_tendsto_ae_of_le'` for a version that also works,
-e.g., for `l = l' = at_top`. -/
-theorem measure_integral_sub_linear_isLittleO_of_tendsto_ae_of_le
-    (hfm : StronglyMeasurableAtFilter f l' μ) (hf : Tendsto f (l' ⊓ μ.ae) (𝓝 c))
-    (hu : Tendsto u lt l) (hv : Tendsto v lt l) (huv : u ≤ᶠ[lt] v) :
-    (fun t => (∫ x in u t..v t, f x ∂μ) - (μ (Ioc (u t) (v t))).toReal • c) =o[lt] fun t =>
-      (μ <| Ioc (u t) (v t)).toReal :=
-  measure_integral_sub_linear_isLittleO_of_tendsto_ae_of_le' hfm hf (FTCFilter.finiteAtInner l) hu
-    hv huv
-#align interval_integral.measure_integral_sub_linear_is_o_of_tendsto_ae_of_le intervalIntegral.measure_integral_sub_linear_isLittleO_of_tendsto_ae_of_le
-
-/-- Fundamental theorem of calculus-1, local version for any measure.
-Let filters `l` and `l'` be related by `[FTC_filter a l l']`; let `μ` be a locally finite measure.
-If `f` has a finite limit `c` at `l' ⊓ μ.ae`, then
-`∫ x in u..v, f x ∂μ = -μ (Ioc v u) • c + o(μ(Ioc v u))` as both `u` and `v` tend to `l`.
-
-See also `measure_integral_sub_linear_is_o_of_tendsto_ae_of_ge'` for a version that also works,
-e.g., for `l = l' = at_top`. -/
-theorem measure_integral_sub_linear_isLittleO_of_tendsto_ae_of_ge
-    (hfm : StronglyMeasurableAtFilter f l' μ) (hf : Tendsto f (l' ⊓ μ.ae) (𝓝 c))
-    (hu : Tendsto u lt l) (hv : Tendsto v lt l) (huv : v ≤ᶠ[lt] u) :
-    (fun t => (∫ x in u t..v t, f x ∂μ) + (μ (Ioc (v t) (u t))).toReal • c) =o[lt] fun t =>
-      (μ <| Ioc (v t) (u t)).toReal :=
-  measure_integral_sub_linear_isLittleO_of_tendsto_ae_of_ge' hfm hf (FTCFilter.finiteAtInner l) hu
-    hv huv
-#align interval_integral.measure_integral_sub_linear_is_o_of_tendsto_ae_of_ge intervalIntegral.measure_integral_sub_linear_isLittleO_of_tendsto_ae_of_ge
-
-end
-
-attribute [local instance] FTC_filter.meas_gen
-
-variable [FTCFilter a la la'] [FTCFilter b lb lb'] [IsLocallyFiniteMeasure μ]
-
-/-- Fundamental theorem of calculus-1, strict derivative in both limits for a locally finite
-measure.
-
-Let `f` be a measurable function integrable on `a..b`. Let `(la, la')` be a pair of `FTC_filter`s
-around `a`; let `(lb, lb')` be a pair of `FTC_filter`s around `b`. Suppose that `f` has finite
-limits `ca` and `cb` at `la' ⊓ μ.ae` and `lb' ⊓ μ.ae`, respectively.
-Then `∫ x in va..vb, f x ∂μ - ∫ x in ua..ub, f x ∂μ =
-  ∫ x in ub..vb, cb ∂μ - ∫ x in ua..va, ca ∂μ +
-    o(‖∫ x in ua..va, (1:ℝ) ∂μ‖ + ‖∫ x in ub..vb, (1:ℝ) ∂μ‖)`
-as `ua` and `va` tend to `la` while `ub` and `vb` tend to `lb`.
--/
-theorem measure_integral_sub_integral_sub_linear_isLittleO_of_tendsto_ae
-    (hab : IntervalIntegrable f μ a b) (hmeas_a : StronglyMeasurableAtFilter f la' μ)
-    (hmeas_b : StronglyMeasurableAtFilter f lb' μ) (ha_lim : Tendsto f (la' ⊓ μ.ae) (𝓝 ca))
-    (hb_lim : Tendsto f (lb' ⊓ μ.ae) (𝓝 cb)) (hua : Tendsto ua lt la) (hva : Tendsto va lt la)
-    (hub : Tendsto ub lt lb) (hvb : Tendsto vb lt lb) :
-    (fun t =>
-        ((∫ x in va t..vb t, f x ∂μ) - ∫ x in ua t..ub t, f x ∂μ) -
-          ((∫ x in ub t..vb t, cb ∂μ) - ∫ x in ua t..va t, ca ∂μ)) =o[lt]
-      fun t => ‖∫ x in ua t..va t, (1 : ℝ) ∂μ‖ + ‖∫ x in ub t..vb t, (1 : ℝ) ∂μ‖ :=
-  by
-  refine'
-    ((measure_integral_sub_linear_is_o_of_tendsto_ae hmeas_a ha_lim hua hva).neg_left.add_add
-          (measure_integral_sub_linear_is_o_of_tendsto_ae hmeas_b hb_lim hub hvb)).congr'
-      _ eventually_eq.rfl
-  have A : ∀ᶠ t in lt, IntervalIntegrable f μ (ua t) (va t) :=
-    ha_lim.eventually_interval_integrable_ae hmeas_a (FTC_filter.finite_at_inner la) hua hva
-  have A' : ∀ᶠ t in lt, IntervalIntegrable f μ a (ua t) :=
-    ha_lim.eventually_interval_integrable_ae hmeas_a (FTC_filter.finite_at_inner la)
-      (tendsto_const_pure.mono_right FTC_filter.pure_le) hua
-  have B : ∀ᶠ t in lt, IntervalIntegrable f μ (ub t) (vb t) :=
-    hb_lim.eventually_interval_integrable_ae hmeas_b (FTC_filter.finite_at_inner lb) hub hvb
-  have B' : ∀ᶠ t in lt, IntervalIntegrable f μ b (ub t) :=
-    hb_lim.eventually_interval_integrable_ae hmeas_b (FTC_filter.finite_at_inner lb)
-      (tendsto_const_pure.mono_right FTC_filter.pure_le) hub
-  filter_upwards [A, A', B, B']with _ ua_va a_ua ub_vb b_ub
-  rw [← integral_interval_sub_interval_comm']
-  · dsimp only
-    abel
-  exacts[ub_vb, ua_va, b_ub.symm.trans <| hab.symm.trans a_ua]
-#align interval_integral.measure_integral_sub_integral_sub_linear_is_o_of_tendsto_ae intervalIntegral.measure_integral_sub_integral_sub_linear_isLittleO_of_tendsto_ae
-
-/-- Fundamental theorem of calculus-1, strict derivative in right endpoint for a locally finite
-measure.
-
-Let `f` be a measurable function integrable on `a..b`. Let `(lb, lb')` be a pair of `FTC_filter`s
-around `b`. Suppose that `f` has a finite limit `c` at `lb' ⊓ μ.ae`.
-
-Then `∫ x in a..v, f x ∂μ - ∫ x in a..u, f x ∂μ = ∫ x in u..v, c ∂μ + o(∫ x in u..v, (1:ℝ) ∂μ)`
-as `u` and `v` tend to `lb`.
--/
-theorem measure_integral_sub_integral_sub_linear_isLittleO_of_tendsto_ae_right
-    (hab : IntervalIntegrable f μ a b) (hmeas : StronglyMeasurableAtFilter f lb' μ)
-    (hf : Tendsto f (lb' ⊓ μ.ae) (𝓝 c)) (hu : Tendsto u lt lb) (hv : Tendsto v lt lb) :
-    (fun t => ((∫ x in a..v t, f x ∂μ) - ∫ x in a..u t, f x ∂μ) - ∫ x in u t..v t, c ∂μ) =o[lt]
-      fun t => ∫ x in u t..v t, (1 : ℝ) ∂μ :=
-  by
-  simpa using
-    measure_integral_sub_integral_sub_linear_is_o_of_tendsto_ae hab stronglyMeasurableAtBot hmeas
-      ((tendsto_bot : tendsto _ ⊥ (𝓝 0)).mono_left inf_le_left) hf
-      (tendsto_const_pure : tendsto _ _ (pure a)) tendsto_const_pure hu hv
-#align interval_integral.measure_integral_sub_integral_sub_linear_is_o_of_tendsto_ae_right intervalIntegral.measure_integral_sub_integral_sub_linear_isLittleO_of_tendsto_ae_right
-
-/-- Fundamental theorem of calculus-1, strict derivative in left endpoint for a locally finite
-measure.
-
-Let `f` be a measurable function integrable on `a..b`. Let `(la, la')` be a pair of `FTC_filter`s
-around `a`. Suppose that `f` has a finite limit `c` at `la' ⊓ μ.ae`.
-
-Then `∫ x in v..b, f x ∂μ - ∫ x in u..b, f x ∂μ = -∫ x in u..v, c ∂μ + o(∫ x in u..v, (1:ℝ) ∂μ)`
-as `u` and `v` tend to `la`.
--/
-theorem measure_integral_sub_integral_sub_linear_isLittleO_of_tendsto_ae_left
-    (hab : IntervalIntegrable f μ a b) (hmeas : StronglyMeasurableAtFilter f la' μ)
-    (hf : Tendsto f (la' ⊓ μ.ae) (𝓝 c)) (hu : Tendsto u lt la) (hv : Tendsto v lt la) :
-    (fun t => ((∫ x in v t..b, f x ∂μ) - ∫ x in u t..b, f x ∂μ) + ∫ x in u t..v t, c ∂μ) =o[lt]
-      fun t => ∫ x in u t..v t, (1 : ℝ) ∂μ :=
-  by
-  simpa using
-    measure_integral_sub_integral_sub_linear_is_o_of_tendsto_ae hab hmeas stronglyMeasurableAtBot hf
-      ((tendsto_bot : tendsto _ ⊥ (𝓝 0)).mono_left inf_le_left) hu hv
-      (tendsto_const_pure : tendsto _ _ (pure b)) tendsto_const_pure
-#align interval_integral.measure_integral_sub_integral_sub_linear_is_o_of_tendsto_ae_left intervalIntegral.measure_integral_sub_integral_sub_linear_isLittleO_of_tendsto_ae_left
-
-end
-
-/-!
-### Fundamental theorem of calculus-1 for Lebesgue measure
-
-In this section we restate theorems from the previous section for Lebesgue measure.
-In particular, we prove that `∫ x in u..v, f x` is strictly differentiable in `(u, v)`
-at `(a, b)` provided that `f` is integrable on `a..b` and is continuous at `a` and `b`.
--/
-
-
-variable {f : ℝ → E} {c ca cb : E} {l l' la la' lb lb' : Filter ℝ} {lt : Filter ι} {a b z : ℝ}
-  {u v ua ub va vb : ι → ℝ} [FTCFilter a la la'] [FTCFilter b lb lb']
-
-/-!
-#### Auxiliary `is_o` statements
-
-In this section we prove several lemmas that can be interpreted as strict differentiability of
-`(u, v) ↦ ∫ x in u..v, f x ∂μ` in `u` and/or `v` at a filter. The statements use `is_o` because
-we have no definition of `has_strict_(f)deriv_at_filter` in the library.
--/
-
-
-/-- Fundamental theorem of calculus-1, local version. If `f` has a finite limit `c` almost surely at
-`l'`, where `(l, l')` is an `FTC_filter` pair around `a`, then
-`∫ x in u..v, f x ∂μ = (v - u) • c + o (v - u)` as both `u` and `v` tend to `l`. -/
-theorem integral_sub_linear_isLittleO_of_tendsto_ae [FTCFilter a l l']
-    (hfm : StronglyMeasurableAtFilter f l') (hf : Tendsto f (l' ⊓ volume.ae) (𝓝 c)) {u v : ι → ℝ}
-    (hu : Tendsto u lt l) (hv : Tendsto v lt l) :
-    (fun t => (∫ x in u t..v t, f x) - (v t - u t) • c) =o[lt] (v - u) := by
-  simpa [integral_const] using measure_integral_sub_linear_is_o_of_tendsto_ae hfm hf hu hv
-#align interval_integral.integral_sub_linear_is_o_of_tendsto_ae intervalIntegral.integral_sub_linear_isLittleO_of_tendsto_ae
-
-/-- Fundamental theorem of calculus-1, strict differentiability at filter in both endpoints.
-If `f` is a measurable function integrable on `a..b`, `(la, la')` is an `FTC_filter` pair around
-`a`, and `(lb, lb')` is an `FTC_filter` pair around `b`, and `f` has finite limits `ca` and `cb`
-almost surely at `la'` and `lb'`, respectively, then
-`(∫ x in va..vb, f x) - ∫ x in ua..ub, f x = (vb - ub) • cb - (va - ua) • ca +
-  o(‖va - ua‖ + ‖vb - ub‖)` as `ua` and `va` tend to `la` while `ub` and `vb` tend to `lb`.
-
-This lemma could've been formulated using `has_strict_fderiv_at_filter` if we had this
-definition. -/
-theorem integral_sub_integral_sub_linear_isLittleO_of_tendsto_ae
-    (hab : IntervalIntegrable f volume a b) (hmeas_a : StronglyMeasurableAtFilter f la')
-    (hmeas_b : StronglyMeasurableAtFilter f lb') (ha_lim : Tendsto f (la' ⊓ volume.ae) (𝓝 ca))
-    (hb_lim : Tendsto f (lb' ⊓ volume.ae) (𝓝 cb)) (hua : Tendsto ua lt la) (hva : Tendsto va lt la)
-    (hub : Tendsto ub lt lb) (hvb : Tendsto vb lt lb) :
-    (fun t =>
-        ((∫ x in va t..vb t, f x) - ∫ x in ua t..ub t, f x) -
-          ((vb t - ub t) • cb - (va t - ua t) • ca)) =o[lt]
-      fun t => ‖va t - ua t‖ + ‖vb t - ub t‖ :=
-  by
-  simpa [integral_const] using
-    measure_integral_sub_integral_sub_linear_is_o_of_tendsto_ae hab hmeas_a hmeas_b ha_lim hb_lim
-      hua hva hub hvb
-#align interval_integral.integral_sub_integral_sub_linear_is_o_of_tendsto_ae intervalIntegral.integral_sub_integral_sub_linear_isLittleO_of_tendsto_ae
-
-/-- Fundamental theorem of calculus-1, strict differentiability at filter in both endpoints.
-If `f` is a measurable function integrable on `a..b`, `(lb, lb')` is an `FTC_filter` pair
-around `b`, and `f` has a finite limit `c` almost surely at `lb'`, then
-`(∫ x in a..v, f x) - ∫ x in a..u, f x = (v - u) • c + o(‖v - u‖)` as `u` and `v` tend to `lb`.
-
-This lemma could've been formulated using `has_strict_deriv_at_filter` if we had this definition. -/
-theorem integral_sub_integral_sub_linear_isLittleO_of_tendsto_ae_right
-    (hab : IntervalIntegrable f volume a b) (hmeas : StronglyMeasurableAtFilter f lb')
-    (hf : Tendsto f (lb' ⊓ volume.ae) (𝓝 c)) (hu : Tendsto u lt lb) (hv : Tendsto v lt lb) :
-    (fun t => ((∫ x in a..v t, f x) - ∫ x in a..u t, f x) - (v t - u t) • c) =o[lt] (v - u) := by
-  simpa only [integral_const, smul_eq_mul, mul_one] using
-    measure_integral_sub_integral_sub_linear_is_o_of_tendsto_ae_right hab hmeas hf hu hv
-#align interval_integral.integral_sub_integral_sub_linear_is_o_of_tendsto_ae_right intervalIntegral.integral_sub_integral_sub_linear_isLittleO_of_tendsto_ae_right
-
-/-- Fundamental theorem of calculus-1, strict differentiability at filter in both endpoints.
-If `f` is a measurable function integrable on `a..b`, `(la, la')` is an `FTC_filter` pair
-around `a`, and `f` has a finite limit `c` almost surely at `la'`, then
-`(∫ x in v..b, f x) - ∫ x in u..b, f x = -(v - u) • c + o(‖v - u‖)` as `u` and `v` tend to `la`.
-
-This lemma could've been formulated using `has_strict_deriv_at_filter` if we had this definition. -/
-theorem integral_sub_integral_sub_linear_isLittleO_of_tendsto_ae_left
-    (hab : IntervalIntegrable f volume a b) (hmeas : StronglyMeasurableAtFilter f la')
-    (hf : Tendsto f (la' ⊓ volume.ae) (𝓝 c)) (hu : Tendsto u lt la) (hv : Tendsto v lt la) :
-    (fun t => ((∫ x in v t..b, f x) - ∫ x in u t..b, f x) + (v t - u t) • c) =o[lt] (v - u) := by
-  simpa only [integral_const, smul_eq_mul, mul_one] using
-    measure_integral_sub_integral_sub_linear_is_o_of_tendsto_ae_left hab hmeas hf hu hv
-#align interval_integral.integral_sub_integral_sub_linear_is_o_of_tendsto_ae_left intervalIntegral.integral_sub_integral_sub_linear_isLittleO_of_tendsto_ae_left
-
-open ContinuousLinearMap (fst snd smul_right sub_apply smulRight_apply coe_fst' coe_snd' map_sub)
-
-/-!
-#### Strict differentiability
-
-In this section we prove that for a measurable function `f` integrable on `a..b`,
-
-* `integral_has_strict_fderiv_at_of_tendsto_ae`: the function `(u, v) ↦ ∫ x in u..v, f x` has
-  derivative `(u, v) ↦ v • cb - u • ca` at `(a, b)` in the sense of strict differentiability
-  provided that `f` tends to `ca` and `cb` almost surely as `x` tendsto to `a` and `b`,
-  respectively;
-
-* `integral_has_strict_fderiv_at`: the function `(u, v) ↦ ∫ x in u..v, f x` has
-  derivative `(u, v) ↦ v • f b - u • f a` at `(a, b)` in the sense of strict differentiability
-  provided that `f` is continuous at `a` and `b`;
-
-* `integral_has_strict_deriv_at_of_tendsto_ae_right`: the function `u ↦ ∫ x in a..u, f x` has
-  derivative `c` at `b` in the sense of strict differentiability provided that `f` tends to `c`
-  almost surely as `x` tends to `b`;
-
-* `integral_has_strict_deriv_at_right`: the function `u ↦ ∫ x in a..u, f x` has derivative `f b` at
-  `b` in the sense of strict differentiability provided that `f` is continuous at `b`;
-
-* `integral_has_strict_deriv_at_of_tendsto_ae_left`: the function `u ↦ ∫ x in u..b, f x` has
-  derivative `-c` at `a` in the sense of strict differentiability provided that `f` tends to `c`
-  almost surely as `x` tends to `a`;
-
-* `integral_has_strict_deriv_at_left`: the function `u ↦ ∫ x in u..b, f x` has derivative `-f a` at
-  `a` in the sense of strict differentiability provided that `f` is continuous at `a`.
--/
-
-
-/-- Fundamental theorem of calculus-1: if `f : ℝ → E` is integrable on `a..b` and `f x` has finite
-limits `ca` and `cb` almost surely as `x` tends to `a` and `b`, respectively, then
-`(u, v) ↦ ∫ x in u..v, f x` has derivative `(u, v) ↦ v • cb - u • ca` at `(a, b)`
-in the sense of strict differentiability. -/
-theorem integral_hasStrictFderivAt_of_tendsto_ae (hf : IntervalIntegrable f volume a b)
-    (hmeas_a : StronglyMeasurableAtFilter f (𝓝 a)) (hmeas_b : StronglyMeasurableAtFilter f (𝓝 b))
-    (ha : Tendsto f (𝓝 a ⊓ volume.ae) (𝓝 ca)) (hb : Tendsto f (𝓝 b ⊓ volume.ae) (𝓝 cb)) :
-    HasStrictFderivAt (fun p : ℝ × ℝ => ∫ x in p.1 ..p.2, f x)
-      ((snd ℝ ℝ ℝ).smul_right cb - (fst ℝ ℝ ℝ).smul_right ca) (a, b) :=
-  by
-  have :=
-    integral_sub_integral_sub_linear_is_o_of_tendsto_ae hf hmeas_a hmeas_b ha hb
-      ((continuous_fst.comp continuous_snd).Tendsto ((a, b), (a, b)))
-      ((continuous_fst.comp continuous_fst).Tendsto ((a, b), (a, b)))
-      ((continuous_snd.comp continuous_snd).Tendsto ((a, b), (a, b)))
-      ((continuous_snd.comp continuous_fst).Tendsto ((a, b), (a, b)))
-  refine' (this.congr_left _).trans_isBigO _
-  · intro x
-    simp [sub_smul]
-  · exact is_O_fst_prod.norm_left.add is_O_snd_prod.norm_left
-#align interval_integral.integral_has_strict_fderiv_at_of_tendsto_ae intervalIntegral.integral_hasStrictFderivAt_of_tendsto_ae
-
-/-- Fundamental theorem of calculus-1: if `f : ℝ → E` is integrable on `a..b` and `f` is continuous
-at `a` and `b`, then `(u, v) ↦ ∫ x in u..v, f x` has derivative `(u, v) ↦ v • cb - u • ca`
-at `(a, b)` in the sense of strict differentiability. -/
-theorem integral_hasStrictFderivAt (hf : IntervalIntegrable f volume a b)
-    (hmeas_a : StronglyMeasurableAtFilter f (𝓝 a)) (hmeas_b : StronglyMeasurableAtFilter f (𝓝 b))
-    (ha : ContinuousAt f a) (hb : ContinuousAt f b) :
-    HasStrictFderivAt (fun p : ℝ × ℝ => ∫ x in p.1 ..p.2, f x)
-      ((snd ℝ ℝ ℝ).smul_right (f b) - (fst ℝ ℝ ℝ).smul_right (f a)) (a, b) :=
-  integral_hasStrictFderivAt_of_tendsto_ae hf hmeas_a hmeas_b (ha.mono_left inf_le_left)
-    (hb.mono_left inf_le_left)
-#align interval_integral.integral_has_strict_fderiv_at intervalIntegral.integral_hasStrictFderivAt
-
-/-- **First Fundamental Theorem of Calculus**: if `f : ℝ → E` is integrable on `a..b` and `f x` has
-a finite limit `c` almost surely at `b`, then `u ↦ ∫ x in a..u, f x` has derivative `c` at `b` in
-the sense of strict differentiability. -/
-theorem integral_hasStrictDerivAt_of_tendsto_ae_right (hf : IntervalIntegrable f volume a b)
-    (hmeas : StronglyMeasurableAtFilter f (𝓝 b)) (hb : Tendsto f (𝓝 b ⊓ volume.ae) (𝓝 c)) :
-    HasStrictDerivAt (fun u => ∫ x in a..u, f x) c b :=
-  integral_sub_integral_sub_linear_isLittleO_of_tendsto_ae_right hf hmeas hb continuousAt_snd
-    continuousAt_fst
-#align interval_integral.integral_has_strict_deriv_at_of_tendsto_ae_right intervalIntegral.integral_hasStrictDerivAt_of_tendsto_ae_right
-
-/-- Fundamental theorem of calculus-1: if `f : ℝ → E` is integrable on `a..b` and `f` is continuous
-at `b`, then `u ↦ ∫ x in a..u, f x` has derivative `f b` at `b` in the sense of strict
-differentiability. -/
-theorem integral_hasStrictDerivAt_right (hf : IntervalIntegrable f volume a b)
-    (hmeas : StronglyMeasurableAtFilter f (𝓝 b)) (hb : ContinuousAt f b) :
-    HasStrictDerivAt (fun u => ∫ x in a..u, f x) (f b) b :=
-  integral_hasStrictDerivAt_of_tendsto_ae_right hf hmeas (hb.mono_left inf_le_left)
-#align interval_integral.integral_has_strict_deriv_at_right intervalIntegral.integral_hasStrictDerivAt_right
-
-/-- Fundamental theorem of calculus-1: if `f : ℝ → E` is integrable on `a..b` and `f x` has a finite
-limit `c` almost surely at `a`, then `u ↦ ∫ x in u..b, f x` has derivative `-c` at `a` in the sense
-of strict differentiability. -/
-theorem integral_hasStrictDerivAt_of_tendsto_ae_left (hf : IntervalIntegrable f volume a b)
-    (hmeas : StronglyMeasurableAtFilter f (𝓝 a)) (ha : Tendsto f (𝓝 a ⊓ volume.ae) (𝓝 c)) :
-    HasStrictDerivAt (fun u => ∫ x in u..b, f x) (-c) a := by
-  simpa only [← integral_symm] using
-    (integral_has_strict_deriv_at_of_tendsto_ae_right hf.symm hmeas ha).neg
-#align interval_integral.integral_has_strict_deriv_at_of_tendsto_ae_left intervalIntegral.integral_hasStrictDerivAt_of_tendsto_ae_left
-
-/-- Fundamental theorem of calculus-1: if `f : ℝ → E` is integrable on `a..b` and `f` is continuous
-at `a`, then `u ↦ ∫ x in u..b, f x` has derivative `-f a` at `a` in the sense of strict
-differentiability. -/
-theorem integral_hasStrictDerivAt_left (hf : IntervalIntegrable f volume a b)
-    (hmeas : StronglyMeasurableAtFilter f (𝓝 a)) (ha : ContinuousAt f a) :
-    HasStrictDerivAt (fun u => ∫ x in u..b, f x) (-f a) a := by
-  simpa only [← integral_symm] using (integral_has_strict_deriv_at_right hf.symm hmeas ha).neg
-#align interval_integral.integral_has_strict_deriv_at_left intervalIntegral.integral_hasStrictDerivAt_left
-
-/-- Fundamental theorem of calculus-1: if `f : ℝ → E` is continuous, then `u ↦ ∫ x in a..u, f x`
-has derivative `f b` at `b` in the sense of strict differentiability. -/
-theorem Continuous.integral_hasStrictDerivAt {f : ℝ → E} (hf : Continuous f) (a b : ℝ) :
-    HasStrictDerivAt (fun u => ∫ x : ℝ in a..u, f x) (f b) b :=
-  integral_hasStrictDerivAt_right (hf.IntervalIntegrable _ _) (hf.StronglyMeasurableAtFilter _ _)
-    hf.ContinuousAt
-#align continuous.integral_has_strict_deriv_at Continuous.integral_hasStrictDerivAt
-
-/-- Fundamental theorem of calculus-1: if `f : ℝ → E` is continuous, then the derivative
-of `u ↦ ∫ x in a..u, f x` at `b` is `f b`. -/
-theorem Continuous.deriv_integral (f : ℝ → E) (hf : Continuous f) (a b : ℝ) :
-    deriv (fun u => ∫ x : ℝ in a..u, f x) b = f b :=
-  (hf.integral_hasStrictDerivAt a b).HasDerivAt.deriv
-#align continuous.deriv_integral Continuous.deriv_integral
-
-/-!
-#### Fréchet differentiability
-
-In this subsection we restate results from the previous subsection in terms of `has_fderiv_at`,
-`has_deriv_at`, `fderiv`, and `deriv`.
--/
-
-
-/-- Fundamental theorem of calculus-1: if `f : ℝ → E` is integrable on `a..b` and `f x` has finite
-limits `ca` and `cb` almost surely as `x` tends to `a` and `b`, respectively, then
-`(u, v) ↦ ∫ x in u..v, f x` has derivative `(u, v) ↦ v • cb - u • ca` at `(a, b)`. -/
-theorem integral_hasFderivAt_of_tendsto_ae (hf : IntervalIntegrable f volume a b)
-    (hmeas_a : StronglyMeasurableAtFilter f (𝓝 a)) (hmeas_b : StronglyMeasurableAtFilter f (𝓝 b))
-    (ha : Tendsto f (𝓝 a ⊓ volume.ae) (𝓝 ca)) (hb : Tendsto f (𝓝 b ⊓ volume.ae) (𝓝 cb)) :
-    HasFderivAt (fun p : ℝ × ℝ => ∫ x in p.1 ..p.2, f x)
-      ((snd ℝ ℝ ℝ).smul_right cb - (fst ℝ ℝ ℝ).smul_right ca) (a, b) :=
-  (integral_hasStrictFderivAt_of_tendsto_ae hf hmeas_a hmeas_b ha hb).HasFderivAt
-#align interval_integral.integral_has_fderiv_at_of_tendsto_ae intervalIntegral.integral_hasFderivAt_of_tendsto_ae
-
-/-- Fundamental theorem of calculus-1: if `f : ℝ → E` is integrable on `a..b` and `f` is continuous
-at `a` and `b`, then `(u, v) ↦ ∫ x in u..v, f x` has derivative `(u, v) ↦ v • cb - u • ca`
-at `(a, b)`. -/
-theorem integral_hasFderivAt (hf : IntervalIntegrable f volume a b)
-    (hmeas_a : StronglyMeasurableAtFilter f (𝓝 a)) (hmeas_b : StronglyMeasurableAtFilter f (𝓝 b))
-    (ha : ContinuousAt f a) (hb : ContinuousAt f b) :
-    HasFderivAt (fun p : ℝ × ℝ => ∫ x in p.1 ..p.2, f x)
-      ((snd ℝ ℝ ℝ).smul_right (f b) - (fst ℝ ℝ ℝ).smul_right (f a)) (a, b) :=
-  (integral_hasStrictFderivAt hf hmeas_a hmeas_b ha hb).HasFderivAt
-#align interval_integral.integral_has_fderiv_at intervalIntegral.integral_hasFderivAt
-
-/-- Fundamental theorem of calculus-1: if `f : ℝ → E` is integrable on `a..b` and `f x` has finite
-limits `ca` and `cb` almost surely as `x` tends to `a` and `b`, respectively, then `fderiv`
-derivative of `(u, v) ↦ ∫ x in u..v, f x` at `(a, b)` equals `(u, v) ↦ v • cb - u • ca`. -/
-theorem fderiv_integral_of_tendsto_ae (hf : IntervalIntegrable f volume a b)
-    (hmeas_a : StronglyMeasurableAtFilter f (𝓝 a)) (hmeas_b : StronglyMeasurableAtFilter f (𝓝 b))
-    (ha : Tendsto f (𝓝 a ⊓ volume.ae) (𝓝 ca)) (hb : Tendsto f (𝓝 b ⊓ volume.ae) (𝓝 cb)) :
-    fderiv ℝ (fun p : ℝ × ℝ => ∫ x in p.1 ..p.2, f x) (a, b) =
-      (snd ℝ ℝ ℝ).smul_right cb - (fst ℝ ℝ ℝ).smul_right ca :=
-  (integral_hasFderivAt_of_tendsto_ae hf hmeas_a hmeas_b ha hb).fderiv
-#align interval_integral.fderiv_integral_of_tendsto_ae intervalIntegral.fderiv_integral_of_tendsto_ae
-
-/-- Fundamental theorem of calculus-1: if `f : ℝ → E` is integrable on `a..b` and `f` is continuous
-at `a` and `b`, then `fderiv` derivative of `(u, v) ↦ ∫ x in u..v, f x` at `(a, b)` equals `(u, v) ↦
-v • cb - u • ca`. -/
-theorem fderiv_integral (hf : IntervalIntegrable f volume a b)
-    (hmeas_a : StronglyMeasurableAtFilter f (𝓝 a)) (hmeas_b : StronglyMeasurableAtFilter f (𝓝 b))
-    (ha : ContinuousAt f a) (hb : ContinuousAt f b) :
-    fderiv ℝ (fun p : ℝ × ℝ => ∫ x in p.1 ..p.2, f x) (a, b) =
-      (snd ℝ ℝ ℝ).smul_right (f b) - (fst ℝ ℝ ℝ).smul_right (f a) :=
-  (integral_hasFderivAt hf hmeas_a hmeas_b ha hb).fderiv
-#align interval_integral.fderiv_integral intervalIntegral.fderiv_integral
-
-/-- Fundamental theorem of calculus-1: if `f : ℝ → E` is integrable on `a..b` and `f x` has a finite
-limit `c` almost surely at `b`, then `u ↦ ∫ x in a..u, f x` has derivative `c` at `b`. -/
-theorem integral_hasDerivAt_of_tendsto_ae_right (hf : IntervalIntegrable f volume a b)
-    (hmeas : StronglyMeasurableAtFilter f (𝓝 b)) (hb : Tendsto f (𝓝 b ⊓ volume.ae) (𝓝 c)) :
-    HasDerivAt (fun u => ∫ x in a..u, f x) c b :=
-  (integral_hasStrictDerivAt_of_tendsto_ae_right hf hmeas hb).HasDerivAt
-#align interval_integral.integral_has_deriv_at_of_tendsto_ae_right intervalIntegral.integral_hasDerivAt_of_tendsto_ae_right
-
-/-- Fundamental theorem of calculus-1: if `f : ℝ → E` is integrable on `a..b` and `f` is continuous
-at `b`, then `u ↦ ∫ x in a..u, f x` has derivative `f b` at `b`. -/
-theorem integral_hasDerivAt_right (hf : IntervalIntegrable f volume a b)
-    (hmeas : StronglyMeasurableAtFilter f (𝓝 b)) (hb : ContinuousAt f b) :
-    HasDerivAt (fun u => ∫ x in a..u, f x) (f b) b :=
-  (integral_hasStrictDerivAt_right hf hmeas hb).HasDerivAt
-#align interval_integral.integral_has_deriv_at_right intervalIntegral.integral_hasDerivAt_right
-
-/-- Fundamental theorem of calculus: if `f : ℝ → E` is integrable on `a..b` and `f` has a finite
-limit `c` almost surely at `b`, then the derivative of `u ↦ ∫ x in a..u, f x` at `b` equals `c`. -/
-theorem deriv_integral_of_tendsto_ae_right (hf : IntervalIntegrable f volume a b)
-    (hmeas : StronglyMeasurableAtFilter f (𝓝 b)) (hb : Tendsto f (𝓝 b ⊓ volume.ae) (𝓝 c)) :
-    deriv (fun u => ∫ x in a..u, f x) b = c :=
-  (integral_hasDerivAt_of_tendsto_ae_right hf hmeas hb).deriv
-#align interval_integral.deriv_integral_of_tendsto_ae_right intervalIntegral.deriv_integral_of_tendsto_ae_right
-
-/-- Fundamental theorem of calculus: if `f : ℝ → E` is integrable on `a..b` and `f` is continuous
-at `b`, then the derivative of `u ↦ ∫ x in a..u, f x` at `b` equals `f b`. -/
-theorem deriv_integral_right (hf : IntervalIntegrable f volume a b)
-    (hmeas : StronglyMeasurableAtFilter f (𝓝 b)) (hb : ContinuousAt f b) :
-    deriv (fun u => ∫ x in a..u, f x) b = f b :=
-  (integral_hasDerivAt_right hf hmeas hb).deriv
-#align interval_integral.deriv_integral_right intervalIntegral.deriv_integral_right
-
-/-- Fundamental theorem of calculus-1: if `f : ℝ → E` is integrable on `a..b` and `f x` has a finite
-limit `c` almost surely at `a`, then `u ↦ ∫ x in u..b, f x` has derivative `-c` at `a`. -/
-theorem integral_hasDerivAt_of_tendsto_ae_left (hf : IntervalIntegrable f volume a b)
-    (hmeas : StronglyMeasurableAtFilter f (𝓝 a)) (ha : Tendsto f (𝓝 a ⊓ volume.ae) (𝓝 c)) :
-    HasDerivAt (fun u => ∫ x in u..b, f x) (-c) a :=
-  (integral_hasStrictDerivAt_of_tendsto_ae_left hf hmeas ha).HasDerivAt
-#align interval_integral.integral_has_deriv_at_of_tendsto_ae_left intervalIntegral.integral_hasDerivAt_of_tendsto_ae_left
-
-/-- Fundamental theorem of calculus-1: if `f : ℝ → E` is integrable on `a..b` and `f` is continuous
-at `a`, then `u ↦ ∫ x in u..b, f x` has derivative `-f a` at `a`. -/
-theorem integral_hasDerivAt_left (hf : IntervalIntegrable f volume a b)
-    (hmeas : StronglyMeasurableAtFilter f (𝓝 a)) (ha : ContinuousAt f a) :
-    HasDerivAt (fun u => ∫ x in u..b, f x) (-f a) a :=
-  (integral_hasStrictDerivAt_left hf hmeas ha).HasDerivAt
-#align interval_integral.integral_has_deriv_at_left intervalIntegral.integral_hasDerivAt_left
-
-/-- Fundamental theorem of calculus: if `f : ℝ → E` is integrable on `a..b` and `f` has a finite
-limit `c` almost surely at `a`, then the derivative of `u ↦ ∫ x in u..b, f x` at `a` equals `-c`. -/
-theorem deriv_integral_of_tendsto_ae_left (hf : IntervalIntegrable f volume a b)
-    (hmeas : StronglyMeasurableAtFilter f (𝓝 a)) (hb : Tendsto f (𝓝 a ⊓ volume.ae) (𝓝 c)) :
-    deriv (fun u => ∫ x in u..b, f x) a = -c :=
-  (integral_hasDerivAt_of_tendsto_ae_left hf hmeas hb).deriv
-#align interval_integral.deriv_integral_of_tendsto_ae_left intervalIntegral.deriv_integral_of_tendsto_ae_left
-
-/-- Fundamental theorem of calculus: if `f : ℝ → E` is integrable on `a..b` and `f` is continuous
-at `a`, then the derivative of `u ↦ ∫ x in u..b, f x` at `a` equals `-f a`. -/
-theorem deriv_integral_left (hf : IntervalIntegrable f volume a b)
-    (hmeas : StronglyMeasurableAtFilter f (𝓝 a)) (hb : ContinuousAt f a) :
-    deriv (fun u => ∫ x in u..b, f x) a = -f a :=
-  (integral_hasDerivAt_left hf hmeas hb).deriv
-#align interval_integral.deriv_integral_left intervalIntegral.deriv_integral_left
-
-/-!
-#### One-sided derivatives
--/
-
-
-/- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
-/-- Let `f` be a measurable function integrable on `a..b`. The function `(u, v) ↦ ∫ x in u..v, f x`
-has derivative `(u, v) ↦ v • cb - u • ca` within `s × t` at `(a, b)`, where
-`s ∈ {Iic a, {a}, Ici a, univ}` and `t ∈ {Iic b, {b}, Ici b, univ}` provided that `f` tends to `ca`
-and `cb` almost surely at the filters `la` and `lb` from the following table.
-
-| `s`     | `la`     | `t`     | `lb`     |
-| ------- | ----     | ---     | ----     |
-| `Iic a` | `𝓝[≤] a` | `Iic b` | `𝓝[≤] b` |
-| `Ici a` | `𝓝[>] a` | `Ici b` | `𝓝[>] b` |
-| `{a}`   | `⊥`      | `{b}`   | `⊥`      |
-| `univ`  | `𝓝 a`    | `univ`  | `𝓝 b`    |
--/
-theorem integral_hasFderivWithinAt_of_tendsto_ae (hf : IntervalIntegrable f volume a b)
-    {s t : Set ℝ} [FTCFilter a (𝓝[s] a) la] [FTCFilter b (𝓝[t] b) lb]
-    (hmeas_a : StronglyMeasurableAtFilter f la) (hmeas_b : StronglyMeasurableAtFilter f lb)
-    (ha : Tendsto f (la ⊓ volume.ae) (𝓝 ca)) (hb : Tendsto f (lb ⊓ volume.ae) (𝓝 cb)) :
-    HasFderivWithinAt (fun p : ℝ × ℝ => ∫ x in p.1 ..p.2, f x)
-      ((snd ℝ ℝ ℝ).smul_right cb - (fst ℝ ℝ ℝ).smul_right ca) (s ×ˢ t) (a, b) :=
-  by
-  rw [HasFderivWithinAt, nhdsWithin_prod_eq]
-  have :=
-    integral_sub_integral_sub_linear_is_o_of_tendsto_ae hf hmeas_a hmeas_b ha hb
-      (tendsto_const_pure.mono_right FTC_filter.pure_le : tendsto _ _ (𝓝[s] a)) tendsto_fst
-      (tendsto_const_pure.mono_right FTC_filter.pure_le : tendsto _ _ (𝓝[t] b)) tendsto_snd
-  refine' (this.congr_left _).trans_isBigO _
-  · intro x
-    simp [sub_smul]
-  · exact is_O_fst_prod.norm_left.add is_O_snd_prod.norm_left
-#align interval_integral.integral_has_fderiv_within_at_of_tendsto_ae intervalIntegral.integral_hasFderivWithinAt_of_tendsto_ae
-
-/- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
-/-- Let `f` be a measurable function integrable on `a..b`. The function `(u, v) ↦ ∫ x in u..v, f x`
-has derivative `(u, v) ↦ v • f b - u • f a` within `s × t` at `(a, b)`, where
-`s ∈ {Iic a, {a}, Ici a, univ}` and `t ∈ {Iic b, {b}, Ici b, univ}` provided that `f` tends to
-`f a` and `f b` at the filters `la` and `lb` from the following table. In most cases this assumption
-is definitionally equal `continuous_at f _` or `continuous_within_at f _ _`.
-
-| `s`     | `la`     | `t`     | `lb`     |
-| ------- | ----     | ---     | ----     |
-| `Iic a` | `𝓝[≤] a` | `Iic b` | `𝓝[≤] b` |
-| `Ici a` | `𝓝[>] a` | `Ici b` | `𝓝[>] b` |
-| `{a}`   | `⊥`      | `{b}`   | `⊥`      |
-| `univ`  | `𝓝 a`    | `univ`  | `𝓝 b`    |
--/
-theorem integral_hasFderivWithinAt (hf : IntervalIntegrable f volume a b)
-    (hmeas_a : StronglyMeasurableAtFilter f la) (hmeas_b : StronglyMeasurableAtFilter f lb)
-    {s t : Set ℝ} [FTCFilter a (𝓝[s] a) la] [FTCFilter b (𝓝[t] b) lb] (ha : Tendsto f la (𝓝 <| f a))
-    (hb : Tendsto f lb (𝓝 <| f b)) :
-    HasFderivWithinAt (fun p : ℝ × ℝ => ∫ x in p.1 ..p.2, f x)
-      ((snd ℝ ℝ ℝ).smul_right (f b) - (fst ℝ ℝ ℝ).smul_right (f a)) (s ×ˢ t) (a, b) :=
-  integral_hasFderivWithinAt_of_tendsto_ae hf hmeas_a hmeas_b (ha.mono_left inf_le_left)
-    (hb.mono_left inf_le_left)
-#align interval_integral.integral_has_fderiv_within_at intervalIntegral.integral_hasFderivWithinAt
-
-/- ./././Mathport/Syntax/Translate/Expr.lean:330:4: warning: unsupported (TODO): `[tacs] -/
-/-- An auxiliary tactic closing goals `unique_diff_within_at ℝ s a` where
-`s ∈ {Iic a, Ici a, univ}`. -/
-unsafe def unique_diff_within_at_Ici_Iic_univ : tactic Unit :=
-  sorry
-#align interval_integral.unique_diff_within_at_Ici_Iic_univ interval_integral.unique_diff_within_at_Ici_Iic_univ
-
-/- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
-/-- Let `f` be a measurable function integrable on `a..b`. Choose `s ∈ {Iic a, Ici a, univ}`
-and `t ∈ {Iic b, Ici b, univ}`. Suppose that `f` tends to `ca` and `cb` almost surely at the filters
-`la` and `lb` from the table below. Then `fderiv_within ℝ (λ p, ∫ x in p.1..p.2, f x) (s ×ˢ t)`
-is equal to `(u, v) ↦ u • cb - v • ca`.
-
-| `s`     | `la`     | `t`     | `lb`     |
-| ------- | ----     | ---     | ----     |
-| `Iic a` | `𝓝[≤] a` | `Iic b` | `𝓝[≤] b` |
-| `Ici a` | `𝓝[>] a` | `Ici b` | `𝓝[>] b` |
-| `{a}`   | `⊥`      | `{b}`   | `⊥`      |
-| `univ`  | `𝓝 a`    | `univ`  | `𝓝 b`    |
--/
-theorem fderivWithin_integral_of_tendsto_ae (hf : IntervalIntegrable f volume a b)
-    (hmeas_a : StronglyMeasurableAtFilter f la) (hmeas_b : StronglyMeasurableAtFilter f lb)
-    {s t : Set ℝ} [FTCFilter a (𝓝[s] a) la] [FTCFilter b (𝓝[t] b) lb]
-    (ha : Tendsto f (la ⊓ volume.ae) (𝓝 ca)) (hb : Tendsto f (lb ⊓ volume.ae) (𝓝 cb))
-    (hs : UniqueDiffWithinAt ℝ s a := by uniqueDiffWithinAt_Ici_Iic_univ)
-    (ht : UniqueDiffWithinAt ℝ t b := by uniqueDiffWithinAt_Ici_Iic_univ) :
-    fderivWithin ℝ (fun p : ℝ × ℝ => ∫ x in p.1 ..p.2, f x) (s ×ˢ t) (a, b) =
-      (snd ℝ ℝ ℝ).smul_right cb - (fst ℝ ℝ ℝ).smul_right ca :=
-  (integral_hasFderivWithinAt_of_tendsto_ae hf hmeas_a hmeas_b ha hb).fderivWithin <| hs.Prod ht
-#align interval_integral.fderiv_within_integral_of_tendsto_ae intervalIntegral.fderivWithin_integral_of_tendsto_ae
-
-/-- Fundamental theorem of calculus: if `f : ℝ → E` is integrable on `a..b` and `f x` has a finite
-limit `c` almost surely as `x` tends to `b` from the right or from the left,
-then `u ↦ ∫ x in a..u, f x` has right (resp., left) derivative `c` at `b`. -/
-theorem integral_hasDerivWithinAt_of_tendsto_ae_right (hf : IntervalIntegrable f volume a b)
-    {s t : Set ℝ} [FTCFilter b (𝓝[s] b) (𝓝[t] b)] (hmeas : StronglyMeasurableAtFilter f (𝓝[t] b))
-    (hb : Tendsto f (𝓝[t] b ⊓ volume.ae) (𝓝 c)) :
-    HasDerivWithinAt (fun u => ∫ x in a..u, f x) c s b :=
-  integral_sub_integral_sub_linear_isLittleO_of_tendsto_ae_right hf hmeas hb
-    (tendsto_const_pure.mono_right FTCFilter.pure_le) tendsto_id
-#align interval_integral.integral_has_deriv_within_at_of_tendsto_ae_right intervalIntegral.integral_hasDerivWithinAt_of_tendsto_ae_right
-
-/-- Fundamental theorem of calculus: if `f : ℝ → E` is integrable on `a..b` and `f x` is continuous
-from the left or from the right at `b`, then `u ↦ ∫ x in a..u, f x` has left (resp., right)
-derivative `f b` at `b`. -/
-theorem integral_hasDerivWithinAt_right (hf : IntervalIntegrable f volume a b) {s t : Set ℝ}
-    [FTCFilter b (𝓝[s] b) (𝓝[t] b)] (hmeas : StronglyMeasurableAtFilter f (𝓝[t] b))
-    (hb : ContinuousWithinAt f t b) : HasDerivWithinAt (fun u => ∫ x in a..u, f x) (f b) s b :=
-  integral_hasDerivWithinAt_of_tendsto_ae_right hf hmeas (hb.mono_left inf_le_left)
-#align interval_integral.integral_has_deriv_within_at_right intervalIntegral.integral_hasDerivWithinAt_right
-
-/-- Fundamental theorem of calculus: if `f : ℝ → E` is integrable on `a..b` and `f x` has a finite
-limit `c` almost surely as `x` tends to `b` from the right or from the left, then the right
-(resp., left) derivative of `u ↦ ∫ x in a..u, f x` at `b` equals `c`. -/
-theorem derivWithin_integral_of_tendsto_ae_right (hf : IntervalIntegrable f volume a b)
-    {s t : Set ℝ} [FTCFilter b (𝓝[s] b) (𝓝[t] b)] (hmeas : StronglyMeasurableAtFilter f (𝓝[t] b))
-    (hb : Tendsto f (𝓝[t] b ⊓ volume.ae) (𝓝 c))
-    (hs : UniqueDiffWithinAt ℝ s b := by uniqueDiffWithinAt_Ici_Iic_univ) :
-    derivWithin (fun u => ∫ x in a..u, f x) s b = c :=
-  (integral_hasDerivWithinAt_of_tendsto_ae_right hf hmeas hb).derivWithin hs
-#align interval_integral.deriv_within_integral_of_tendsto_ae_right intervalIntegral.derivWithin_integral_of_tendsto_ae_right
-
-/-- Fundamental theorem of calculus: if `f : ℝ → E` is integrable on `a..b` and `f x` is continuous
-on the right or on the left at `b`, then the right (resp., left) derivative of
-`u ↦ ∫ x in a..u, f x` at `b` equals `f b`. -/
-theorem derivWithin_integral_right (hf : IntervalIntegrable f volume a b) {s t : Set ℝ}
-    [FTCFilter b (𝓝[s] b) (𝓝[t] b)] (hmeas : StronglyMeasurableAtFilter f (𝓝[t] b))
-    (hb : ContinuousWithinAt f t b)
-    (hs : UniqueDiffWithinAt ℝ s b := by uniqueDiffWithinAt_Ici_Iic_univ) :
-    derivWithin (fun u => ∫ x in a..u, f x) s b = f b :=
-  (integral_hasDerivWithinAt_right hf hmeas hb).derivWithin hs
-#align interval_integral.deriv_within_integral_right intervalIntegral.derivWithin_integral_right
-
-/-- Fundamental theorem of calculus: if `f : ℝ → E` is integrable on `a..b` and `f x` has a finite
-limit `c` almost surely as `x` tends to `a` from the right or from the left,
-then `u ↦ ∫ x in u..b, f x` has right (resp., left) derivative `-c` at `a`. -/
-theorem integral_hasDerivWithinAt_of_tendsto_ae_left (hf : IntervalIntegrable f volume a b)
-    {s t : Set ℝ} [FTCFilter a (𝓝[s] a) (𝓝[t] a)] (hmeas : StronglyMeasurableAtFilter f (𝓝[t] a))
-    (ha : Tendsto f (𝓝[t] a ⊓ volume.ae) (𝓝 c)) :
-    HasDerivWithinAt (fun u => ∫ x in u..b, f x) (-c) s a :=
-  by
-  simp only [integral_symm b]
-  exact (integral_has_deriv_within_at_of_tendsto_ae_right hf.symm hmeas ha).neg
-#align interval_integral.integral_has_deriv_within_at_of_tendsto_ae_left intervalIntegral.integral_hasDerivWithinAt_of_tendsto_ae_left
-
-/-- Fundamental theorem of calculus: if `f : ℝ → E` is integrable on `a..b` and `f x` is continuous
-from the left or from the right at `a`, then `u ↦ ∫ x in u..b, f x` has left (resp., right)
-derivative `-f a` at `a`. -/
-theorem integral_hasDerivWithinAt_left (hf : IntervalIntegrable f volume a b) {s t : Set ℝ}
-    [FTCFilter a (𝓝[s] a) (𝓝[t] a)] (hmeas : StronglyMeasurableAtFilter f (𝓝[t] a))
-    (ha : ContinuousWithinAt f t a) : HasDerivWithinAt (fun u => ∫ x in u..b, f x) (-f a) s a :=
-  integral_hasDerivWithinAt_of_tendsto_ae_left hf hmeas (ha.mono_left inf_le_left)
-#align interval_integral.integral_has_deriv_within_at_left intervalIntegral.integral_hasDerivWithinAt_left
-
-/-- Fundamental theorem of calculus: if `f : ℝ → E` is integrable on `a..b` and `f x` has a finite
-limit `c` almost surely as `x` tends to `a` from the right or from the left, then the right
-(resp., left) derivative of `u ↦ ∫ x in u..b, f x` at `a` equals `-c`. -/
-theorem derivWithin_integral_of_tendsto_ae_left (hf : IntervalIntegrable f volume a b) {s t : Set ℝ}
-    [FTCFilter a (𝓝[s] a) (𝓝[t] a)] (hmeas : StronglyMeasurableAtFilter f (𝓝[t] a))
-    (ha : Tendsto f (𝓝[t] a ⊓ volume.ae) (𝓝 c))
-    (hs : UniqueDiffWithinAt ℝ s a := by uniqueDiffWithinAt_Ici_Iic_univ) :
-    derivWithin (fun u => ∫ x in u..b, f x) s a = -c :=
-  (integral_hasDerivWithinAt_of_tendsto_ae_left hf hmeas ha).derivWithin hs
-#align interval_integral.deriv_within_integral_of_tendsto_ae_left intervalIntegral.derivWithin_integral_of_tendsto_ae_left
-
-/-- Fundamental theorem of calculus: if `f : ℝ → E` is integrable on `a..b` and `f x` is continuous
-on the right or on the left at `a`, then the right (resp., left) derivative of
-`u ↦ ∫ x in u..b, f x` at `a` equals `-f a`. -/
-theorem derivWithin_integral_left (hf : IntervalIntegrable f volume a b) {s t : Set ℝ}
-    [FTCFilter a (𝓝[s] a) (𝓝[t] a)] (hmeas : StronglyMeasurableAtFilter f (𝓝[t] a))
-    (ha : ContinuousWithinAt f t a)
-    (hs : UniqueDiffWithinAt ℝ s a := by uniqueDiffWithinAt_Ici_Iic_univ) :
-    derivWithin (fun u => ∫ x in u..b, f x) s a = -f a :=
-  (integral_hasDerivWithinAt_left hf hmeas ha).derivWithin hs
-#align interval_integral.deriv_within_integral_left intervalIntegral.derivWithin_integral_left
-
-/-- The integral of a continuous function is differentiable on a real set `s`. -/
-theorem differentiableOn_integral_of_continuous {s : Set ℝ}
-    (hintg : ∀ x ∈ s, IntervalIntegrable f volume a x) (hcont : Continuous f) :
-    DifferentiableOn ℝ (fun u => ∫ x in a..u, f x) s := fun y hy =>
-  (integral_hasDerivAt_right (hintg y hy) hcont.AeStronglyMeasurable.StronglyMeasurableAtFilter
-        hcont.ContinuousAt).DifferentiableAt.DifferentiableWithinAt
-#align interval_integral.differentiable_on_integral_of_continuous intervalIntegral.differentiableOn_integral_of_continuous
-
-/-!
-### Fundamental theorem of calculus, part 2
-
-This section contains theorems pertaining to FTC-2 for interval integrals, i.e., the assertion
-that `∫ x in a..b, f' x = f b - f a` under suitable assumptions.
-
-The most classical version of this theorem assumes that `f'` is continuous. However, this is
-unnecessarily strong: the result holds if `f'` is just integrable. We prove the strong version,
-following [Rudin, *Real and Complex Analysis* (Theorem 7.21)][rudin2006real]. The proof is first
-given for real-valued functions, and then deduced for functions with a general target space. For
-a real-valued function `g`, it suffices to show that `g b - g a ≤ (∫ x in a..b, g' x) + ε` for all
-positive `ε`. To prove this, choose a lower-semicontinuous function `G'` with `g' < G'` and with
-integral close to that of `g'` (its existence is guaranteed by the Vitali-Carathéodory theorem).
-It satisfies `g t - g a ≤ ∫ x in a..t, G' x` for all `t ∈ [a, b]`: this inequality holds at `a`,
-and if it holds at `t` then it holds for `u` close to `t` on its right, as the left hand side
-increases by `g u - g t ∼ (u -t) g' t`, while the right hand side increases by
-`∫ x in t..u, G' x` which is roughly at least `∫ x in t..u, G' t = (u - t) G' t`, by lower
-semicontinuity. As  `g' t < G' t`, this gives the conclusion. One can therefore push progressively
-this inequality to the right until the point `b`, where it gives the desired conclusion.
--/
-
-
-variable {g' g φ : ℝ → ℝ}
-
-/-- Hard part of FTC-2 for integrable derivatives, real-valued functions: one has
-`g b - g a ≤ ∫ y in a..b, g' y` when `g'` is integrable.
-Auxiliary lemma in the proof of `integral_eq_sub_of_has_deriv_right_of_le`.
-We give the slightly more general version that `g b - g a ≤ ∫ y in a..b, φ y` when `g' ≤ φ` and
-`φ` is integrable (even if `g'` is not known to be integrable).
-Version assuming that `g` is differentiable on `[a, b)`. -/
-theorem sub_le_integral_of_has_deriv_right_of_le_Ico (hab : a ≤ b)
-    (hcont : ContinuousOn g (Icc a b)) (hderiv : ∀ x ∈ Ico a b, HasDerivWithinAt g (g' x) (Ioi x) x)
-    (φint : IntegrableOn φ (Icc a b)) (hφg : ∀ x ∈ Ico a b, g' x ≤ φ x) :
-    g b - g a ≤ ∫ y in a..b, φ y :=
-  by
-  refine' le_of_forall_pos_le_add fun ε εpos => _
-  -- Bound from above `g'` by a lower-semicontinuous function `G'`.
-  rcases exists_lt_lower_semicontinuous_integral_lt φ φint εpos with
-    ⟨G', f_lt_G', G'cont, G'int, G'lt_top, hG'⟩
-  -- we will show by "induction" that `g t - g a ≤ ∫ u in a..t, G' u` for all `t ∈ [a, b]`.
-  set s := { t | g t - g a ≤ ∫ u in a..t, (G' u).toReal } ∩ Icc a b
-  -- the set `s` of points where this property holds is closed.
-  have s_closed : IsClosed s :=
-    by
-    have : ContinuousOn (fun t => (g t - g a, ∫ u in a..t, (G' u).toReal)) (Icc a b) :=
-      by
-      rw [← uIcc_of_le hab] at G'int hcont⊢
-      exact (hcont.sub continuousOn_const).Prod (continuous_on_primitive_interval G'int)
-    simp only [s, inter_comm]
-    exact this.preimage_closed_of_closed isClosed_Icc OrderClosedTopology.isClosed_le'
-  have main : Icc a b ⊆ { t | g t - g a ≤ ∫ u in a..t, (G' u).toReal } :=
-    by
-    -- to show that the set `s` is all `[a, b]`, it suffices to show that any point `t` in `s`
-    -- with `t < b` admits another point in `s` slightly to its right
-    -- (this is a sort of real induction).
-    apply
-      s_closed.Icc_subset_of_forall_exists_gt
-        (by simp only [integral_same, mem_set_of_eq, sub_self]) fun t ht v t_lt_v => _
-    obtain ⟨y, g'_lt_y', y_lt_G'⟩ : ∃ y : ℝ, (g' t : EReal) < y ∧ (y : EReal) < G' t :=
-      EReal.lt_iff_exists_real_btwn.1 ((EReal.coe_le_coe_iff.2 (hφg t ht.2)).trans_lt (f_lt_G' t))
-    -- bound from below the increase of `∫ x in a..u, G' x` on the right of `t`, using the lower
-    -- semicontinuity of `G'`.
-    have I1 : ∀ᶠ u in 𝓝[>] t, (u - t) * y ≤ ∫ w in t..u, (G' w).toReal :=
-      by
-      have B : ∀ᶠ u in 𝓝 t, (y : EReal) < G' u := G'cont.lower_semicontinuous_at _ _ y_lt_G'
-      rcases mem_nhds_iff_exists_Ioo_subset.1 B with ⟨m, M, ⟨hm, hM⟩, H⟩
-      have : Ioo t (min M b) ∈ 𝓝[>] t :=
-        mem_nhdsWithin_Ioi_iff_exists_Ioo_subset.2
-          ⟨min M b, by simp only [hM, ht.right.right, lt_min_iff, mem_Ioi, and_self_iff],
-            subset.refl _⟩
-      filter_upwards [this]with u hu
-      have I : Icc t u ⊆ Icc a b := Icc_subset_Icc ht.2.1 (hu.2.le.trans (min_le_right _ _))
-      calc
-        (u - t) * y = ∫ v in Icc t u, y := by
-          simp only [hu.left.le, MeasureTheory.integral_const, Algebra.id.smul_eq_mul, sub_nonneg,
-            MeasurableSet.univ, Real.volume_Icc, measure.restrict_apply, univ_inter,
-            ENNReal.toReal_ofReal]
-        _ ≤ ∫ w in t..u, (G' w).toReal :=
-          by
-          rw [intervalIntegral.integral_of_le hu.1.le, ← integral_Icc_eq_integral_Ioc]
-          apply set_integral_mono_ae_restrict
-          · simp only [integrable_on_const, Real.volume_Icc, ENNReal.ofReal_lt_top, or_true_iff]
-          · exact integrable_on.mono_set G'int I
-          · have C1 : ∀ᵐ x : ℝ ∂volume.restrict (Icc t u), G' x < ∞ :=
-              ae_mono (measure.restrict_mono I le_rfl) G'lt_top
-            have C2 : ∀ᵐ x : ℝ ∂volume.restrict (Icc t u), x ∈ Icc t u :=
-              ae_restrict_mem measurableSet_Icc
-            filter_upwards [C1, C2]with x G'x hx
-            apply EReal.coe_le_coe_iff.1
-            have : x ∈ Ioo m M := by
-              simp only [hm.trans_le hx.left,
-                (hx.right.trans_lt hu.right).trans_le (min_le_left M b), mem_Ioo, and_self_iff]
-            convert le_of_lt (H this)
-            exact EReal.coe_toReal G'x.ne (ne_bot_of_gt (f_lt_G' x))
-        
-    -- bound from above the increase of `g u - g a` on the right of `t`, using the derivative at `t`
-    have I2 : ∀ᶠ u in 𝓝[>] t, g u - g t ≤ (u - t) * y :=
-      by
-      have g'_lt_y : g' t < y := EReal.coe_lt_coe_iff.1 g'_lt_y'
-      filter_upwards [(hderiv t ⟨ht.2.1, ht.2.2⟩).limsup_slope_le' (not_mem_Ioi.2 le_rfl) g'_lt_y,
-        self_mem_nhdsWithin]with u hu t_lt_u
-      have := mul_le_mul_of_nonneg_left hu.le (sub_pos.2 t_lt_u).le
-      rwa [← smul_eq_mul, sub_smul_slope] at this
-    -- combine the previous two bounds to show that `g u - g a` increases less quickly than
-    -- `∫ x in a..u, G' x`.
-    have I3 : ∀ᶠ u in 𝓝[>] t, g u - g t ≤ ∫ w in t..u, (G' w).toReal := by
-      filter_upwards [I1, I2]with u hu1 hu2 using hu2.trans hu1
-    have I4 : ∀ᶠ u in 𝓝[>] t, u ∈ Ioc t (min v b) :=
-      by
-      refine' mem_nhdsWithin_Ioi_iff_exists_Ioc_subset.2 ⟨min v b, _, subset.refl _⟩
-      simp only [lt_min_iff, mem_Ioi]
-      exact ⟨t_lt_v, ht.2.2⟩
-    -- choose a point `x` slightly to the right of `t` which satisfies the above bound
-    rcases(I3.and I4).exists with ⟨x, hx, h'x⟩
-    -- we check that it belongs to `s`, essentially by construction
-    refine' ⟨x, _, Ioc_subset_Ioc le_rfl (min_le_left _ _) h'x⟩
-    calc
-      g x - g a = g t - g a + (g x - g t) := by abel
-      _ ≤ (∫ w in a..t, (G' w).toReal) + ∫ w in t..x, (G' w).toReal := (add_le_add ht.1 hx)
-      _ = ∫ w in a..x, (G' w).toReal :=
-        by
-        apply integral_add_adjacent_intervals
-        · rw [intervalIntegrable_iff_integrable_Ioc_of_le ht.2.1]
-          exact
-            integrable_on.mono_set G'int
-              (Ioc_subset_Icc_self.trans (Icc_subset_Icc le_rfl ht.2.2.le))
-        · rw [intervalIntegrable_iff_integrable_Ioc_of_le h'x.1.le]
-          apply integrable_on.mono_set G'int
-          refine' Ioc_subset_Icc_self.trans (Icc_subset_Icc ht.2.1 (h'x.2.trans (min_le_right _ _)))
-      
-  -- now that we know that `s` contains `[a, b]`, we get the desired result by applying this to `b`.
-  calc
-    g b - g a ≤ ∫ y in a..b, (G' y).toReal := main (right_mem_Icc.2 hab)
-    _ ≤ (∫ y in a..b, φ y) + ε := by
-      convert hG'.le <;>
-        · rw [intervalIntegral.integral_of_le hab]
-          simp only [integral_Icc_eq_integral_Ioc', Real.volume_singleton]
-    
-#align interval_integral.sub_le_integral_of_has_deriv_right_of_le_Ico intervalIntegral.sub_le_integral_of_has_deriv_right_of_le_Ico
-
-/-- Hard part of FTC-2 for integrable derivatives, real-valued functions: one has
-`g b - g a ≤ ∫ y in a..b, g' y` when `g'` is integrable.
-Auxiliary lemma in the proof of `integral_eq_sub_of_has_deriv_right_of_le`.
-We give the slightly more general version that `g b - g a ≤ ∫ y in a..b, φ y` when `g' ≤ φ` and
-`φ` is integrable (even if `g'` is not known to be integrable).
-Version assuming that `g` is differentiable on `(a, b)`. -/
-theorem sub_le_integral_of_has_deriv_right_of_le (hab : a ≤ b) (hcont : ContinuousOn g (Icc a b))
-    (hderiv : ∀ x ∈ Ioo a b, HasDerivWithinAt g (g' x) (Ioi x) x) (φint : IntegrableOn φ (Icc a b))
-    (hφg : ∀ x ∈ Ioo a b, g' x ≤ φ x) : g b - g a ≤ ∫ y in a..b, φ y :=
-  by
-  -- This follows from the version on a closed-open interval (applied to `[t, b)` for `t` close to
-  -- `a`) and a continuity argument.
-  obtain rfl | a_lt_b := hab.eq_or_lt
-  · simp
-  set s := { t | g b - g t ≤ ∫ u in t..b, φ u } ∩ Icc a b
-  have s_closed : IsClosed s :=
-    by
-    have : ContinuousOn (fun t => (g b - g t, ∫ u in t..b, φ u)) (Icc a b) :=
-      by
-      rw [← uIcc_of_le hab] at hcont φint⊢
-      exact (continuous_on_const.sub hcont).Prod (continuous_on_primitive_interval_left φint)
-    simp only [s, inter_comm]
-    exact this.preimage_closed_of_closed isClosed_Icc isClosed_le_prod
-  have A : closure (Ioc a b) ⊆ s :=
-    by
-    apply s_closed.closure_subset_iff.2
-    intro t ht
-    refine' ⟨_, ⟨ht.1.le, ht.2⟩⟩
-    exact
-      sub_le_integral_of_has_deriv_right_of_le_Ico ht.2 (hcont.mono (Icc_subset_Icc ht.1.le le_rfl))
-        (fun x hx => hderiv x ⟨ht.1.trans_le hx.1, hx.2⟩)
-        (φint.mono_set (Icc_subset_Icc ht.1.le le_rfl)) fun x hx => hφg x ⟨ht.1.trans_le hx.1, hx.2⟩
-  rw [closure_Ioc a_lt_b.ne] at A
-  exact (A (left_mem_Icc.2 hab)).1
-#align interval_integral.sub_le_integral_of_has_deriv_right_of_le intervalIntegral.sub_le_integral_of_has_deriv_right_of_le
-
-/-- Auxiliary lemma in the proof of `integral_eq_sub_of_has_deriv_right_of_le`. -/
-theorem integral_le_sub_of_has_deriv_right_of_le (hab : a ≤ b) (hcont : ContinuousOn g (Icc a b))
-    (hderiv : ∀ x ∈ Ioo a b, HasDerivWithinAt g (g' x) (Ioi x) x) (φint : IntegrableOn φ (Icc a b))
-    (hφg : ∀ x ∈ Ioo a b, φ x ≤ g' x) : (∫ y in a..b, φ y) ≤ g b - g a :=
-  by
-  rw [← neg_le_neg_iff]
-  convert sub_le_integral_of_has_deriv_right_of_le hab hcont.neg (fun x hx => (hderiv x hx).neg)
-      φint.neg fun x hx => neg_le_neg (hφg x hx)
-  · abel
-  · simp only [← integral_neg]
-    rfl
-#align interval_integral.integral_le_sub_of_has_deriv_right_of_le intervalIntegral.integral_le_sub_of_has_deriv_right_of_le
-
-/-- Auxiliary lemma in the proof of `integral_eq_sub_of_has_deriv_right_of_le`: real version -/
-theorem integral_eq_sub_of_has_deriv_right_of_le_real (hab : a ≤ b)
-    (hcont : ContinuousOn g (Icc a b)) (hderiv : ∀ x ∈ Ioo a b, HasDerivWithinAt g (g' x) (Ioi x) x)
-    (g'int : IntegrableOn g' (Icc a b)) : (∫ y in a..b, g' y) = g b - g a :=
-  le_antisymm (integral_le_sub_of_has_deriv_right_of_le hab hcont hderiv g'int fun x hx => le_rfl)
-    (sub_le_integral_of_has_deriv_right_of_le hab hcont hderiv g'int fun x hx => le_rfl)
-#align interval_integral.integral_eq_sub_of_has_deriv_right_of_le_real intervalIntegral.integral_eq_sub_of_has_deriv_right_of_le_real
-
-variable {f' : ℝ → E}
-
-/-- **Fundamental theorem of calculus-2**: If `f : ℝ → E` is continuous on `[a, b]` (where `a ≤ b`)
-  and has a right derivative at `f' x` for all `x` in `(a, b)`, and `f'` is integrable on `[a, b]`,
-  then `∫ y in a..b, f' y` equals `f b - f a`. -/
-theorem integral_eq_sub_of_has_deriv_right_of_le (hab : a ≤ b) (hcont : ContinuousOn f (Icc a b))
-    (hderiv : ∀ x ∈ Ioo a b, HasDerivWithinAt f (f' x) (Ioi x) x)
-    (f'int : IntervalIntegrable f' volume a b) : (∫ y in a..b, f' y) = f b - f a :=
-  by
-  refine' (NormedSpace.eq_iff_forall_dual_eq ℝ).2 fun g => _
-  rw [← g.interval_integral_comp_comm f'int, g.map_sub]
-  exact
-    integral_eq_sub_of_has_deriv_right_of_le_real hab (g.continuous.comp_continuous_on hcont)
-      (fun x hx => g.has_fderiv_at.comp_has_deriv_within_at x (hderiv x hx))
-      (g.integrable_comp ((intervalIntegrable_iff_integrable_Icc_of_le hab).1 f'int))
-#align interval_integral.integral_eq_sub_of_has_deriv_right_of_le intervalIntegral.integral_eq_sub_of_has_deriv_right_of_le
-
-/-- Fundamental theorem of calculus-2: If `f : ℝ → E` is continuous on `[a, b]` and
-  has a right derivative at `f' x` for all `x` in `[a, b)`, and `f'` is integrable on `[a, b]` then
-  `∫ y in a..b, f' y` equals `f b - f a`. -/
-theorem integral_eq_sub_of_has_deriv_right (hcont : ContinuousOn f (uIcc a b))
-    (hderiv : ∀ x ∈ Ioo (min a b) (max a b), HasDerivWithinAt f (f' x) (Ioi x) x)
-    (hint : IntervalIntegrable f' volume a b) : (∫ y in a..b, f' y) = f b - f a :=
-  by
-  cases' le_total a b with hab hab
-  · simp only [uIcc_of_le, min_eq_left, max_eq_right, hab] at hcont hderiv hint
-    apply integral_eq_sub_of_has_deriv_right_of_le hab hcont hderiv hint
-  · simp only [uIcc_of_ge, min_eq_right, max_eq_left, hab] at hcont hderiv
-    rw [integral_symm, integral_eq_sub_of_has_deriv_right_of_le hab hcont hderiv hint.symm, neg_sub]
-#align interval_integral.integral_eq_sub_of_has_deriv_right intervalIntegral.integral_eq_sub_of_has_deriv_right
-
-/-- Fundamental theorem of calculus-2: If `f : ℝ → E` is continuous on `[a, b]` (where `a ≤ b`) and
-  has a derivative at `f' x` for all `x` in `(a, b)`, and `f'` is integrable on `[a, b]`, then
-  `∫ y in a..b, f' y` equals `f b - f a`. -/
-theorem integral_eq_sub_of_hasDerivAt_of_le (hab : a ≤ b) (hcont : ContinuousOn f (Icc a b))
-    (hderiv : ∀ x ∈ Ioo a b, HasDerivAt f (f' x) x) (hint : IntervalIntegrable f' volume a b) :
-    (∫ y in a..b, f' y) = f b - f a :=
-  integral_eq_sub_of_has_deriv_right_of_le hab hcont (fun x hx => (hderiv x hx).HasDerivWithinAt)
-    hint
-#align interval_integral.integral_eq_sub_of_has_deriv_at_of_le intervalIntegral.integral_eq_sub_of_hasDerivAt_of_le
-
-/-- Fundamental theorem of calculus-2: If `f : ℝ → E` has a derivative at `f' x` for all `x` in
-  `[a, b]` and `f'` is integrable on `[a, b]`, then `∫ y in a..b, f' y` equals `f b - f a`. -/
-theorem integral_eq_sub_of_hasDerivAt (hderiv : ∀ x ∈ uIcc a b, HasDerivAt f (f' x) x)
-    (hint : IntervalIntegrable f' volume a b) : (∫ y in a..b, f' y) = f b - f a :=
-  integral_eq_sub_of_has_deriv_right (HasDerivAt.continuousOn hderiv)
-    (fun x hx => (hderiv _ (mem_Icc_of_Ioo hx)).HasDerivWithinAt) hint
-#align interval_integral.integral_eq_sub_of_has_deriv_at intervalIntegral.integral_eq_sub_of_hasDerivAt
-
-theorem integral_eq_sub_of_hasDerivAt_of_tendsto (hab : a < b) {fa fb}
-    (hderiv : ∀ x ∈ Ioo a b, HasDerivAt f (f' x) x) (hint : IntervalIntegrable f' volume a b)
-    (ha : Tendsto f (𝓝[>] a) (𝓝 fa)) (hb : Tendsto f (𝓝[<] b) (𝓝 fb)) :
-    (∫ y in a..b, f' y) = fb - fa :=
-  by
-  set F : ℝ → E := update (update f a fa) b fb
-  have Fderiv : ∀ x ∈ Ioo a b, HasDerivAt F (f' x) x :=
-    by
-    refine' fun x hx => (hderiv x hx).congr_of_eventuallyEq _
-    filter_upwards [Ioo_mem_nhds hx.1 hx.2]with _ hy
-    simp only [F]
-    rw [update_noteq hy.2.Ne, update_noteq hy.1.ne']
-  have hcont : ContinuousOn F (Icc a b) :=
-    by
-    rw [continuousOn_update_iff, continuousOn_update_iff, Icc_diff_right, Ico_diff_left]
-    refine' ⟨⟨fun z hz => (hderiv z hz).ContinuousAt.ContinuousWithinAt, _⟩, _⟩
-    · exact fun _ => ha.mono_left (nhdsWithin_mono _ Ioo_subset_Ioi_self)
-    · rintro -
-      refine' (hb.congr' _).mono_left (nhdsWithin_mono _ Ico_subset_Iio_self)
-      filter_upwards [Ioo_mem_nhdsWithin_Iio
-          (right_mem_Ioc.2 hab)]with _ hz using(update_noteq hz.1.ne' _ _).symm
-  simpa [F, hab.ne, hab.ne'] using integral_eq_sub_of_has_deriv_at_of_le hab.le hcont Fderiv hint
-#align interval_integral.integral_eq_sub_of_has_deriv_at_of_tendsto intervalIntegral.integral_eq_sub_of_hasDerivAt_of_tendsto
-
-/-- Fundamental theorem of calculus-2: If `f : ℝ → E` is differentiable at every `x` in `[a, b]` and
-  its derivative is integrable on `[a, b]`, then `∫ y in a..b, deriv f y` equals `f b - f a`. -/
-theorem integral_deriv_eq_sub (hderiv : ∀ x ∈ uIcc a b, DifferentiableAt ℝ f x)
-    (hint : IntervalIntegrable (deriv f) volume a b) : (∫ y in a..b, deriv f y) = f b - f a :=
-  integral_eq_sub_of_hasDerivAt (fun x hx => (hderiv x hx).HasDerivAt) hint
-#align interval_integral.integral_deriv_eq_sub intervalIntegral.integral_deriv_eq_sub
-
-theorem integral_deriv_eq_sub' (f) (hderiv : deriv f = f')
-    (hdiff : ∀ x ∈ uIcc a b, DifferentiableAt ℝ f x) (hcont : ContinuousOn f' (uIcc a b)) :
-    (∫ y in a..b, f' y) = f b - f a :=
-  by
-  rw [← hderiv, integral_deriv_eq_sub hdiff]
-  rw [hderiv]
-  exact hcont.interval_integrable
-#align interval_integral.integral_deriv_eq_sub' intervalIntegral.integral_deriv_eq_sub'
-
-/-!
-### Automatic integrability for nonnegative derivatives
--/
-
-
-/-- When the right derivative of a function is nonnegative, then it is automatically integrable. -/
-theorem integrableOnDerivRightOfNonneg (hcont : ContinuousOn g (Icc a b))
-    (hderiv : ∀ x ∈ Ioo a b, HasDerivWithinAt g (g' x) (Ioi x) x)
-    (g'pos : ∀ x ∈ Ioo a b, 0 ≤ g' x) : IntegrableOn g' (Ioc a b) :=
-  by
-  by_cases hab : a < b
-  swap
-  · simp [Ioc_eq_empty hab]
-  rw [integrableOn_Ioc_iff_integrableOn_Ioo]
-  have meas_g' : AeMeasurable g' (volume.restrict (Ioo a b)) :=
-    by
-    apply (aeMeasurableDerivWithinIoi g _).congr
-    refine' (ae_restrict_mem measurableSet_Ioo).mono fun x hx => _
-    exact (hderiv x hx).derivWithin (uniqueDiffWithinAt_Ioi _)
-  suffices H : (∫⁻ x in Ioo a b, ‖g' x‖₊) ≤ ENNReal.ofReal (g b - g a)
-  exact ⟨meas_g'.ae_strongly_measurable, H.trans_lt ENNReal.ofReal_lt_top⟩
-  by_contra' H
-  obtain ⟨f, fle, fint, hf⟩ :
-    ∃ f : simple_func ℝ ℝ≥0,
-      (∀ x, f x ≤ ‖g' x‖₊) ∧
-        (∫⁻ x : ℝ in Ioo a b, f x) < ∞ ∧ ENNReal.ofReal (g b - g a) < ∫⁻ x : ℝ in Ioo a b, f x :=
-    exists_lt_lintegral_simple_func_of_lt_lintegral H
-  let F : ℝ → ℝ := coe ∘ f
-  have intF : integrable_on F (Ioo a b) :=
-    by
-    refine' ⟨f.measurable.coe_nnreal_real.ae_strongly_measurable, _⟩
-    simpa only [has_finite_integral, NNReal.nnnorm_eq] using fint
-  have A : (∫⁻ x : ℝ in Ioo a b, f x) = ENNReal.ofReal (∫ x in Ioo a b, F x) :=
-    lintegral_coe_eq_integral _ intF
-  rw [A] at hf
-  have B : (∫ x : ℝ in Ioo a b, F x) ≤ g b - g a :=
-    by
-    rw [← integral_Ioc_eq_integral_Ioo, ← intervalIntegral.integral_of_le hab.le]
-    apply integral_le_sub_of_has_deriv_right_of_le hab.le hcont hderiv _ fun x hx => _
-    · rwa [integrableOn_Icc_iff_integrableOn_Ioo]
-    · convert NNReal.coe_le_coe.2 (fle x)
-      simp only [Real.norm_of_nonneg (g'pos x hx), coe_nnnorm]
-  exact lt_irrefl _ (hf.trans_le (ENNReal.ofReal_le_ofReal B))
-#align interval_integral.integrable_on_deriv_right_of_nonneg intervalIntegral.integrableOnDerivRightOfNonneg
-
-/-- When the derivative of a function is nonnegative, then it is automatically integrable,
-Ioc version. -/
-theorem integrableOnDerivOfNonneg (hcont : ContinuousOn g (Icc a b))
-    (hderiv : ∀ x ∈ Ioo a b, HasDerivAt g (g' x) x) (g'pos : ∀ x ∈ Ioo a b, 0 ≤ g' x) :
-    IntegrableOn g' (Ioc a b) :=
-  integrableOnDerivRightOfNonneg hcont (fun x hx => (hderiv x hx).HasDerivWithinAt) g'pos
-#align interval_integral.integrable_on_deriv_of_nonneg intervalIntegral.integrableOnDerivOfNonneg
-
-/-- When the derivative of a function is nonnegative, then it is automatically integrable,
-interval version. -/
-theorem intervalIntegrableDerivOfNonneg (hcont : ContinuousOn g (uIcc a b))
-    (hderiv : ∀ x ∈ Ioo (min a b) (max a b), HasDerivAt g (g' x) x)
-    (hpos : ∀ x ∈ Ioo (min a b) (max a b), 0 ≤ g' x) : IntervalIntegrable g' volume a b :=
-  by
-  cases' le_total a b with hab hab
-  · simp only [uIcc_of_le, min_eq_left, max_eq_right, hab, IntervalIntegrable, hab,
-      Ioc_eq_empty_of_le, integrable_on_empty, and_true_iff] at hcont hderiv hpos⊢
-    exact integrable_on_deriv_of_nonneg hcont hderiv hpos
-  · simp only [uIcc_of_ge, min_eq_right, max_eq_left, hab, IntervalIntegrable, Ioc_eq_empty_of_le,
-      integrable_on_empty, true_and_iff] at hcont hderiv hpos⊢
-    exact integrable_on_deriv_of_nonneg hcont hderiv hpos
-#align interval_integral.interval_integrable_deriv_of_nonneg intervalIntegral.intervalIntegrableDerivOfNonneg
-
-/-!
-### Integration by parts
--/
-
-
-section Parts
-
-variable [NormedRing A] [NormedAlgebra ℝ A] [CompleteSpace A]
-
-theorem integral_deriv_mul_eq_sub {u v u' v' : ℝ → A} (hu : ∀ x ∈ uIcc a b, HasDerivAt u (u' x) x)
-    (hv : ∀ x ∈ uIcc a b, HasDerivAt v (v' x) x) (hu' : IntervalIntegrable u' volume a b)
-    (hv' : IntervalIntegrable v' volume a b) :
-    (∫ x in a..b, u' x * v x + u x * v' x) = u b * v b - u a * v a :=
-  (integral_eq_sub_of_hasDerivAt fun x hx => (hu x hx).mul (hv x hx)) <|
-    (hu'.mulContinuousOn (HasDerivAt.continuousOn hv)).add
-      (hv'.continuousOnMul (HasDerivAt.continuousOn hu))
-#align interval_integral.integral_deriv_mul_eq_sub intervalIntegral.integral_deriv_mul_eq_sub
-
-theorem integral_mul_deriv_eq_deriv_mul {u v u' v' : ℝ → A}
-    (hu : ∀ x ∈ uIcc a b, HasDerivAt u (u' x) x) (hv : ∀ x ∈ uIcc a b, HasDerivAt v (v' x) x)
-    (hu' : IntervalIntegrable u' volume a b) (hv' : IntervalIntegrable v' volume a b) :
-    (∫ x in a..b, u x * v' x) = u b * v b - u a * v a - ∫ x in a..b, u' x * v x :=
-  by
-  rw [← integral_deriv_mul_eq_sub hu hv hu' hv', ← integral_sub]
-  · exact integral_congr fun x hx => by simp only [add_sub_cancel']
-  ·
-    exact
-      (hu'.mul_continuous_on (HasDerivAt.continuousOn hv)).add
-        (hv'.continuous_on_mul (HasDerivAt.continuousOn hu))
-  · exact hu'.mul_continuous_on (HasDerivAt.continuousOn hv)
-#align interval_integral.integral_mul_deriv_eq_deriv_mul intervalIntegral.integral_mul_deriv_eq_deriv_mul
-
-end Parts
-
-/-!
-### Integration by substitution / Change of variables
--/
-
-
-section Smul
-
-/-- Change of variables, general form. If `f` is continuous on `[a, b]` and has
-right-derivative `f'` in `(a, b)`, `g` is continuous on `f '' (a, b)` and integrable on
-`f '' [a, b]`, and `f' x • (g ∘ f) x` is integrable on `[a, b]`,
-then we can substitute `u = f x` to get `∫ x in a..b, f' x • (g ∘ f) x = ∫ u in f a..f b, g u`.
--/
-theorem integral_comp_smul_deriv''' {f f' : ℝ → ℝ} {g : ℝ → E} (hf : ContinuousOn f [a, b])
-    (hff' : ∀ x ∈ Ioo (min a b) (max a b), HasDerivWithinAt f (f' x) (Ioi x) x)
-    (hg_cont : ContinuousOn g (f '' Ioo (min a b) (max a b))) (hg1 : IntegrableOn g (f '' [a, b]))
-    (hg2 : IntegrableOn (fun x => f' x • (g ∘ f) x) [a, b]) :
-    (∫ x in a..b, f' x • (g ∘ f) x) = ∫ u in f a..f b, g u :=
-  by
-  rw [hf.image_uIcc, ← intervalIntegrable_iff'] at hg1
-  have h_cont : ContinuousOn (fun u => ∫ t in f a..f u, g t) [a, b] :=
-    by
-    refine' (continuous_on_primitive_interval' hg1 _).comp hf _
-    · rw [← hf.image_uIcc]
-      exact mem_image_of_mem f left_mem_uIcc
-    · rw [← hf.image_uIcc]
-      exact maps_to_image _ _
-  have h_der :
-    ∀ x ∈ Ioo (min a b) (max a b),
-      HasDerivWithinAt (fun u => ∫ t in f a..f u, g t) (f' x • (g ∘ f) x) (Ioi x) x :=
-    by
-    intro x hx
-    obtain ⟨c, hc⟩ := nonempty_Ioo.mpr hx.1
-    obtain ⟨d, hd⟩ := nonempty_Ioo.mpr hx.2
-    have cdsub : [c, d] ⊆ Ioo (min a b) (max a b) :=
-      by
-      rw [uIcc_of_le (hc.2.trans hd.1).le]
-      exact Icc_subset_Ioo hc.1 hd.2
-    replace hg_cont := hg_cont.mono (image_subset f cdsub)
-    let J := [Inf (f '' [c, d]), Sup (f '' [c, d])]
-    have hJ : f '' [c, d] = J := (hf.mono (cdsub.trans Ioo_subset_Icc_self)).image_uIcc
-    rw [hJ] at hg_cont
-    have h2x : f x ∈ J := by
-      rw [← hJ]
-      exact mem_image_of_mem _ (mem_uIcc_of_le hc.2.le hd.1.le)
-    have h2g : IntervalIntegrable g volume (f a) (f x) :=
-      by
-      refine' hg1.mono_set _
-      rw [← hf.image_uIcc]
-      exact hf.surj_on_uIcc left_mem_uIcc (Ioo_subset_Icc_self hx)
-    have h3g := hg_cont.strongly_measurable_at_filter_nhds_within measurableSet_Icc (f x)
-    haveI : Fact (f x ∈ J) := ⟨h2x⟩
-    have : HasDerivWithinAt (fun u => ∫ x in f a..u, g x) (g (f x)) J (f x) :=
-      intervalIntegral.integral_hasDerivWithinAt_right h2g h3g (hg_cont (f x) h2x)
-    refine' (this.scomp x ((hff' x hx).Ioo_of_Ioi hd.1) _).Ioi_of_Ioo hd.1
-    rw [← hJ]
-    refine' (maps_to_image _ _).mono _ subset.rfl
-    exact Ioo_subset_Icc_self.trans ((Icc_subset_Icc_left hc.2.le).trans Icc_subset_uIcc)
-  rw [← intervalIntegrable_iff'] at hg2
-  simp_rw [integral_eq_sub_of_has_deriv_right h_cont h_der hg2, integral_same, sub_zero]
-#align interval_integral.integral_comp_smul_deriv''' intervalIntegral.integral_comp_smul_deriv'''
-
-/-- Change of variables for continuous integrands. If `f` is continuous on `[a, b]` and has
-continuous right-derivative `f'` in `(a, b)`, and `g` is continuous on `f '' [a, b]` then we can
-substitute `u = f x` to get `∫ x in a..b, f' x • (g ∘ f) x = ∫ u in f a..f b, g u`.
--/
-theorem integral_comp_smul_deriv'' {f f' : ℝ → ℝ} {g : ℝ → E} (hf : ContinuousOn f [a, b])
-    (hff' : ∀ x ∈ Ioo (min a b) (max a b), HasDerivWithinAt f (f' x) (Ioi x) x)
-    (hf' : ContinuousOn f' [a, b]) (hg : ContinuousOn g (f '' [a, b])) :
-    (∫ x in a..b, f' x • (g ∘ f) x) = ∫ u in f a..f b, g u :=
-  by
-  refine'
-    integral_comp_smul_deriv''' hf hff' (hg.mono <| image_subset _ Ioo_subset_Icc_self) _
-      (hf'.smul (hg.comp hf <| subset_preimage_image f _)).integrableOnIcc
-  rw [hf.image_uIcc] at hg⊢
-  exact hg.integrable_on_Icc
-#align interval_integral.integral_comp_smul_deriv'' intervalIntegral.integral_comp_smul_deriv''
-
-/-- Change of variables. If `f` is has continuous derivative `f'` on `[a, b]`,
-and `g` is continuous on `f '' [a, b]`, then we can substitute `u = f x` to get
-`∫ x in a..b, f' x • (g ∘ f) x = ∫ u in f a..f b, g u`.
-Compared to `interval_integral.integral_comp_smul_deriv` we only require that `g` is continuous on
-`f '' [a, b]`.
--/
-theorem integral_comp_smul_deriv' {f f' : ℝ → ℝ} {g : ℝ → E}
-    (h : ∀ x ∈ uIcc a b, HasDerivAt f (f' x) x) (h' : ContinuousOn f' (uIcc a b))
-    (hg : ContinuousOn g (f '' [a, b])) : (∫ x in a..b, f' x • (g ∘ f) x) = ∫ x in f a..f b, g x :=
-  integral_comp_smul_deriv'' (fun x hx => (h x hx).ContinuousAt.ContinuousWithinAt)
-    (fun x hx => (h x <| Ioo_subset_Icc_self hx).HasDerivWithinAt) h' hg
-#align interval_integral.integral_comp_smul_deriv' intervalIntegral.integral_comp_smul_deriv'
-
-/-- Change of variables, most common version. If `f` is has continuous derivative `f'` on `[a, b]`,
-and `g` is continuous, then we can substitute `u = f x` to get
-`∫ x in a..b, f' x • (g ∘ f) x = ∫ u in f a..f b, g u`.
--/
-theorem integral_comp_smul_deriv {f f' : ℝ → ℝ} {g : ℝ → E}
-    (h : ∀ x ∈ uIcc a b, HasDerivAt f (f' x) x) (h' : ContinuousOn f' (uIcc a b))
-    (hg : Continuous g) : (∫ x in a..b, f' x • (g ∘ f) x) = ∫ x in f a..f b, g x :=
-  integral_comp_smul_deriv' h h' hg.ContinuousOn
-#align interval_integral.integral_comp_smul_deriv intervalIntegral.integral_comp_smul_deriv
-
-theorem integral_deriv_comp_smul_deriv' {f f' : ℝ → ℝ} {g g' : ℝ → E} (hf : ContinuousOn f [a, b])
-    (hff' : ∀ x ∈ Ioo (min a b) (max a b), HasDerivWithinAt f (f' x) (Ioi x) x)
-    (hf' : ContinuousOn f' [a, b]) (hg : ContinuousOn g [f a, f b])
-    (hgg' : ∀ x ∈ Ioo (min (f a) (f b)) (max (f a) (f b)), HasDerivWithinAt g (g' x) (Ioi x) x)
-    (hg' : ContinuousOn g' (f '' [a, b])) :
-    (∫ x in a..b, f' x • (g' ∘ f) x) = (g ∘ f) b - (g ∘ f) a :=
-  by
-  rw [integral_comp_smul_deriv'' hf hff' hf' hg',
-    integral_eq_sub_of_has_deriv_right hg hgg' (hg'.mono _).IntervalIntegrable]
-  exact intermediate_value_uIcc hf
-#align interval_integral.integral_deriv_comp_smul_deriv' intervalIntegral.integral_deriv_comp_smul_deriv'
-
-theorem integral_deriv_comp_smul_deriv {f f' : ℝ → ℝ} {g g' : ℝ → E}
-    (hf : ∀ x ∈ uIcc a b, HasDerivAt f (f' x) x)
-    (hg : ∀ x ∈ uIcc a b, HasDerivAt g (g' (f x)) (f x)) (hf' : ContinuousOn f' (uIcc a b))
-    (hg' : Continuous g') : (∫ x in a..b, f' x • (g' ∘ f) x) = (g ∘ f) b - (g ∘ f) a :=
-  integral_eq_sub_of_hasDerivAt (fun x hx => (hg x hx).scomp x <| hf x hx)
-    (hf'.smul (hg'.comp_continuousOn <| HasDerivAt.continuousOn hf)).IntervalIntegrable
-#align interval_integral.integral_deriv_comp_smul_deriv intervalIntegral.integral_deriv_comp_smul_deriv
-
-end Smul
-
-section Mul
-
-/-- Change of variables, general form for scalar functions. If `f` is continuous on `[a, b]` and has
-continuous right-derivative `f'` in `(a, b)`, `g` is continuous on `f '' (a, b)` and integrable on
-`f '' [a, b]`, and `(g ∘ f) x * f' x` is integrable on `[a, b]`, then we can substitute `u = f x`
-to get `∫ x in a..b, (g ∘ f) x * f' x = ∫ u in f a..f b, g u`.
--/
-theorem integral_comp_mul_deriv''' {a b : ℝ} {f f' : ℝ → ℝ} {g : ℝ → ℝ} (hf : ContinuousOn f [a, b])
-    (hff' : ∀ x ∈ Ioo (min a b) (max a b), HasDerivWithinAt f (f' x) (Ioi x) x)
-    (hg_cont : ContinuousOn g (f '' Ioo (min a b) (max a b))) (hg1 : IntegrableOn g (f '' [a, b]))
-    (hg2 : IntegrableOn (fun x => (g ∘ f) x * f' x) [a, b]) :
-    (∫ x in a..b, (g ∘ f) x * f' x) = ∫ u in f a..f b, g u :=
-  by
-  have hg2' : integrable_on (fun x => f' x • (g ∘ f) x) [a, b] := by simpa [mul_comm] using hg2
-  simpa [mul_comm] using integral_comp_smul_deriv''' hf hff' hg_cont hg1 hg2'
-#align interval_integral.integral_comp_mul_deriv''' intervalIntegral.integral_comp_mul_deriv'''
-
-/-- Change of variables for continuous integrands. If `f` is continuous on `[a, b]` and has
-continuous right-derivative `f'` in `(a, b)`, and `g` is continuous on `f '' [a, b]` then we can
-substitute `u = f x` to get `∫ x in a..b, (g ∘ f) x * f' x = ∫ u in f a..f b, g u`.
--/
-theorem integral_comp_mul_deriv'' {f f' g : ℝ → ℝ} (hf : ContinuousOn f [a, b])
-    (hff' : ∀ x ∈ Ioo (min a b) (max a b), HasDerivWithinAt f (f' x) (Ioi x) x)
-    (hf' : ContinuousOn f' [a, b]) (hg : ContinuousOn g (f '' [a, b])) :
-    (∫ x in a..b, (g ∘ f) x * f' x) = ∫ u in f a..f b, g u := by
-  simpa [mul_comm] using integral_comp_smul_deriv'' hf hff' hf' hg
-#align interval_integral.integral_comp_mul_deriv'' intervalIntegral.integral_comp_mul_deriv''
-
-/-- Change of variables. If `f` is has continuous derivative `f'` on `[a, b]`,
-and `g` is continuous on `f '' [a, b]`, then we can substitute `u = f x` to get
-`∫ x in a..b, (g ∘ f) x * f' x = ∫ u in f a..f b, g u`.
-Compared to `interval_integral.integral_comp_mul_deriv` we only require that `g` is continuous on
-`f '' [a, b]`.
--/
-theorem integral_comp_mul_deriv' {f f' g : ℝ → ℝ} (h : ∀ x ∈ uIcc a b, HasDerivAt f (f' x) x)
-    (h' : ContinuousOn f' (uIcc a b)) (hg : ContinuousOn g (f '' [a, b])) :
-    (∫ x in a..b, (g ∘ f) x * f' x) = ∫ x in f a..f b, g x := by
-  simpa [mul_comm] using integral_comp_smul_deriv' h h' hg
-#align interval_integral.integral_comp_mul_deriv' intervalIntegral.integral_comp_mul_deriv'
-
-/-- Change of variables, most common version. If `f` is has continuous derivative `f'` on `[a, b]`,
-and `g` is continuous, then we can substitute `u = f x` to get
-`∫ x in a..b, (g ∘ f) x * f' x = ∫ u in f a..f b, g u`.
--/
-theorem integral_comp_mul_deriv {f f' g : ℝ → ℝ} (h : ∀ x ∈ uIcc a b, HasDerivAt f (f' x) x)
-    (h' : ContinuousOn f' (uIcc a b)) (hg : Continuous g) :
-    (∫ x in a..b, (g ∘ f) x * f' x) = ∫ x in f a..f b, g x :=
-  integral_comp_mul_deriv' h h' hg.ContinuousOn
-#align interval_integral.integral_comp_mul_deriv intervalIntegral.integral_comp_mul_deriv
-
-theorem integral_deriv_comp_mul_deriv' {f f' g g' : ℝ → ℝ} (hf : ContinuousOn f [a, b])
-    (hff' : ∀ x ∈ Ioo (min a b) (max a b), HasDerivWithinAt f (f' x) (Ioi x) x)
-    (hf' : ContinuousOn f' [a, b]) (hg : ContinuousOn g [f a, f b])
-    (hgg' : ∀ x ∈ Ioo (min (f a) (f b)) (max (f a) (f b)), HasDerivWithinAt g (g' x) (Ioi x) x)
-    (hg' : ContinuousOn g' (f '' [a, b])) :
-    (∫ x in a..b, (g' ∘ f) x * f' x) = (g ∘ f) b - (g ∘ f) a := by
-  simpa [mul_comm] using integral_deriv_comp_smul_deriv' hf hff' hf' hg hgg' hg'
-#align interval_integral.integral_deriv_comp_mul_deriv' intervalIntegral.integral_deriv_comp_mul_deriv'
-
-theorem integral_deriv_comp_mul_deriv {f f' g g' : ℝ → ℝ}
-    (hf : ∀ x ∈ uIcc a b, HasDerivAt f (f' x) x)
-    (hg : ∀ x ∈ uIcc a b, HasDerivAt g (g' (f x)) (f x)) (hf' : ContinuousOn f' (uIcc a b))
-    (hg' : Continuous g') : (∫ x in a..b, (g' ∘ f) x * f' x) = (g ∘ f) b - (g ∘ f) a := by
-  simpa [mul_comm] using integral_deriv_comp_smul_deriv hf hg hf' hg'
-#align interval_integral.integral_deriv_comp_mul_deriv intervalIntegral.integral_deriv_comp_mul_deriv
-
-end Mul
-
 end intervalIntegral
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/7e281deff072232a3c5b3e90034bd65dde396312

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury G. Kudryashov, Patrick Massot, Sébastien Gouëzel
 
 ! This file was ported from Lean 3 source module measure_theory.integral.interval_integral
-! leanprover-community/mathlib commit 08a4542bec7242a5c60f179e4e49de8c0d677b1b
+! leanprover-community/mathlib commit d4817f8867c368d6c5571f7379b3888aaec1d95a
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -2806,10 +2806,13 @@ theorem integral_deriv_eq_sub' (f) (hderiv : deriv f = f')
 
 
 /-- When the right derivative of a function is nonnegative, then it is automatically integrable. -/
-theorem integrableOnDerivRightOfNonneg (hab : a ≤ b) (hcont : ContinuousOn g (Icc a b))
+theorem integrableOnDerivRightOfNonneg (hcont : ContinuousOn g (Icc a b))
     (hderiv : ∀ x ∈ Ioo a b, HasDerivWithinAt g (g' x) (Ioi x) x)
     (g'pos : ∀ x ∈ Ioo a b, 0 ≤ g' x) : IntegrableOn g' (Ioc a b) :=
   by
+  by_cases hab : a < b
+  swap
+  · simp [Ioc_eq_empty hab]
   rw [integrableOn_Ioc_iff_integrableOn_Ioo]
   have meas_g' : AeMeasurable g' (volume.restrict (Ioo a b)) :=
     by
@@ -2834,8 +2837,8 @@ theorem integrableOnDerivRightOfNonneg (hab : a ≤ b) (hcont : ContinuousOn g (
   rw [A] at hf
   have B : (∫ x : ℝ in Ioo a b, F x) ≤ g b - g a :=
     by
-    rw [← integral_Ioc_eq_integral_Ioo, ← intervalIntegral.integral_of_le hab]
-    apply integral_le_sub_of_has_deriv_right_of_le hab hcont hderiv _ fun x hx => _
+    rw [← integral_Ioc_eq_integral_Ioo, ← intervalIntegral.integral_of_le hab.le]
+    apply integral_le_sub_of_has_deriv_right_of_le hab.le hcont hderiv _ fun x hx => _
     · rwa [integrableOn_Icc_iff_integrableOn_Ioo]
     · convert NNReal.coe_le_coe.2 (fle x)
       simp only [Real.norm_of_nonneg (g'pos x hx), coe_nnnorm]
@@ -2844,10 +2847,10 @@ theorem integrableOnDerivRightOfNonneg (hab : a ≤ b) (hcont : ContinuousOn g (
 
 /-- When the derivative of a function is nonnegative, then it is automatically integrable,
 Ioc version. -/
-theorem integrableOnDerivOfNonneg (hab : a ≤ b) (hcont : ContinuousOn g (Icc a b))
+theorem integrableOnDerivOfNonneg (hcont : ContinuousOn g (Icc a b))
     (hderiv : ∀ x ∈ Ioo a b, HasDerivAt g (g' x) x) (g'pos : ∀ x ∈ Ioo a b, 0 ≤ g' x) :
     IntegrableOn g' (Ioc a b) :=
-  integrableOnDerivRightOfNonneg hab hcont (fun x hx => (hderiv x hx).HasDerivWithinAt) g'pos
+  integrableOnDerivRightOfNonneg hcont (fun x hx => (hderiv x hx).HasDerivWithinAt) g'pos
 #align interval_integral.integrable_on_deriv_of_nonneg intervalIntegral.integrableOnDerivOfNonneg
 
 /-- When the derivative of a function is nonnegative, then it is automatically integrable,
@@ -2859,10 +2862,10 @@ theorem intervalIntegrableDerivOfNonneg (hcont : ContinuousOn g (uIcc a b))
   cases' le_total a b with hab hab
   · simp only [uIcc_of_le, min_eq_left, max_eq_right, hab, IntervalIntegrable, hab,
       Ioc_eq_empty_of_le, integrable_on_empty, and_true_iff] at hcont hderiv hpos⊢
-    exact integrable_on_deriv_of_nonneg hab hcont hderiv hpos
+    exact integrable_on_deriv_of_nonneg hcont hderiv hpos
   · simp only [uIcc_of_ge, min_eq_right, max_eq_left, hab, IntervalIntegrable, Ioc_eq_empty_of_le,
       integrable_on_empty, true_and_iff] at hcont hderiv hpos⊢
-    exact integrable_on_deriv_of_nonneg hab hcont hderiv hpos
+    exact integrable_on_deriv_of_nonneg hcont hderiv hpos
 #align interval_integral.interval_integrable_deriv_of_nonneg intervalIntegral.intervalIntegrableDerivOfNonneg
 
 /-!

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

@@ -1803,7 +1803,7 @@ The primed version also works, e.g., for `l = l' = at_top`.
 
 We use integrals of constants instead of measures because this way it is easier to formulate
 a statement that works in both cases `u ≤ v` and `v ≤ u`. -/
-theorem measure_integral_sub_linear_isOCat_of_tendsto_ae' [IsMeasurablyGenerated l']
+theorem measure_integral_sub_linear_isLittleO_of_tendsto_ae' [IsMeasurablyGenerated l']
     [TendstoIxxClass Ioc l l'] (hfm : StronglyMeasurableAtFilter f l' μ)
     (hf : Tendsto f (l' ⊓ μ.ae) (𝓝 c)) (hl : μ.FiniteAtFilter l') (hu : Tendsto u lt l)
     (hv : Tendsto v lt l) :
@@ -1818,7 +1818,7 @@ theorem measure_integral_sub_linear_isOCat_of_tendsto_ae' [IsMeasurablyGenerated
     simp_rw [intervalIntegral, sub_smul]
     abel
   all_goals intro t; cases' le_total (u t) (v t) with huv huv <;> simp [huv]
-#align interval_integral.measure_integral_sub_linear_is_o_of_tendsto_ae' intervalIntegral.measure_integral_sub_linear_isOCat_of_tendsto_ae'
+#align interval_integral.measure_integral_sub_linear_is_o_of_tendsto_ae' intervalIntegral.measure_integral_sub_linear_isLittleO_of_tendsto_ae'
 
 /-- Fundamental theorem of calculus-1, local version for any measure.
 Let filters `l` and `l'` be related by `tendsto_Ixx_class Ioc`.
@@ -1830,16 +1830,16 @@ See also `measure_integral_sub_linear_is_o_of_tendsto_ae_of_le` for a version as
 `[FTC_filter a l l']` and `[is_locally_finite_measure μ]`. If `l` is one of `𝓝[≥] a`,
 `𝓝[≤] a`, `𝓝 a`, then it's easier to apply the non-primed version.
 The primed version also works, e.g., for `l = l' = at_top`. -/
-theorem measure_integral_sub_linear_isOCat_of_tendsto_ae_of_le' [IsMeasurablyGenerated l']
+theorem measure_integral_sub_linear_isLittleO_of_tendsto_ae_of_le' [IsMeasurablyGenerated l']
     [TendstoIxxClass Ioc l l'] (hfm : StronglyMeasurableAtFilter f l' μ)
     (hf : Tendsto f (l' ⊓ μ.ae) (𝓝 c)) (hl : μ.FiniteAtFilter l') (hu : Tendsto u lt l)
     (hv : Tendsto v lt l) (huv : u ≤ᶠ[lt] v) :
     (fun t => (∫ x in u t..v t, f x ∂μ) - (μ (Ioc (u t) (v t))).toReal • c) =o[lt] fun t =>
       (μ <| Ioc (u t) (v t)).toReal :=
-  (measure_integral_sub_linear_isOCat_of_tendsto_ae' hfm hf hl hu hv).congr'
+  (measure_integral_sub_linear_isLittleO_of_tendsto_ae' hfm hf hl hu hv).congr'
     (huv.mono fun x hx => by simp [integral_const', hx])
     (huv.mono fun x hx => by simp [integral_const', hx])
-#align interval_integral.measure_integral_sub_linear_is_o_of_tendsto_ae_of_le' intervalIntegral.measure_integral_sub_linear_isOCat_of_tendsto_ae_of_le'
+#align interval_integral.measure_integral_sub_linear_is_o_of_tendsto_ae_of_le' intervalIntegral.measure_integral_sub_linear_isLittleO_of_tendsto_ae_of_le'
 
 /-- Fundamental theorem of calculus-1, local version for any measure.
 Let filters `l` and `l'` be related by `tendsto_Ixx_class Ioc`.
@@ -1851,15 +1851,16 @@ See also `measure_integral_sub_linear_is_o_of_tendsto_ae_of_ge` for a version as
 `[FTC_filter a l l']` and `[is_locally_finite_measure μ]`. If `l` is one of `𝓝[≥] a`,
 `𝓝[≤] a`, `𝓝 a`, then it's easier to apply the non-primed version.
 The primed version also works, e.g., for `l = l' = at_top`. -/
-theorem measure_integral_sub_linear_isOCat_of_tendsto_ae_of_ge' [IsMeasurablyGenerated l']
+theorem measure_integral_sub_linear_isLittleO_of_tendsto_ae_of_ge' [IsMeasurablyGenerated l']
     [TendstoIxxClass Ioc l l'] (hfm : StronglyMeasurableAtFilter f l' μ)
     (hf : Tendsto f (l' ⊓ μ.ae) (𝓝 c)) (hl : μ.FiniteAtFilter l') (hu : Tendsto u lt l)
     (hv : Tendsto v lt l) (huv : v ≤ᶠ[lt] u) :
     (fun t => (∫ x in u t..v t, f x ∂μ) + (μ (Ioc (v t) (u t))).toReal • c) =o[lt] fun t =>
       (μ <| Ioc (v t) (u t)).toReal :=
-  (measure_integral_sub_linear_isOCat_of_tendsto_ae_of_le' hfm hf hl hv hu huv).neg_left.congr_left
+  (measure_integral_sub_linear_isLittleO_of_tendsto_ae_of_le' hfm hf hl hv hu
+          huv).neg_left.congr_left
     fun t => by simp [integral_symm (u t), add_comm]
-#align interval_integral.measure_integral_sub_linear_is_o_of_tendsto_ae_of_ge' intervalIntegral.measure_integral_sub_linear_isOCat_of_tendsto_ae_of_ge'
+#align interval_integral.measure_integral_sub_linear_is_o_of_tendsto_ae_of_ge' intervalIntegral.measure_integral_sub_linear_isLittleO_of_tendsto_ae_of_ge'
 
 section
 
@@ -1879,12 +1880,13 @@ See also `measure_integral_sub_linear_is_o_of_tendsto_ae'` for a version that al
 
 We use integrals of constants instead of measures because this way it is easier to formulate
 a statement that works in both cases `u ≤ v` and `v ≤ u`. -/
-theorem measure_integral_sub_linear_isOCat_of_tendsto_ae (hfm : StronglyMeasurableAtFilter f l' μ)
-    (hf : Tendsto f (l' ⊓ μ.ae) (𝓝 c)) (hu : Tendsto u lt l) (hv : Tendsto v lt l) :
+theorem measure_integral_sub_linear_isLittleO_of_tendsto_ae
+    (hfm : StronglyMeasurableAtFilter f l' μ) (hf : Tendsto f (l' ⊓ μ.ae) (𝓝 c))
+    (hu : Tendsto u lt l) (hv : Tendsto v lt l) :
     (fun t => (∫ x in u t..v t, f x ∂μ) - ∫ x in u t..v t, c ∂μ) =o[lt] fun t =>
       ∫ x in u t..v t, (1 : ℝ) ∂μ :=
-  measure_integral_sub_linear_isOCat_of_tendsto_ae' hfm hf (FTCFilter.finiteAtInner l) hu hv
-#align interval_integral.measure_integral_sub_linear_is_o_of_tendsto_ae intervalIntegral.measure_integral_sub_linear_isOCat_of_tendsto_ae
+  measure_integral_sub_linear_isLittleO_of_tendsto_ae' hfm hf (FTCFilter.finiteAtInner l) hu hv
+#align interval_integral.measure_integral_sub_linear_is_o_of_tendsto_ae intervalIntegral.measure_integral_sub_linear_isLittleO_of_tendsto_ae
 
 /-- Fundamental theorem of calculus-1, local version for any measure.
 Let filters `l` and `l'` be related by `[FTC_filter a l l']`; let `μ` be a locally finite measure.
@@ -1893,14 +1895,14 @@ If `f` has a finite limit `c` at `l' ⊓ μ.ae`, then
 
 See also `measure_integral_sub_linear_is_o_of_tendsto_ae_of_le'` for a version that also works,
 e.g., for `l = l' = at_top`. -/
-theorem measure_integral_sub_linear_isOCat_of_tendsto_ae_of_le
+theorem measure_integral_sub_linear_isLittleO_of_tendsto_ae_of_le
     (hfm : StronglyMeasurableAtFilter f l' μ) (hf : Tendsto f (l' ⊓ μ.ae) (𝓝 c))
     (hu : Tendsto u lt l) (hv : Tendsto v lt l) (huv : u ≤ᶠ[lt] v) :
     (fun t => (∫ x in u t..v t, f x ∂μ) - (μ (Ioc (u t) (v t))).toReal • c) =o[lt] fun t =>
       (μ <| Ioc (u t) (v t)).toReal :=
-  measure_integral_sub_linear_isOCat_of_tendsto_ae_of_le' hfm hf (FTCFilter.finiteAtInner l) hu hv
-    huv
-#align interval_integral.measure_integral_sub_linear_is_o_of_tendsto_ae_of_le intervalIntegral.measure_integral_sub_linear_isOCat_of_tendsto_ae_of_le
+  measure_integral_sub_linear_isLittleO_of_tendsto_ae_of_le' hfm hf (FTCFilter.finiteAtInner l) hu
+    hv huv
+#align interval_integral.measure_integral_sub_linear_is_o_of_tendsto_ae_of_le intervalIntegral.measure_integral_sub_linear_isLittleO_of_tendsto_ae_of_le
 
 /-- Fundamental theorem of calculus-1, local version for any measure.
 Let filters `l` and `l'` be related by `[FTC_filter a l l']`; let `μ` be a locally finite measure.
@@ -1909,14 +1911,14 @@ If `f` has a finite limit `c` at `l' ⊓ μ.ae`, then
 
 See also `measure_integral_sub_linear_is_o_of_tendsto_ae_of_ge'` for a version that also works,
 e.g., for `l = l' = at_top`. -/
-theorem measure_integral_sub_linear_isOCat_of_tendsto_ae_of_ge
+theorem measure_integral_sub_linear_isLittleO_of_tendsto_ae_of_ge
     (hfm : StronglyMeasurableAtFilter f l' μ) (hf : Tendsto f (l' ⊓ μ.ae) (𝓝 c))
     (hu : Tendsto u lt l) (hv : Tendsto v lt l) (huv : v ≤ᶠ[lt] u) :
     (fun t => (∫ x in u t..v t, f x ∂μ) + (μ (Ioc (v t) (u t))).toReal • c) =o[lt] fun t =>
       (μ <| Ioc (v t) (u t)).toReal :=
-  measure_integral_sub_linear_isOCat_of_tendsto_ae_of_ge' hfm hf (FTCFilter.finiteAtInner l) hu hv
-    huv
-#align interval_integral.measure_integral_sub_linear_is_o_of_tendsto_ae_of_ge intervalIntegral.measure_integral_sub_linear_isOCat_of_tendsto_ae_of_ge
+  measure_integral_sub_linear_isLittleO_of_tendsto_ae_of_ge' hfm hf (FTCFilter.finiteAtInner l) hu
+    hv huv
+#align interval_integral.measure_integral_sub_linear_is_o_of_tendsto_ae_of_ge intervalIntegral.measure_integral_sub_linear_isLittleO_of_tendsto_ae_of_ge
 
 end
 
@@ -1935,7 +1937,7 @@ Then `∫ x in va..vb, f x ∂μ - ∫ x in ua..ub, f x ∂μ =
     o(‖∫ x in ua..va, (1:ℝ) ∂μ‖ + ‖∫ x in ub..vb, (1:ℝ) ∂μ‖)`
 as `ua` and `va` tend to `la` while `ub` and `vb` tend to `lb`.
 -/
-theorem measure_integral_sub_integral_sub_linear_isOCat_of_tendsto_ae
+theorem measure_integral_sub_integral_sub_linear_isLittleO_of_tendsto_ae
     (hab : IntervalIntegrable f μ a b) (hmeas_a : StronglyMeasurableAtFilter f la' μ)
     (hmeas_b : StronglyMeasurableAtFilter f lb' μ) (ha_lim : Tendsto f (la' ⊓ μ.ae) (𝓝 ca))
     (hb_lim : Tendsto f (lb' ⊓ μ.ae) (𝓝 cb)) (hua : Tendsto ua lt la) (hva : Tendsto va lt la)
@@ -1964,7 +1966,7 @@ theorem measure_integral_sub_integral_sub_linear_isOCat_of_tendsto_ae
   · dsimp only
     abel
   exacts[ub_vb, ua_va, b_ub.symm.trans <| hab.symm.trans a_ua]
-#align interval_integral.measure_integral_sub_integral_sub_linear_is_o_of_tendsto_ae intervalIntegral.measure_integral_sub_integral_sub_linear_isOCat_of_tendsto_ae
+#align interval_integral.measure_integral_sub_integral_sub_linear_is_o_of_tendsto_ae intervalIntegral.measure_integral_sub_integral_sub_linear_isLittleO_of_tendsto_ae
 
 /-- Fundamental theorem of calculus-1, strict derivative in right endpoint for a locally finite
 measure.
@@ -1975,7 +1977,7 @@ around `b`. Suppose that `f` has a finite limit `c` at `lb' ⊓ μ.ae`.
 Then `∫ x in a..v, f x ∂μ - ∫ x in a..u, f x ∂μ = ∫ x in u..v, c ∂μ + o(∫ x in u..v, (1:ℝ) ∂μ)`
 as `u` and `v` tend to `lb`.
 -/
-theorem measure_integral_sub_integral_sub_linear_isOCat_of_tendsto_ae_right
+theorem measure_integral_sub_integral_sub_linear_isLittleO_of_tendsto_ae_right
     (hab : IntervalIntegrable f μ a b) (hmeas : StronglyMeasurableAtFilter f lb' μ)
     (hf : Tendsto f (lb' ⊓ μ.ae) (𝓝 c)) (hu : Tendsto u lt lb) (hv : Tendsto v lt lb) :
     (fun t => ((∫ x in a..v t, f x ∂μ) - ∫ x in a..u t, f x ∂μ) - ∫ x in u t..v t, c ∂μ) =o[lt]
@@ -1985,7 +1987,7 @@ theorem measure_integral_sub_integral_sub_linear_isOCat_of_tendsto_ae_right
     measure_integral_sub_integral_sub_linear_is_o_of_tendsto_ae hab stronglyMeasurableAtBot hmeas
       ((tendsto_bot : tendsto _ ⊥ (𝓝 0)).mono_left inf_le_left) hf
       (tendsto_const_pure : tendsto _ _ (pure a)) tendsto_const_pure hu hv
-#align interval_integral.measure_integral_sub_integral_sub_linear_is_o_of_tendsto_ae_right intervalIntegral.measure_integral_sub_integral_sub_linear_isOCat_of_tendsto_ae_right
+#align interval_integral.measure_integral_sub_integral_sub_linear_is_o_of_tendsto_ae_right intervalIntegral.measure_integral_sub_integral_sub_linear_isLittleO_of_tendsto_ae_right
 
 /-- Fundamental theorem of calculus-1, strict derivative in left endpoint for a locally finite
 measure.
@@ -1996,7 +1998,7 @@ around `a`. Suppose that `f` has a finite limit `c` at `la' ⊓ μ.ae`.
 Then `∫ x in v..b, f x ∂μ - ∫ x in u..b, f x ∂μ = -∫ x in u..v, c ∂μ + o(∫ x in u..v, (1:ℝ) ∂μ)`
 as `u` and `v` tend to `la`.
 -/
-theorem measure_integral_sub_integral_sub_linear_isOCat_of_tendsto_ae_left
+theorem measure_integral_sub_integral_sub_linear_isLittleO_of_tendsto_ae_left
     (hab : IntervalIntegrable f μ a b) (hmeas : StronglyMeasurableAtFilter f la' μ)
     (hf : Tendsto f (la' ⊓ μ.ae) (𝓝 c)) (hu : Tendsto u lt la) (hv : Tendsto v lt la) :
     (fun t => ((∫ x in v t..b, f x ∂μ) - ∫ x in u t..b, f x ∂μ) + ∫ x in u t..v t, c ∂μ) =o[lt]
@@ -2006,7 +2008,7 @@ theorem measure_integral_sub_integral_sub_linear_isOCat_of_tendsto_ae_left
     measure_integral_sub_integral_sub_linear_is_o_of_tendsto_ae hab hmeas stronglyMeasurableAtBot hf
       ((tendsto_bot : tendsto _ ⊥ (𝓝 0)).mono_left inf_le_left) hu hv
       (tendsto_const_pure : tendsto _ _ (pure b)) tendsto_const_pure
-#align interval_integral.measure_integral_sub_integral_sub_linear_is_o_of_tendsto_ae_left intervalIntegral.measure_integral_sub_integral_sub_linear_isOCat_of_tendsto_ae_left
+#align interval_integral.measure_integral_sub_integral_sub_linear_is_o_of_tendsto_ae_left intervalIntegral.measure_integral_sub_integral_sub_linear_isLittleO_of_tendsto_ae_left
 
 end
 
@@ -2034,12 +2036,12 @@ we have no definition of `has_strict_(f)deriv_at_filter` in the library.
 /-- Fundamental theorem of calculus-1, local version. If `f` has a finite limit `c` almost surely at
 `l'`, where `(l, l')` is an `FTC_filter` pair around `a`, then
 `∫ x in u..v, f x ∂μ = (v - u) • c + o (v - u)` as both `u` and `v` tend to `l`. -/
-theorem integral_sub_linear_isOCat_of_tendsto_ae [FTCFilter a l l']
+theorem integral_sub_linear_isLittleO_of_tendsto_ae [FTCFilter a l l']
     (hfm : StronglyMeasurableAtFilter f l') (hf : Tendsto f (l' ⊓ volume.ae) (𝓝 c)) {u v : ι → ℝ}
     (hu : Tendsto u lt l) (hv : Tendsto v lt l) :
     (fun t => (∫ x in u t..v t, f x) - (v t - u t) • c) =o[lt] (v - u) := by
   simpa [integral_const] using measure_integral_sub_linear_is_o_of_tendsto_ae hfm hf hu hv
-#align interval_integral.integral_sub_linear_is_o_of_tendsto_ae intervalIntegral.integral_sub_linear_isOCat_of_tendsto_ae
+#align interval_integral.integral_sub_linear_is_o_of_tendsto_ae intervalIntegral.integral_sub_linear_isLittleO_of_tendsto_ae
 
 /-- Fundamental theorem of calculus-1, strict differentiability at filter in both endpoints.
 If `f` is a measurable function integrable on `a..b`, `(la, la')` is an `FTC_filter` pair around
@@ -2050,7 +2052,7 @@ almost surely at `la'` and `lb'`, respectively, then
 
 This lemma could've been formulated using `has_strict_fderiv_at_filter` if we had this
 definition. -/
-theorem integral_sub_integral_sub_linear_isOCat_of_tendsto_ae
+theorem integral_sub_integral_sub_linear_isLittleO_of_tendsto_ae
     (hab : IntervalIntegrable f volume a b) (hmeas_a : StronglyMeasurableAtFilter f la')
     (hmeas_b : StronglyMeasurableAtFilter f lb') (ha_lim : Tendsto f (la' ⊓ volume.ae) (𝓝 ca))
     (hb_lim : Tendsto f (lb' ⊓ volume.ae) (𝓝 cb)) (hua : Tendsto ua lt la) (hva : Tendsto va lt la)
@@ -2063,7 +2065,7 @@ theorem integral_sub_integral_sub_linear_isOCat_of_tendsto_ae
   simpa [integral_const] using
     measure_integral_sub_integral_sub_linear_is_o_of_tendsto_ae hab hmeas_a hmeas_b ha_lim hb_lim
       hua hva hub hvb
-#align interval_integral.integral_sub_integral_sub_linear_is_o_of_tendsto_ae intervalIntegral.integral_sub_integral_sub_linear_isOCat_of_tendsto_ae
+#align interval_integral.integral_sub_integral_sub_linear_is_o_of_tendsto_ae intervalIntegral.integral_sub_integral_sub_linear_isLittleO_of_tendsto_ae
 
 /-- Fundamental theorem of calculus-1, strict differentiability at filter in both endpoints.
 If `f` is a measurable function integrable on `a..b`, `(lb, lb')` is an `FTC_filter` pair
@@ -2071,13 +2073,13 @@ around `b`, and `f` has a finite limit `c` almost surely at `lb'`, then
 `(∫ x in a..v, f x) - ∫ x in a..u, f x = (v - u) • c + o(‖v - u‖)` as `u` and `v` tend to `lb`.
 
 This lemma could've been formulated using `has_strict_deriv_at_filter` if we had this definition. -/
-theorem integral_sub_integral_sub_linear_isOCat_of_tendsto_ae_right
+theorem integral_sub_integral_sub_linear_isLittleO_of_tendsto_ae_right
     (hab : IntervalIntegrable f volume a b) (hmeas : StronglyMeasurableAtFilter f lb')
     (hf : Tendsto f (lb' ⊓ volume.ae) (𝓝 c)) (hu : Tendsto u lt lb) (hv : Tendsto v lt lb) :
     (fun t => ((∫ x in a..v t, f x) - ∫ x in a..u t, f x) - (v t - u t) • c) =o[lt] (v - u) := by
   simpa only [integral_const, smul_eq_mul, mul_one] using
     measure_integral_sub_integral_sub_linear_is_o_of_tendsto_ae_right hab hmeas hf hu hv
-#align interval_integral.integral_sub_integral_sub_linear_is_o_of_tendsto_ae_right intervalIntegral.integral_sub_integral_sub_linear_isOCat_of_tendsto_ae_right
+#align interval_integral.integral_sub_integral_sub_linear_is_o_of_tendsto_ae_right intervalIntegral.integral_sub_integral_sub_linear_isLittleO_of_tendsto_ae_right
 
 /-- Fundamental theorem of calculus-1, strict differentiability at filter in both endpoints.
 If `f` is a measurable function integrable on `a..b`, `(la, la')` is an `FTC_filter` pair
@@ -2085,13 +2087,13 @@ around `a`, and `f` has a finite limit `c` almost surely at `la'`, then
 `(∫ x in v..b, f x) - ∫ x in u..b, f x = -(v - u) • c + o(‖v - u‖)` as `u` and `v` tend to `la`.
 
 This lemma could've been formulated using `has_strict_deriv_at_filter` if we had this definition. -/
-theorem integral_sub_integral_sub_linear_isOCat_of_tendsto_ae_left
+theorem integral_sub_integral_sub_linear_isLittleO_of_tendsto_ae_left
     (hab : IntervalIntegrable f volume a b) (hmeas : StronglyMeasurableAtFilter f la')
     (hf : Tendsto f (la' ⊓ volume.ae) (𝓝 c)) (hu : Tendsto u lt la) (hv : Tendsto v lt la) :
     (fun t => ((∫ x in v t..b, f x) - ∫ x in u t..b, f x) + (v t - u t) • c) =o[lt] (v - u) := by
   simpa only [integral_const, smul_eq_mul, mul_one] using
     measure_integral_sub_integral_sub_linear_is_o_of_tendsto_ae_left hab hmeas hf hu hv
-#align interval_integral.integral_sub_integral_sub_linear_is_o_of_tendsto_ae_left intervalIntegral.integral_sub_integral_sub_linear_isOCat_of_tendsto_ae_left
+#align interval_integral.integral_sub_integral_sub_linear_is_o_of_tendsto_ae_left intervalIntegral.integral_sub_integral_sub_linear_isLittleO_of_tendsto_ae_left
 
 open ContinuousLinearMap (fst snd smul_right sub_apply smulRight_apply coe_fst' coe_snd' map_sub)
 
@@ -2141,7 +2143,7 @@ theorem integral_hasStrictFderivAt_of_tendsto_ae (hf : IntervalIntegrable f volu
       ((continuous_fst.comp continuous_fst).Tendsto ((a, b), (a, b)))
       ((continuous_snd.comp continuous_snd).Tendsto ((a, b), (a, b)))
       ((continuous_snd.comp continuous_fst).Tendsto ((a, b), (a, b)))
-  refine' (this.congr_left _).trans_isO _
+  refine' (this.congr_left _).trans_isBigO _
   · intro x
     simp [sub_smul]
   · exact is_O_fst_prod.norm_left.add is_O_snd_prod.norm_left
@@ -2165,7 +2167,7 @@ the sense of strict differentiability. -/
 theorem integral_hasStrictDerivAt_of_tendsto_ae_right (hf : IntervalIntegrable f volume a b)
     (hmeas : StronglyMeasurableAtFilter f (𝓝 b)) (hb : Tendsto f (𝓝 b ⊓ volume.ae) (𝓝 c)) :
     HasStrictDerivAt (fun u => ∫ x in a..u, f x) c b :=
-  integral_sub_integral_sub_linear_isOCat_of_tendsto_ae_right hf hmeas hb continuousAt_snd
+  integral_sub_integral_sub_linear_isLittleO_of_tendsto_ae_right hf hmeas hb continuousAt_snd
     continuousAt_fst
 #align interval_integral.integral_has_strict_deriv_at_of_tendsto_ae_right intervalIntegral.integral_hasStrictDerivAt_of_tendsto_ae_right
 
@@ -2358,7 +2360,7 @@ theorem integral_hasFderivWithinAt_of_tendsto_ae (hf : IntervalIntegrable f volu
     integral_sub_integral_sub_linear_is_o_of_tendsto_ae hf hmeas_a hmeas_b ha hb
       (tendsto_const_pure.mono_right FTC_filter.pure_le : tendsto _ _ (𝓝[s] a)) tendsto_fst
       (tendsto_const_pure.mono_right FTC_filter.pure_le : tendsto _ _ (𝓝[t] b)) tendsto_snd
-  refine' (this.congr_left _).trans_isO _
+  refine' (this.congr_left _).trans_isBigO _
   · intro x
     simp [sub_smul]
   · exact is_O_fst_prod.norm_left.add is_O_snd_prod.norm_left
@@ -2426,7 +2428,7 @@ theorem integral_hasDerivWithinAt_of_tendsto_ae_right (hf : IntervalIntegrable f
     {s t : Set ℝ} [FTCFilter b (𝓝[s] b) (𝓝[t] b)] (hmeas : StronglyMeasurableAtFilter f (𝓝[t] b))
     (hb : Tendsto f (𝓝[t] b ⊓ volume.ae) (𝓝 c)) :
     HasDerivWithinAt (fun u => ∫ x in a..u, f x) c s b :=
-  integral_sub_integral_sub_linear_isOCat_of_tendsto_ae_right hf hmeas hb
+  integral_sub_integral_sub_linear_isLittleO_of_tendsto_ae_right hf hmeas hb
     (tendsto_const_pure.mono_right FTCFilter.pure_le) tendsto_id
 #align interval_integral.integral_has_deriv_within_at_of_tendsto_ae_right intervalIntegral.integral_hasDerivWithinAt_of_tendsto_ae_right
 

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: Yury G. Kudryashov, Patrick Massot, Sébastien Gouëzel
 
 ! This file was ported from Lean 3 source module measure_theory.integral.interval_integral
-! leanprover-community/mathlib commit 733fa0048f88bd38678c283c8c1bb1445ac5e23b
+! leanprover-community/mathlib commit 08a4542bec7242a5c60f179e4e49de8c0d677b1b
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -689,8 +689,9 @@ theorem integral_cases (f : ℝ → E) (a b) :
 theorem integral_undef (h : ¬IntervalIntegrable f μ a b) : (∫ x in a..b, f x ∂μ) = 0 := by
   cases' le_total a b with hab hab <;>
         simp only [integral_of_le, integral_of_ge, hab, neg_eq_zero] <;>
-      refine' integral_undef (not_imp_not.mpr integrable.integrable_on' _) <;>
-    simpa [hab] using not_and_distrib.mp h
+      refine' integral_undef (not_imp_not.mpr _ h) <;>
+    simpa only [hab, Ioc_eq_empty_of_le, integrable_on_empty, not_true, false_or_iff,
+      or_false_iff] using not_and_distrib.mp h
 #align interval_integral.integral_undef intervalIntegral.integral_undef
 
 theorem intervalIntegrableOfIntegralNeZero {a b : ℝ} {f : ℝ → E} {μ : Measure ℝ}

mathlib commit https://github.com/leanprover-community/mathlib/commit/ce7e9d53d4bbc38065db3b595cd5bd73c323bc1d

@@ -498,7 +498,7 @@ theorem compAddRight (hf : IntervalIntegrable f volume a b) (c : ℝ) :
   have Am : measure.map (fun x => x + c) volume = volume :=
     is_add_left_invariant.is_add_right_invariant.map_add_right_eq_self _
   rw [← Am] at hf
-  convert (MeasurableEmbedding.integrableOn_map_iff A).mp hf
+  convert(MeasurableEmbedding.integrableOn_map_iff A).mp hf
   rw [preimage_add_const_uIcc]
 #align interval_integrable.comp_add_right IntervalIntegrable.compAddRight
 
@@ -1812,7 +1812,7 @@ theorem measure_integral_sub_linear_isOCat_of_tendsto_ae' [IsMeasurablyGenerated
   have A := hf.integral_sub_linear_is_o_ae hfm hl (hu.Ioc hv)
   have B := hf.integral_sub_linear_is_o_ae hfm hl (hv.Ioc hu)
   simp only [integral_const']
-  convert (A.trans_le _).sub (B.trans_le _)
+  convert(A.trans_le _).sub (B.trans_le _)
   · ext t
     simp_rw [intervalIntegral, sub_smul]
     abel
@@ -2693,9 +2693,8 @@ theorem integral_le_sub_of_has_deriv_right_of_le (hab : a ≤ b) (hcont : Contin
     (hφg : ∀ x ∈ Ioo a b, φ x ≤ g' x) : (∫ y in a..b, φ y) ≤ g b - g a :=
   by
   rw [← neg_le_neg_iff]
-  convert
-    sub_le_integral_of_has_deriv_right_of_le hab hcont.neg (fun x hx => (hderiv x hx).neg) φint.neg
-      fun x hx => neg_le_neg (hφg x hx)
+  convert sub_le_integral_of_has_deriv_right_of_le hab hcont.neg (fun x hx => (hderiv x hx).neg)
+      φint.neg fun x hx => neg_le_neg (hφg x hx)
   · abel
   · simp only [← integral_neg]
     rfl

mathlib commit https://github.com/leanprover-community/mathlib/commit/ddec54a71a0dd025c05445d467f1a2b7d586a3ba

@@ -841,7 +841,7 @@ end Basic
 
 theorem integral_of_real {a b : ℝ} {μ : Measure ℝ} {f : ℝ → ℝ} :
     (∫ x in a..b, (f x : ℂ) ∂μ) = ↑(∫ x in a..b, f x ∂μ) := by
-  simp only [intervalIntegral, integral_of_real, Complex.of_real_sub]
+  simp only [intervalIntegral, integral_of_real, Complex.ofReal_sub]
 #align interval_integral.integral_of_real intervalIntegral.integral_of_real
 
 section ContinuousLinearMap

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

@@ -1634,7 +1634,7 @@ theorem integral_mono_interval {c d} (hca : c ≤ a) (hab : a ≤ b) (hbd : b 
     (∫ x in a..b, f x ∂μ) ≤ ∫ x in c..d, f x ∂μ :=
   by
   rw [integral_of_le hab, integral_of_le (hca.trans (hab.trans hbd))]
-  exact set_integral_mono_set hfi.1 hf (Ioc_subset_Ioc hca hbd).EventuallyLe
+  exact set_integral_mono_set hfi.1 hf (Ioc_subset_Ioc hca hbd).EventuallyLE
 #align interval_integral.integral_mono_interval intervalIntegral.integral_mono_interval
 
 theorem abs_integral_mono_interval {c d} (h : Ι a b ⊆ Ι c d) (hf : 0 ≤ᵐ[μ.restrict (Ι c d)] f)
@@ -1643,7 +1643,7 @@ theorem abs_integral_mono_interval {c d} (h : Ι a b ⊆ Ι c d) (hf : 0 ≤ᵐ[
   calc
     |∫ x in a..b, f x ∂μ| = |∫ x in Ι a b, f x ∂μ| := abs_integral_eq_abs_integral_uIoc f
     _ = ∫ x in Ι a b, f x ∂μ := (abs_of_nonneg (MeasureTheory.integral_nonneg_of_ae hf'))
-    _ ≤ ∫ x in Ι c d, f x ∂μ := (set_integral_mono_set hfi.def hf h.EventuallyLe)
+    _ ≤ ∫ x in Ι c d, f x ∂μ := (set_integral_mono_set hfi.def hf h.EventuallyLE)
     _ ≤ |∫ x in Ι c d, f x ∂μ| := (le_abs_self _)
     _ = |∫ x in c..d, f x ∂μ| := (abs_integral_eq_abs_integral_uIoc f).symm
     

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

@@ -1642,9 +1642,9 @@ theorem abs_integral_mono_interval {c d} (h : Ι a b ⊆ Ι c d) (hf : 0 ≤ᵐ[
   have hf' : 0 ≤ᵐ[μ.restrict (Ι a b)] f := ae_mono (Measure.restrict_mono h le_rfl) hf
   calc
     |∫ x in a..b, f x ∂μ| = |∫ x in Ι a b, f x ∂μ| := abs_integral_eq_abs_integral_uIoc f
-    _ = ∫ x in Ι a b, f x ∂μ := abs_of_nonneg (MeasureTheory.integral_nonneg_of_ae hf')
-    _ ≤ ∫ x in Ι c d, f x ∂μ := set_integral_mono_set hfi.def hf h.EventuallyLe
-    _ ≤ |∫ x in Ι c d, f x ∂μ| := le_abs_self _
+    _ = ∫ x in Ι a b, f x ∂μ := (abs_of_nonneg (MeasureTheory.integral_nonneg_of_ae hf'))
+    _ ≤ ∫ x in Ι c d, f x ∂μ := (set_integral_mono_set hfi.def hf h.EventuallyLe)
+    _ ≤ |∫ x in Ι c d, f x ∂μ| := (le_abs_self _)
     _ = |∫ x in c..d, f x ∂μ| := (abs_integral_eq_abs_integral_uIoc f).symm
     
 #align interval_integral.abs_integral_mono_interval intervalIntegral.abs_integral_mono_interval
@@ -2387,7 +2387,7 @@ theorem integral_hasFderivWithinAt (hf : IntervalIntegrable f volume a b)
     (hb.mono_left inf_le_left)
 #align interval_integral.integral_has_fderiv_within_at intervalIntegral.integral_hasFderivWithinAt
 
-/- ./././Mathport/Syntax/Translate/Expr.lean:334:4: warning: unsupported (TODO): `[tacs] -/
+/- ./././Mathport/Syntax/Translate/Expr.lean:330:4: warning: unsupported (TODO): `[tacs] -/
 /-- An auxiliary tactic closing goals `unique_diff_within_at ℝ s a` where
 `s ∈ {Iic a, Ici a, univ}`. -/
 unsafe def unique_diff_within_at_Ici_Iic_univ : tactic Unit :=
@@ -2629,7 +2629,7 @@ theorem sub_le_integral_of_has_deriv_right_of_le_Ico (hab : a ≤ b)
     refine' ⟨x, _, Ioc_subset_Ioc le_rfl (min_le_left _ _) h'x⟩
     calc
       g x - g a = g t - g a + (g x - g t) := by abel
-      _ ≤ (∫ w in a..t, (G' w).toReal) + ∫ w in t..x, (G' w).toReal := add_le_add ht.1 hx
+      _ ≤ (∫ w in a..t, (G' w).toReal) + ∫ w in t..x, (G' w).toReal := (add_le_add ht.1 hx)
       _ = ∫ w in a..x, (G' w).toReal :=
         by
         apply integral_add_adjacent_intervals

mathlib commit https://github.com/leanprover-community/mathlib/commit/9da1b3534b65d9661eb8f42443598a92bbb49211

@@ -2569,13 +2569,13 @@ theorem sub_le_integral_of_has_deriv_right_of_le_Ico (hab : a ≤ b)
     apply
       s_closed.Icc_subset_of_forall_exists_gt
         (by simp only [integral_same, mem_set_of_eq, sub_self]) fun t ht v t_lt_v => _
-    obtain ⟨y, g'_lt_y', y_lt_G'⟩ : ∃ y : ℝ, (g' t : Ereal) < y ∧ (y : Ereal) < G' t :=
-      Ereal.lt_iff_exists_real_btwn.1 ((Ereal.coe_le_coe_iff.2 (hφg t ht.2)).trans_lt (f_lt_G' t))
+    obtain ⟨y, g'_lt_y', y_lt_G'⟩ : ∃ y : ℝ, (g' t : EReal) < y ∧ (y : EReal) < G' t :=
+      EReal.lt_iff_exists_real_btwn.1 ((EReal.coe_le_coe_iff.2 (hφg t ht.2)).trans_lt (f_lt_G' t))
     -- bound from below the increase of `∫ x in a..u, G' x` on the right of `t`, using the lower
     -- semicontinuity of `G'`.
     have I1 : ∀ᶠ u in 𝓝[>] t, (u - t) * y ≤ ∫ w in t..u, (G' w).toReal :=
       by
-      have B : ∀ᶠ u in 𝓝 t, (y : Ereal) < G' u := G'cont.lower_semicontinuous_at _ _ y_lt_G'
+      have B : ∀ᶠ u in 𝓝 t, (y : EReal) < G' u := G'cont.lower_semicontinuous_at _ _ y_lt_G'
       rcases mem_nhds_iff_exists_Ioo_subset.1 B with ⟨m, M, ⟨hm, hM⟩, H⟩
       have : Ioo t (min M b) ∈ 𝓝[>] t :=
         mem_nhdsWithin_Ioi_iff_exists_Ioo_subset.2
@@ -2599,17 +2599,17 @@ theorem sub_le_integral_of_has_deriv_right_of_le_Ico (hab : a ≤ b)
             have C2 : ∀ᵐ x : ℝ ∂volume.restrict (Icc t u), x ∈ Icc t u :=
               ae_restrict_mem measurableSet_Icc
             filter_upwards [C1, C2]with x G'x hx
-            apply Ereal.coe_le_coe_iff.1
+            apply EReal.coe_le_coe_iff.1
             have : x ∈ Ioo m M := by
               simp only [hm.trans_le hx.left,
                 (hx.right.trans_lt hu.right).trans_le (min_le_left M b), mem_Ioo, and_self_iff]
             convert le_of_lt (H this)
-            exact Ereal.coe_toReal G'x.ne (ne_bot_of_gt (f_lt_G' x))
+            exact EReal.coe_toReal G'x.ne (ne_bot_of_gt (f_lt_G' x))
         
     -- bound from above the increase of `g u - g a` on the right of `t`, using the derivative at `t`
     have I2 : ∀ᶠ u in 𝓝[>] t, g u - g t ≤ (u - t) * y :=
       by
-      have g'_lt_y : g' t < y := Ereal.coe_lt_coe_iff.1 g'_lt_y'
+      have g'_lt_y : g' t < y := EReal.coe_lt_coe_iff.1 g'_lt_y'
       filter_upwards [(hderiv t ⟨ht.2.1, ht.2.2⟩).limsup_slope_le' (not_mem_Ioi.2 le_rfl) g'_lt_y,
         self_mem_nhdsWithin]with u hu t_lt_u
       have := mul_le_mul_of_nonneg_left hu.le (sub_pos.2 t_lt_u).le

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

@@ -174,7 +174,7 @@ open TopologicalSpace (SecondCountableTopology)
 
 open MeasureTheory Set Classical Filter Function
 
-open Classical Topology Filter Ennreal BigOperators Interval NNReal
+open Classical Topology Filter ENNReal BigOperators Interval NNReal
 
 variable {ι 𝕜 E F A : Type _} [NormedAddCommGroup E]
 
@@ -470,7 +470,7 @@ theorem compMulLeft (hf : IntervalIntegrable f volume a b) (c : ℝ) :
   have A : MeasurableEmbedding fun x => x * c⁻¹ :=
     (Homeomorph.mulRight₀ _ (inv_ne_zero hc)).ClosedEmbedding.MeasurableEmbedding
   rw [← Real.smul_map_volume_mul_right (inv_ne_zero hc), integrable_on, measure.restrict_smul,
-    integrable_smul_measure (by simpa : Ennreal.ofReal (|c⁻¹|) ≠ 0) Ennreal.ofReal_ne_top, ←
+    integrable_smul_measure (by simpa : ENNReal.ofReal (|c⁻¹|) ≠ 0) ENNReal.ofReal_ne_top, ←
     integrable_on, MeasurableEmbedding.integrableOn_map_iff A]
   convert hf using 1
   · ext
@@ -755,8 +755,8 @@ theorem norm_integral_le_of_norm_le_const_ae {a b C : ℝ} {f : ℝ → E}
   by
   rw [norm_integral_eq_norm_integral_Ioc]
   convert norm_set_integral_le_of_norm_le_const_ae'' _ measurableSet_Ioc h
-  · rw [Real.volume_Ioc, max_sub_min_eq_abs, Ennreal.toReal_ofReal (abs_nonneg _)]
-  · simp only [Real.volume_Ioc, Ennreal.ofReal_lt_top]
+  · rw [Real.volume_Ioc, max_sub_min_eq_abs, ENNReal.toReal_ofReal (abs_nonneg _)]
+  · simp only [Real.volume_Ioc, ENNReal.ofReal_lt_top]
 #align interval_integral.norm_integral_le_of_norm_le_const_ae intervalIntegral.norm_integral_le_of_norm_le_const_ae
 
 theorem norm_integral_le_of_norm_le_const {a b C : ℝ} {f : ℝ → E} (h : ∀ x ∈ Ι a b, ‖f x‖ ≤ C) :
@@ -828,7 +828,7 @@ theorem integral_const' (c : E) :
 
 @[simp]
 theorem integral_const (c : E) : (∫ x in a..b, c) = (b - a) • c := by
-  simp only [integral_const', Real.volume_Ioc, Ennreal.toReal_of_real', ← neg_sub b,
+  simp only [integral_const', Real.volume_Ioc, ENNReal.toReal_ofReal', ← neg_sub b,
     max_zero_sub_eq_self]
 #align interval_integral.integral_const intervalIntegral.integral_const
 
@@ -879,7 +879,7 @@ theorem integral_comp_mul_right (hc : c ≠ 0) :
     (Homeomorph.mulRight₀ c hc).ClosedEmbedding.MeasurableEmbedding
   conv_rhs => rw [← Real.smul_map_volume_mul_right hc]
   simp_rw [integral_smul_measure, intervalIntegral, A.set_integral_map,
-    Ennreal.toReal_ofReal (abs_nonneg c)]
+    ENNReal.toReal_ofReal (abs_nonneg c)]
   cases hc.lt_or_lt
   · simp [h, mul_div_cancel, hc, abs_of_neg, measure.restrict_congr_set Ico_ae_eq_Ioc]
   · simp [h, mul_div_cancel, hc, abs_of_pos]
@@ -2587,12 +2587,12 @@ theorem sub_le_integral_of_has_deriv_right_of_le_Ico (hab : a ≤ b)
         (u - t) * y = ∫ v in Icc t u, y := by
           simp only [hu.left.le, MeasureTheory.integral_const, Algebra.id.smul_eq_mul, sub_nonneg,
             MeasurableSet.univ, Real.volume_Icc, measure.restrict_apply, univ_inter,
-            Ennreal.toReal_ofReal]
+            ENNReal.toReal_ofReal]
         _ ≤ ∫ w in t..u, (G' w).toReal :=
           by
           rw [intervalIntegral.integral_of_le hu.1.le, ← integral_Icc_eq_integral_Ioc]
           apply set_integral_mono_ae_restrict
-          · simp only [integrable_on_const, Real.volume_Icc, Ennreal.ofReal_lt_top, or_true_iff]
+          · simp only [integrable_on_const, Real.volume_Icc, ENNReal.ofReal_lt_top, or_true_iff]
           · exact integrable_on.mono_set G'int I
           · have C1 : ∀ᵐ x : ℝ ∂volume.restrict (Icc t u), G' x < ∞ :=
               ae_mono (measure.restrict_mono I le_rfl) G'lt_top
@@ -2814,20 +2814,20 @@ theorem integrableOnDerivRightOfNonneg (hab : a ≤ b) (hcont : ContinuousOn g (
     apply (aeMeasurableDerivWithinIoi g _).congr
     refine' (ae_restrict_mem measurableSet_Ioo).mono fun x hx => _
     exact (hderiv x hx).derivWithin (uniqueDiffWithinAt_Ioi _)
-  suffices H : (∫⁻ x in Ioo a b, ‖g' x‖₊) ≤ Ennreal.ofReal (g b - g a)
-  exact ⟨meas_g'.ae_strongly_measurable, H.trans_lt Ennreal.ofReal_lt_top⟩
+  suffices H : (∫⁻ x in Ioo a b, ‖g' x‖₊) ≤ ENNReal.ofReal (g b - g a)
+  exact ⟨meas_g'.ae_strongly_measurable, H.trans_lt ENNReal.ofReal_lt_top⟩
   by_contra' H
   obtain ⟨f, fle, fint, hf⟩ :
     ∃ f : simple_func ℝ ℝ≥0,
       (∀ x, f x ≤ ‖g' x‖₊) ∧
-        (∫⁻ x : ℝ in Ioo a b, f x) < ∞ ∧ Ennreal.ofReal (g b - g a) < ∫⁻ x : ℝ in Ioo a b, f x :=
+        (∫⁻ x : ℝ in Ioo a b, f x) < ∞ ∧ ENNReal.ofReal (g b - g a) < ∫⁻ x : ℝ in Ioo a b, f x :=
     exists_lt_lintegral_simple_func_of_lt_lintegral H
   let F : ℝ → ℝ := coe ∘ f
   have intF : integrable_on F (Ioo a b) :=
     by
     refine' ⟨f.measurable.coe_nnreal_real.ae_strongly_measurable, _⟩
     simpa only [has_finite_integral, NNReal.nnnorm_eq] using fint
-  have A : (∫⁻ x : ℝ in Ioo a b, f x) = Ennreal.ofReal (∫ x in Ioo a b, F x) :=
+  have A : (∫⁻ x : ℝ in Ioo a b, f x) = ENNReal.ofReal (∫ x in Ioo a b, F x) :=
     lintegral_coe_eq_integral _ intF
   rw [A] at hf
   have B : (∫ x : ℝ in Ioo a b, F x) ≤ g b - g a :=
@@ -2837,7 +2837,7 @@ theorem integrableOnDerivRightOfNonneg (hab : a ≤ b) (hcont : ContinuousOn g (
     · rwa [integrableOn_Icc_iff_integrableOn_Ioo]
     · convert NNReal.coe_le_coe.2 (fle x)
       simp only [Real.norm_of_nonneg (g'pos x hx), coe_nnnorm]
-  exact lt_irrefl _ (hf.trans_le (Ennreal.ofReal_le_ofReal B))
+  exact lt_irrefl _ (hf.trans_le (ENNReal.ofReal_le_ofReal B))
 #align interval_integral.integrable_on_deriv_right_of_nonneg intervalIntegral.integrableOnDerivRightOfNonneg
 
 /-- When the derivative of a function is nonnegative, then it is automatically integrable,

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

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury G. Kudryashov, Patrick Massot, Sébastien Gouëzel
 
 ! This file was ported from Lean 3 source module measure_theory.integral.interval_integral
-! leanprover-community/mathlib commit e7286cac412124bcb9114d1403c43c8a0f644f09
+! leanprover-community/mathlib commit 733fa0048f88bd38678c283c8c1bb1445ac5e23b
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -1235,6 +1235,32 @@ theorem hasSum_integral_of_dominated_convergence {ι} [Countable ι] {F : ι →
 
 open TopologicalSpace
 
+/-- Interval integrals commute with countable sums, when the supremum norms are summable (a
+special case of the dominated convergence theorem). -/
+theorem hasSum_intervalIntegral_of_summable_norm [Countable ι] {f : ι → C(ℝ, E)}
+    (hf_sum : Summable fun i : ι => ‖(f i).restrict (⟨uIcc a b, isCompact_uIcc⟩ : Compacts ℝ)‖) :
+    HasSum (fun i : ι => ∫ x in a..b, f i x) (∫ x in a..b, ∑' i : ι, f i x) :=
+  by
+  refine'
+    has_sum_integral_of_dominated_convergence
+      (fun i (x : ℝ) => ‖(f i).restrict ↑(⟨uIcc a b, isCompact_uIcc⟩ : compacts ℝ)‖)
+      (fun i => (map_continuous <| f i).AeStronglyMeasurable)
+      (fun i =>
+        ae_of_all _ fun x hx =>
+          ((f i).restrict ↑(⟨uIcc a b, isCompact_uIcc⟩ : compacts ℝ)).norm_coe_le_norm
+            ⟨x, ⟨hx.1.le, hx.2⟩⟩)
+      (ae_of_all _ fun x hx => hf_sum) intervalIntegrableConst
+      (ae_of_all _ fun x hx => Summable.hasSum _)
+  -- next line is slow, & doesn't work with "exact" in place of "apply" -- ?
+  apply ContinuousMap.summable_apply (summable_of_summable_norm hf_sum) ⟨x, ⟨hx.1.le, hx.2⟩⟩
+#align interval_integral.has_sum_interval_integral_of_summable_norm intervalIntegral.hasSum_intervalIntegral_of_summable_norm
+
+theorem tsum_intervalIntegral_eq_of_summable_norm [Countable ι] {f : ι → C(ℝ, E)}
+    (hf_sum : Summable fun i : ι => ‖(f i).restrict (⟨uIcc a b, isCompact_uIcc⟩ : Compacts ℝ)‖) :
+    (∑' i : ι, ∫ x in a..b, f i x) = ∫ x in a..b, ∑' i : ι, f i x :=
+  (hasSum_intervalIntegral_of_summable_norm hf_sum).tsum_eq
+#align interval_integral.tsum_interval_integral_eq_of_summable_norm intervalIntegral.tsum_intervalIntegral_eq_of_summable_norm
+
 variable {X : Type _} [TopologicalSpace X] [FirstCountableTopology X]
 
 /-- Continuity of interval integral with respect to a parameter, at a point within a set.

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

A PR accompanying #12339.

Zulip discussion

@@ -1043,7 +1043,7 @@ nonrec theorem integral_indicator {a₁ a₂ a₃ : ℝ} (h : a₂ ∈ Icc a₁
   have : {x | x ≤ a₂} ∩ Ioc a₁ a₃ = Ioc a₁ a₂ := Iic_inter_Ioc_of_le h.2
   rw [integral_of_le h.1, integral_of_le (h.1.trans h.2), integral_indicator,
     Measure.restrict_restrict, this]
-  exact measurableSet_Iic
+  · exact measurableSet_Iic
   all_goals apply measurableSet_Iic
 #align interval_integral.integral_indicator intervalIntegral.integral_indicator
 

This lets us unify a few lemmas between GroupWithZero and EuclideanDomain and two lemmas that were previously proved separately for Nat, Int, Polynomial.

@@ -315,7 +315,7 @@ theorem comp_mul_left (hf : IntervalIntegrable f volume a b) (c : ℝ) :
     integrable_smul_measure (by simpa : ENNReal.ofReal |c⁻¹| ≠ 0) ENNReal.ofReal_ne_top,
     ← IntegrableOn, MeasurableEmbedding.integrableOn_map_iff A]
   convert hf using 1
-  · ext; simp only [comp_apply]; congr 1; field_simp; ring
+  · ext; simp only [comp_apply]; congr 1; field_simp
   · rw [preimage_mul_const_uIcc (inv_ne_zero hc)]; field_simp [hc]
 #align interval_integrable.comp_mul_left IntervalIntegrable.comp_mul_left
 

Move Set.Ixx, Finset.Ixx, Multiset.Ixx together under two different folders:

• Order.Interval for their definition and basic properties
• Algebra.Order.Interval for their algebraic properties

Move the definitions of Multiset.Ixx to what is now Order.Interval.Multiset. I believe we could just delete this file in a later PR as nothing uses it (and I already had doubts when defining Multiset.Ixx three years ago).

Move the algebraic results out of what is now Order.Interval.Finset.Basic to a new file Algebra.Order.Interval.Finset.Basic.

@@ -3,7 +3,7 @@ Copyright (c) 2020 Yury G. Kudryashov. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury G. Kudryashov, Patrick Massot, Sébastien Gouëzel
 -/
-import Mathlib.Data.Set.Intervals.Disjoint
+import Mathlib.Order.Interval.Set.Disjoint
 import Mathlib.MeasureTheory.Integral.SetIntegral
 import Mathlib.MeasureTheory.Measure.Lebesgue.Basic
 

Done with a global search and replace, and then (to fix the #align lines), replace (#align \S*)setIntegral with $1set_integral.

@@ -587,7 +587,7 @@ nonrec theorem norm_integral_le_of_norm_le {g : ℝ → ℝ} (h : ∀ᵐ t ∂μ
 theorem norm_integral_le_of_norm_le_const_ae {a b C : ℝ} {f : ℝ → E}
     (h : ∀ᵐ x, x ∈ Ι a b → ‖f x‖ ≤ C) : ‖∫ x in a..b, f x‖ ≤ C * |b - a| := by
   rw [norm_integral_eq_norm_integral_Ioc]
-  convert norm_set_integral_le_of_norm_le_const_ae'' _ measurableSet_Ioc h using 1
+  convert norm_setIntegral_le_of_norm_le_const_ae'' _ measurableSet_Ioc h using 1
   · rw [Real.volume_Ioc, max_sub_min_eq_abs, ENNReal.toReal_ofReal (abs_nonneg _)]
   · simp only [Real.volume_Ioc, ENNReal.ofReal_lt_top]
 #align interval_integral.norm_integral_le_of_norm_le_const_ae intervalIntegral.norm_integral_le_of_norm_le_const_ae
@@ -654,7 +654,7 @@ theorem integral_div {𝕜 : Type*} [RCLike 𝕜] (r : 𝕜) (f : ℝ → 𝕜)
 
 theorem integral_const' (c : E) :
     ∫ _ in a..b, c ∂μ = ((μ <| Ioc a b).toReal - (μ <| Ioc b a).toReal) • c := by
-  simp only [intervalIntegral, set_integral_const, sub_smul]
+  simp only [intervalIntegral, setIntegral_const, sub_smul]
 #align interval_integral.integral_const' intervalIntegral.integral_const'
 
 @[simp]
@@ -723,7 +723,7 @@ theorem integral_comp_mul_right (hc : c ≠ 0) :
   have A : MeasurableEmbedding fun x => x * c :=
     (Homeomorph.mulRight₀ c hc).closedEmbedding.measurableEmbedding
   conv_rhs => rw [← Real.smul_map_volume_mul_right hc]
-  simp_rw [integral_smul_measure, intervalIntegral, A.set_integral_map,
+  simp_rw [integral_smul_measure, intervalIntegral, A.setIntegral_map,
     ENNReal.toReal_ofReal (abs_nonneg c)]
   cases' hc.lt_or_lt with h h
   · simp [h, mul_div_cancel_right₀, hc, abs_of_neg,
@@ -765,7 +765,7 @@ theorem integral_comp_add_right (d) : (∫ x in a..b, f (x + d)) = ∫ x in a +
     (Homeomorph.addRight d).closedEmbedding.measurableEmbedding
   calc
     (∫ x in a..b, f (x + d)) = ∫ x in a + d..b + d, f x ∂Measure.map (fun x => x + d) volume := by
-      simp [intervalIntegral, A.set_integral_map]
+      simp [intervalIntegral, A.setIntegral_map]
     _ = ∫ x in a + d..b + d, f x := by rw [map_add_right_eq_self]
 #align interval_integral.integral_comp_add_right intervalIntegral.integral_comp_add_right
 
@@ -908,7 +908,7 @@ theorem integral_congr {a b : ℝ} (h : EqOn f g [[a, b]]) :
     ∫ x in a..b, f x ∂μ = ∫ x in a..b, g x ∂μ := by
   rcases le_total a b with hab | hab <;>
     simpa [hab, integral_of_le, integral_of_ge] using
-      set_integral_congr measurableSet_Ioc (h.mono Ioc_subset_Icc_self)
+      setIntegral_congr measurableSet_Ioc (h.mono Ioc_subset_Icc_self)
 #align interval_integral.integral_congr intervalIntegral.integral_congr
 
 theorem integral_add_adjacent_intervals_cancel (hab : IntervalIntegrable f μ a b)
@@ -1008,7 +1008,7 @@ theorem integral_Iio_add_Ici (h_left : IntegrableOn f (Iio b) μ)
 /-- If `μ` is a finite measure then `∫ x in a..b, c ∂μ = (μ (Iic b) - μ (Iic a)) • c`. -/
 theorem integral_const_of_cdf [IsFiniteMeasure μ] (c : E) :
     ∫ _ in a..b, c ∂μ = ((μ (Iic b)).toReal - (μ (Iic a)).toReal) • c := by
-  simp only [sub_smul, ← set_integral_const]
+  simp only [sub_smul, ← setIntegral_const]
   refine' (integral_Iic_sub_Iic _ _).symm <;>
     simp only [integrableOn_const, measure_lt_top, or_true_iff]
 #align interval_integral.integral_const_of_cdf intervalIntegral.integral_const_of_cdf
@@ -1023,8 +1023,8 @@ theorem integral_eq_integral_of_support_subset {a b} (h : support f ⊆ Ioc a b)
 
 theorem integral_congr_ae' (h : ∀ᵐ x ∂μ, x ∈ Ioc a b → f x = g x)
     (h' : ∀ᵐ x ∂μ, x ∈ Ioc b a → f x = g x) : ∫ x in a..b, f x ∂μ = ∫ x in a..b, g x ∂μ := by
-  simp only [intervalIntegral, set_integral_congr_ae measurableSet_Ioc h,
-    set_integral_congr_ae measurableSet_Ioc h']
+  simp only [intervalIntegral, setIntegral_congr_ae measurableSet_Ioc h,
+    setIntegral_congr_ae measurableSet_Ioc h']
 #align interval_integral.integral_congr_ae' intervalIntegral.integral_congr_ae'
 
 theorem integral_congr_ae (h : ∀ᵐ x ∂μ, x ∈ Ι a b → f x = g x) :
@@ -1076,7 +1076,7 @@ theorem integral_pos_iff_support_of_nonneg_ae' (hf : 0 ≤ᵐ[μ.restrict (Ι a
   cases' lt_or_le a b with hab hba
   · rw [uIoc_of_le hab.le] at hf
     simp only [hab, true_and_iff, integral_of_le hab.le,
-      set_integral_pos_iff_support_of_nonneg_ae hf hfi.1]
+      setIntegral_pos_iff_support_of_nonneg_ae hf hfi.1]
   · suffices (∫ x in a..b, f x ∂μ) ≤ 0 by simp only [this.not_lt, hba.not_lt, false_and_iff]
     rw [integral_of_ge hba, neg_nonpos]
     rw [uIoc_comm, uIoc_of_le hba] at hf
@@ -1151,7 +1151,7 @@ theorem integral_lt_integral_of_continuousOn_of_le_of_exists_lt {f g : ℝ → 
 theorem integral_nonneg_of_ae_restrict (hab : a ≤ b) (hf : 0 ≤ᵐ[μ.restrict (Icc a b)] f) :
     0 ≤ ∫ u in a..b, f u ∂μ := by
   let H := ae_restrict_of_ae_restrict_of_subset Ioc_subset_Icc_self hf
-  simpa only [integral_of_le hab] using set_integral_nonneg_of_ae_restrict H
+  simpa only [integral_of_le hab] using setIntegral_nonneg_of_ae_restrict H
 #align interval_integral.integral_nonneg_of_ae_restrict intervalIntegral.integral_nonneg_of_ae_restrict
 
 theorem integral_nonneg_of_ae (hab : a ≤ b) (hf : 0 ≤ᵐ[μ] f) : 0 ≤ ∫ u in a..b, f u ∂μ :=
@@ -1178,17 +1178,17 @@ variable (hab : a ≤ b) (hf : IntervalIntegrable f μ a b) (hg : IntervalIntegr
 theorem integral_mono_ae_restrict (h : f ≤ᵐ[μ.restrict (Icc a b)] g) :
     (∫ u in a..b, f u ∂μ) ≤ ∫ u in a..b, g u ∂μ := by
   let H := h.filter_mono <| ae_mono <| Measure.restrict_mono Ioc_subset_Icc_self <| le_refl μ
-  simpa only [integral_of_le hab] using set_integral_mono_ae_restrict hf.1 hg.1 H
+  simpa only [integral_of_le hab] using setIntegral_mono_ae_restrict hf.1 hg.1 H
 #align interval_integral.integral_mono_ae_restrict intervalIntegral.integral_mono_ae_restrict
 
 theorem integral_mono_ae (h : f ≤ᵐ[μ] g) : (∫ u in a..b, f u ∂μ) ≤ ∫ u in a..b, g u ∂μ := by
-  simpa only [integral_of_le hab] using set_integral_mono_ae hf.1 hg.1 h
+  simpa only [integral_of_le hab] using setIntegral_mono_ae hf.1 hg.1 h
 #align interval_integral.integral_mono_ae intervalIntegral.integral_mono_ae
 
 theorem integral_mono_on (h : ∀ x ∈ Icc a b, f x ≤ g x) :
     (∫ u in a..b, f u ∂μ) ≤ ∫ u in a..b, g u ∂μ := by
   let H x hx := h x <| Ioc_subset_Icc_self hx
-  simpa only [integral_of_le hab] using set_integral_mono_on hf.1 hg.1 measurableSet_Ioc H
+  simpa only [integral_of_le hab] using setIntegral_mono_on hf.1 hg.1 measurableSet_Ioc H
 #align interval_integral.integral_mono_on intervalIntegral.integral_mono_on
 
 theorem integral_mono (h : f ≤ g) : (∫ u in a..b, f u ∂μ) ≤ ∫ u in a..b, g u ∂μ :=
@@ -1199,7 +1199,7 @@ theorem integral_mono_interval {c d} (hca : c ≤ a) (hab : a ≤ b) (hbd : b 
     (hf : 0 ≤ᵐ[μ.restrict (Ioc c d)] f) (hfi : IntervalIntegrable f μ c d) :
     (∫ x in a..b, f x ∂μ) ≤ ∫ x in c..d, f x ∂μ := by
   rw [integral_of_le hab, integral_of_le (hca.trans (hab.trans hbd))]
-  exact set_integral_mono_set hfi.1 hf (Ioc_subset_Ioc hca hbd).eventuallyLE
+  exact setIntegral_mono_set hfi.1 hf (Ioc_subset_Ioc hca hbd).eventuallyLE
 #align interval_integral.integral_mono_interval intervalIntegral.integral_mono_interval
 
 theorem abs_integral_mono_interval {c d} (h : Ι a b ⊆ Ι c d) (hf : 0 ≤ᵐ[μ.restrict (Ι c d)] f)
@@ -1208,7 +1208,7 @@ theorem abs_integral_mono_interval {c d} (h : Ι a b ⊆ Ι c d) (hf : 0 ≤ᵐ[
   calc
     |∫ x in a..b, f x ∂μ| = |∫ x in Ι a b, f x ∂μ| := abs_integral_eq_abs_integral_uIoc f
     _ = ∫ x in Ι a b, f x ∂μ := abs_of_nonneg (MeasureTheory.integral_nonneg_of_ae hf')
-    _ ≤ ∫ x in Ι c d, f x ∂μ := set_integral_mono_set hfi.def' hf h.eventuallyLE
+    _ ≤ ∫ x in Ι c d, f x ∂μ := setIntegral_mono_set hfi.def' hf h.eventuallyLE
     _ ≤ |∫ x in Ι c d, f x ∂μ| := le_abs_self _
     _ = |∫ x in c..d, f x ∂μ| := (abs_integral_eq_abs_integral_uIoc f).symm
 #align interval_integral.abs_integral_mono_interval intervalIntegral.abs_integral_mono_interval

Now that I am defining NNRat.cast, I want a definitive answer to this naming issue. Plenty of lemmas in mathlib already use natCast/intCast/ratCast over nat_cast/int_cast/rat_cast, and this matches with the general expectation that underscore-separated name parts correspond to a single declaration.

@@ -1224,9 +1224,9 @@ variable {μ : Measure ℝ} {f : ℝ → E}
 theorem _root_.MeasureTheory.Integrable.hasSum_intervalIntegral (hfi : Integrable f μ) (y : ℝ) :
     HasSum (fun n : ℤ => ∫ x in y + n..y + n + 1, f x ∂μ) (∫ x, f x ∂μ) := by
   simp_rw [integral_of_le (le_add_of_nonneg_right zero_le_one)]
-  rw [← integral_univ, ← iUnion_Ioc_add_int_cast y]
+  rw [← integral_univ, ← iUnion_Ioc_add_intCast y]
   exact
-    hasSum_integral_iUnion (fun i => measurableSet_Ioc) (pairwise_disjoint_Ioc_add_int_cast y)
+    hasSum_integral_iUnion (fun i => measurableSet_Ioc) (pairwise_disjoint_Ioc_add_intCast y)
       hfi.integrableOn
 #align measure_theory.integrable.has_sum_interval_integral MeasureTheory.Integrable.hasSum_intervalIntegral
 

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

@@ -1207,9 +1207,9 @@ theorem abs_integral_mono_interval {c d} (h : Ι a b ⊆ Ι c d) (hf : 0 ≤ᵐ[
   have hf' : 0 ≤ᵐ[μ.restrict (Ι a b)] f := ae_mono (Measure.restrict_mono h le_rfl) hf
   calc
     |∫ x in a..b, f x ∂μ| = |∫ x in Ι a b, f x ∂μ| := abs_integral_eq_abs_integral_uIoc f
-    _ = ∫ x in Ι a b, f x ∂μ := (abs_of_nonneg (MeasureTheory.integral_nonneg_of_ae hf'))
-    _ ≤ ∫ x in Ι c d, f x ∂μ := (set_integral_mono_set hfi.def' hf h.eventuallyLE)
-    _ ≤ |∫ x in Ι c d, f x ∂μ| := (le_abs_self _)
+    _ = ∫ x in Ι a b, f x ∂μ := abs_of_nonneg (MeasureTheory.integral_nonneg_of_ae hf')
+    _ ≤ ∫ x in Ι c d, f x ∂μ := set_integral_mono_set hfi.def' hf h.eventuallyLE
+    _ ≤ |∫ x in Ι c d, f x ∂μ| := le_abs_self _
     _ = |∫ x in c..d, f x ∂μ| := (abs_integral_eq_abs_integral_uIoc f).symm
 #align interval_integral.abs_integral_mono_interval intervalIntegral.abs_integral_mono_interval
 

@@ -671,13 +671,15 @@ nonrec theorem integral_smul_measure (c : ℝ≥0∞) :
 end Basic
 
 -- Porting note (#11215): TODO: add `Complex.ofReal` version of `_root_.integral_ofReal`
-nonrec theorem _root_.RCLike.interval_integral_ofReal {𝕜 : Type*} [RCLike 𝕜] {a b : ℝ}
+nonrec theorem _root_.RCLike.intervalIntegral_ofReal {𝕜 : Type*} [RCLike 𝕜] {a b : ℝ}
     {μ : Measure ℝ} {f : ℝ → ℝ} : (∫ x in a..b, (f x : 𝕜) ∂μ) = ↑(∫ x in a..b, f x ∂μ) := by
   simp only [intervalIntegral, integral_ofReal, RCLike.ofReal_sub]
 
+@[deprecated] alias RCLike.interval_integral_ofReal := RCLike.intervalIntegral_ofReal -- 2024-04-06
+
 nonrec theorem integral_ofReal {a b : ℝ} {μ : Measure ℝ} {f : ℝ → ℝ} :
     (∫ x in a..b, (f x : ℂ) ∂μ) = ↑(∫ x in a..b, f x ∂μ) :=
-  RCLike.interval_integral_ofReal
+  RCLike.intervalIntegral_ofReal
 #align interval_integral.integral_of_real intervalIntegral.integral_ofReal
 
 section ContinuousLinearMap

@@ -1105,7 +1105,7 @@ theorem intervalIntegral_pos_of_pos_on {f : ℝ → ℝ} {a b : ℝ} (hfi : Inte
 #align interval_integral.interval_integral_pos_of_pos_on intervalIntegral.intervalIntegral_pos_of_pos_on
 
 /-- If `f : ℝ → ℝ` is strictly positive everywhere, and integrable on `(a, b]` for real numbers
-`a < b`, then its integral over `a..b` is strictly positive. (See `interval_integral_pos_of_pos_on`
+`a < b`, then its integral over `a..b` is strictly positive. (See `intervalIntegral_pos_of_pos_on`
 for a version only assuming positivity of `f` on `(a, b)` rather than everywhere.) -/
 theorem intervalIntegral_pos_of_pos {f : ℝ → ℝ} {a b : ℝ}
     (hfi : IntervalIntegrable f MeasureSpace.volume a b) (hpos : ∀ x, 0 < f x) (hab : a < b) :

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

@@ -629,25 +629,25 @@ nonrec theorem integral_smul {𝕜 : Type*} [NontriviallyNormedField 𝕜] [Norm
 #align interval_integral.integral_smul intervalIntegral.integral_smul
 
 @[simp]
-nonrec theorem integral_smul_const {𝕜 : Type*} [IsROrC 𝕜] [NormedSpace 𝕜 E] (f : ℝ → 𝕜) (c : E) :
+nonrec theorem integral_smul_const {𝕜 : Type*} [RCLike 𝕜] [NormedSpace 𝕜 E] (f : ℝ → 𝕜) (c : E) :
     ∫ x in a..b, f x • c ∂μ = (∫ x in a..b, f x ∂μ) • c := by
   simp only [intervalIntegral_eq_integral_uIoc, integral_smul_const, smul_assoc]
 #align interval_integral.integral_smul_const intervalIntegral.integral_smul_const
 
 @[simp]
-theorem integral_const_mul {𝕜 : Type*} [IsROrC 𝕜] (r : 𝕜) (f : ℝ → 𝕜) :
+theorem integral_const_mul {𝕜 : Type*} [RCLike 𝕜] (r : 𝕜) (f : ℝ → 𝕜) :
     ∫ x in a..b, r * f x ∂μ = r * ∫ x in a..b, f x ∂μ :=
   integral_smul r f
 #align interval_integral.integral_const_mul intervalIntegral.integral_const_mul
 
 @[simp]
-theorem integral_mul_const {𝕜 : Type*} [IsROrC 𝕜] (r : 𝕜) (f : ℝ → 𝕜) :
+theorem integral_mul_const {𝕜 : Type*} [RCLike 𝕜] (r : 𝕜) (f : ℝ → 𝕜) :
     ∫ x in a..b, f x * r ∂μ = (∫ x in a..b, f x ∂μ) * r := by
   simpa only [mul_comm r] using integral_const_mul r f
 #align interval_integral.integral_mul_const intervalIntegral.integral_mul_const
 
 @[simp]
-theorem integral_div {𝕜 : Type*} [IsROrC 𝕜] (r : 𝕜) (f : ℝ → 𝕜) :
+theorem integral_div {𝕜 : Type*} [RCLike 𝕜] (r : 𝕜) (f : ℝ → 𝕜) :
     ∫ x in a..b, f x / r ∂μ = (∫ x in a..b, f x ∂μ) / r := by
   simpa only [div_eq_mul_inv] using integral_mul_const r⁻¹ f
 #align interval_integral.integral_div intervalIntegral.integral_div
@@ -671,19 +671,19 @@ nonrec theorem integral_smul_measure (c : ℝ≥0∞) :
 end Basic
 
 -- Porting note (#11215): TODO: add `Complex.ofReal` version of `_root_.integral_ofReal`
-nonrec theorem _root_.IsROrC.interval_integral_ofReal {𝕜 : Type*} [IsROrC 𝕜] {a b : ℝ}
+nonrec theorem _root_.RCLike.interval_integral_ofReal {𝕜 : Type*} [RCLike 𝕜] {a b : ℝ}
     {μ : Measure ℝ} {f : ℝ → ℝ} : (∫ x in a..b, (f x : 𝕜) ∂μ) = ↑(∫ x in a..b, f x ∂μ) := by
-  simp only [intervalIntegral, integral_ofReal, IsROrC.ofReal_sub]
+  simp only [intervalIntegral, integral_ofReal, RCLike.ofReal_sub]
 
 nonrec theorem integral_ofReal {a b : ℝ} {μ : Measure ℝ} {f : ℝ → ℝ} :
     (∫ x in a..b, (f x : ℂ) ∂μ) = ↑(∫ x in a..b, f x ∂μ) :=
-  IsROrC.interval_integral_ofReal
+  RCLike.interval_integral_ofReal
 #align interval_integral.integral_of_real intervalIntegral.integral_ofReal
 
 section ContinuousLinearMap
 
 variable {a b : ℝ} {μ : Measure ℝ} {f : ℝ → E}
-variable [IsROrC 𝕜] [NormedSpace 𝕜 E] [NormedAddCommGroup F] [NormedSpace 𝕜 F]
+variable [RCLike 𝕜] [NormedSpace 𝕜 E] [NormedAddCommGroup F] [NormedSpace 𝕜 F]
 
 open ContinuousLinearMap
 

Lemma names around cancellation of multiplication and division are a mess.

This PR renames a handful of them according to the following table (each big row contains the multiplicative statement, then the three rows contain the GroupWithZero lemma name, the Group lemma, the AddGroup lemma name).

| Statement | New name | Old name | |

@@ -724,9 +724,9 @@ theorem integral_comp_mul_right (hc : c ≠ 0) :
   simp_rw [integral_smul_measure, intervalIntegral, A.set_integral_map,
     ENNReal.toReal_ofReal (abs_nonneg c)]
   cases' hc.lt_or_lt with h h
-  · simp [h, mul_div_cancel, hc, abs_of_neg,
+  · simp [h, mul_div_cancel_right₀, hc, abs_of_neg,
       Measure.restrict_congr_set (α := ℝ) (μ := volume) Ico_ae_eq_Ioc]
-  · simp [h, mul_div_cancel, hc, abs_of_pos]
+  · simp [h, mul_div_cancel_right₀, hc, abs_of_pos]
 #align interval_integral.integral_comp_mul_right intervalIntegral.integral_comp_mul_right
 
 -- Porting note (#10618): was @[simp]

This will become an error in 2024-03-16 nightly, possibly not permanently.

Co-authored-by: Scott Morrison <scott@tqft.net>

@@ -86,9 +86,9 @@ theorem intervalIntegrable_iff : IntervalIntegrable f μ a b ↔ IntegrableOn f
 
 /-- If a function is interval integrable with respect to a given measure `μ` on `a..b` then
   it is integrable on `uIoc a b` with respect to `μ`. -/
-theorem IntervalIntegrable.def (h : IntervalIntegrable f μ a b) : IntegrableOn f (Ι a b) μ :=
+theorem IntervalIntegrable.def' (h : IntervalIntegrable f μ a b) : IntegrableOn f (Ι a b) μ :=
   intervalIntegrable_iff.mp h
-#align interval_integrable.def IntervalIntegrable.def
+#align interval_integrable.def IntervalIntegrable.def'
 
 theorem intervalIntegrable_iff_integrableOn_Ioc_of_le (hab : a ≤ b) :
     IntervalIntegrable f μ a b ↔ IntegrableOn f (Ioc a b) μ := by
@@ -205,7 +205,7 @@ theorem abs {f : ℝ → ℝ} (h : IntervalIntegrable f μ a b) :
 
 theorem mono (hf : IntervalIntegrable f ν a b) (h1 : [[c, d]] ⊆ [[a, b]]) (h2 : μ ≤ ν) :
     IntervalIntegrable f μ c d :=
-  intervalIntegrable_iff.mpr <| hf.def.mono (uIoc_subset_uIoc_of_uIcc_subset_uIcc h1) h2
+  intervalIntegrable_iff.mpr <| hf.def'.mono (uIoc_subset_uIoc_of_uIcc_subset_uIcc h1) h2
 #align interval_integrable.mono IntervalIntegrable.mono
 
 theorem mono_measure (hf : IntervalIntegrable f ν a b) (h : μ ≤ ν) : IntervalIntegrable f μ a b :=
@@ -219,7 +219,7 @@ theorem mono_set (hf : IntervalIntegrable f μ a b) (h : [[c, d]] ⊆ [[a, b]])
 
 theorem mono_set_ae (hf : IntervalIntegrable f μ a b) (h : Ι c d ≤ᵐ[μ] Ι a b) :
     IntervalIntegrable f μ c d :=
-  intervalIntegrable_iff.mpr <| hf.def.mono_set_ae h
+  intervalIntegrable_iff.mpr <| hf.def'.mono_set_ae h
 #align interval_integrable.mono_set_ae IntervalIntegrable.mono_set_ae
 
 theorem mono_set' (hf : IntervalIntegrable f μ a b) (hsub : Ι c d ⊆ Ι a b) :
@@ -230,13 +230,13 @@ theorem mono_set' (hf : IntervalIntegrable f μ a b) (hsub : Ι c d ⊆ Ι a b)
 theorem mono_fun [NormedAddCommGroup F] {g : ℝ → F} (hf : IntervalIntegrable f μ a b)
     (hgm : AEStronglyMeasurable g (μ.restrict (Ι a b)))
     (hle : (fun x => ‖g x‖) ≤ᵐ[μ.restrict (Ι a b)] fun x => ‖f x‖) : IntervalIntegrable g μ a b :=
-  intervalIntegrable_iff.2 <| hf.def.integrable.mono hgm hle
+  intervalIntegrable_iff.2 <| hf.def'.integrable.mono hgm hle
 #align interval_integrable.mono_fun IntervalIntegrable.mono_fun
 
 theorem mono_fun' {g : ℝ → ℝ} (hg : IntervalIntegrable g μ a b)
     (hfm : AEStronglyMeasurable f (μ.restrict (Ι a b)))
     (hle : (fun x => ‖f x‖) ≤ᵐ[μ.restrict (Ι a b)] g) : IntervalIntegrable f μ a b :=
-  intervalIntegrable_iff.2 <| hg.def.integrable.mono' hfm hle
+  intervalIntegrable_iff.2 <| hg.def'.integrable.mono' hfm hle
 #align interval_integrable.mono_fun' IntervalIntegrable.mono_fun'
 
 protected theorem aestronglyMeasurable (h : IntervalIntegrable f μ a b) :
@@ -581,7 +581,7 @@ nonrec theorem norm_integral_le_of_norm_le {g : ℝ → ℝ} (h : ∀ᵐ t ∂μ
     (hbound : IntervalIntegrable g μ a b) : ‖∫ t in a..b, f t ∂μ‖ ≤ |∫ t in a..b, g t ∂μ| := by
   simp_rw [norm_intervalIntegral_eq, abs_intervalIntegral_eq,
     abs_eq_self.mpr (integral_nonneg_of_ae <| h.mono fun _t ht => (norm_nonneg _).trans ht),
-    norm_integral_le_of_norm_le hbound.def h]
+    norm_integral_le_of_norm_le hbound.def' h]
 #align interval_integral.norm_integral_le_of_norm_le intervalIntegral.norm_integral_le_of_norm_le
 
 theorem norm_integral_le_of_norm_le_const_ae {a b C : ℝ} {f : ℝ → E}
@@ -600,13 +600,13 @@ theorem norm_integral_le_of_norm_le_const {a b C : ℝ} {f : ℝ → E} (h : ∀
 @[simp]
 nonrec theorem integral_add (hf : IntervalIntegrable f μ a b) (hg : IntervalIntegrable g μ a b) :
     ∫ x in a..b, f x + g x ∂μ = (∫ x in a..b, f x ∂μ) + ∫ x in a..b, g x ∂μ := by
-  simp only [intervalIntegral_eq_integral_uIoc, integral_add hf.def hg.def, smul_add]
+  simp only [intervalIntegral_eq_integral_uIoc, integral_add hf.def' hg.def', smul_add]
 #align interval_integral.integral_add intervalIntegral.integral_add
 
 nonrec theorem integral_finset_sum {ι} {s : Finset ι} {f : ι → ℝ → E}
     (h : ∀ i ∈ s, IntervalIntegrable (f i) μ a b) :
     ∫ x in a..b, ∑ i in s, f i x ∂μ = ∑ i in s, ∫ x in a..b, f i x ∂μ := by
-  simp only [intervalIntegral_eq_integral_uIoc, integral_finset_sum s fun i hi => (h i hi).def,
+  simp only [intervalIntegral_eq_integral_uIoc, integral_finset_sum s fun i hi => (h i hi).def',
     Finset.smul_sum]
 #align interval_integral.integral_finset_sum intervalIntegral.integral_finset_sum
 
@@ -690,7 +690,7 @@ open ContinuousLinearMap
 theorem _root_.ContinuousLinearMap.intervalIntegral_apply {a b : ℝ} {φ : ℝ → F →L[𝕜] E}
     (hφ : IntervalIntegrable φ μ a b) (v : F) :
     (∫ x in a..b, φ x ∂μ) v = ∫ x in a..b, φ x v ∂μ := by
-  simp_rw [intervalIntegral_eq_integral_uIoc, ← integral_apply hφ.def v, coe_smul', Pi.smul_apply]
+  simp_rw [intervalIntegral_eq_integral_uIoc, ← integral_apply hφ.def' v, coe_smul', Pi.smul_apply]
 #align continuous_linear_map.interval_integral_apply ContinuousLinearMap.intervalIntegral_apply
 
 variable [NormedSpace ℝ F] [CompleteSpace F]
@@ -1206,7 +1206,7 @@ theorem abs_integral_mono_interval {c d} (h : Ι a b ⊆ Ι c d) (hf : 0 ≤ᵐ[
   calc
     |∫ x in a..b, f x ∂μ| = |∫ x in Ι a b, f x ∂μ| := abs_integral_eq_abs_integral_uIoc f
     _ = ∫ x in Ι a b, f x ∂μ := (abs_of_nonneg (MeasureTheory.integral_nonneg_of_ae hf'))
-    _ ≤ ∫ x in Ι c d, f x ∂μ := (set_integral_mono_set hfi.def hf h.eventuallyLE)
+    _ ≤ ∫ x in Ι c d, f x ∂μ := (set_integral_mono_set hfi.def' hf h.eventuallyLE)
     _ ≤ |∫ x in Ι c d, f x ∂μ| := (le_abs_self _)
     _ = |∫ x in c..d, f x ∂μ| := (abs_integral_eq_abs_integral_uIoc f).symm
 #align interval_integral.abs_integral_mono_interval intervalIntegral.abs_integral_mono_interval

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

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

@@ -1098,7 +1098,8 @@ theorem intervalIntegral_pos_of_pos_on {f : ℝ → ℝ} {a b : ℝ} (hfi : Inte
   have h₀ : 0 ≤ᵐ[volume.restrict (uIoc a b)] f := by
     rw [EventuallyLE, uIoc_of_le hab.le]
     refine' ae_restrict_of_ae_eq_of_ae_restrict Ioo_ae_eq_Ioc _
-    exact (ae_restrict_iff' measurableSet_Ioo).mpr (ae_of_all _ fun x hx => (hpos x hx).le)
+    rw [ae_restrict_iff' measurableSet_Ioo]
+    filter_upwards with x hx using (hpos x hx).le
   rw [integral_pos_iff_support_of_nonneg_ae' h₀ hfi]
   exact ⟨hab, ((Measure.measure_Ioo_pos _).mpr hab).trans_le (measure_mono hsupp)⟩
 #align interval_integral.interval_integral_pos_of_pos_on intervalIntegral.intervalIntegral_pos_of_pos_on

Empty lines were removed by executing the following Python script twice

import os
import re


# Loop through each file in the repository
for dir_path, dirs, files in os.walk('.'):
  for filename in files:
    if filename.endswith('.lean'):
      file_path = os.path.join(dir_path, filename)

      # Open the file and read its contents
      with open(file_path, 'r') as file:
        content = file.read()

      # Use a regular expression to replace sequences of "variable" lines separated by empty lines
      # with sequences without empty lines
      modified_content = re.sub(r'(variable.*\n)\n(variable(?! .* in))', r'\1\2', content)

      # Write the modified content back to the file
      with open(file_path, 'w') as file:
        file.write(modified_content)

@@ -683,7 +683,6 @@ nonrec theorem integral_ofReal {a b : ℝ} {μ : Measure ℝ} {f : ℝ → ℝ}
 section ContinuousLinearMap
 
 variable {a b : ℝ} {μ : Measure ℝ} {f : ℝ → E}
-
 variable [IsROrC 𝕜] [NormedSpace 𝕜 E] [NormedAddCommGroup F] [NormedSpace 𝕜 F]
 
 open ContinuousLinearMap

Classifies by adding issue number #10756 to porting notes claiming anything semantically equivalent to:

• "new lemma"
• "added lemma"

@@ -319,7 +319,7 @@ theorem comp_mul_left (hf : IntervalIntegrable f volume a b) (c : ℝ) :
   · rw [preimage_mul_const_uIcc (inv_ne_zero hc)]; field_simp [hc]
 #align interval_integrable.comp_mul_left IntervalIntegrable.comp_mul_left
 
--- Porting note: new lemma
+-- Porting note (#10756): new lemma
 theorem comp_mul_left_iff {c : ℝ} (hc : c ≠ 0) :
     IntervalIntegrable (fun x ↦ f (c * x)) volume (a / c) (b / c) ↔
       IntervalIntegrable f volume a b :=

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

@@ -670,7 +670,7 @@ nonrec theorem integral_smul_measure (c : ℝ≥0∞) :
 
 end Basic
 
--- Porting note: TODO: add `Complex.ofReal` version of `_root_.integral_ofReal`
+-- Porting note (#11215): TODO: add `Complex.ofReal` version of `_root_.integral_ofReal`
 nonrec theorem _root_.IsROrC.interval_integral_ofReal {𝕜 : Type*} [IsROrC 𝕜] {a b : ℝ}
     {μ : Measure ℝ} {f : ℝ → ℝ} : (∫ x in a..b, (f x : 𝕜) ∂μ) = ↑(∫ x in a..b, f x ∂μ) := by
   simp only [intervalIntegral, integral_ofReal, IsROrC.ofReal_sub]

We remove all but one open Classicals, instead preferring to use open scoped Classical. The only real side-effect this led to is moving a couple declarations to use Exists.choose instead of Classical.choose.

The first few commits are explicitly labelled regex replaces for ease of review.

@@ -50,7 +50,8 @@ integral
 
 noncomputable section
 
-open MeasureTheory Set Classical Filter Function
+open scoped Classical
+open MeasureTheory Set Filter Function
 
 open scoped Classical Topology Filter ENNReal BigOperators Interval NNReal
 

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

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

@@ -1047,334 +1047,6 @@ nonrec theorem integral_indicator {a₁ a₂ a₃ : ℝ} (h : a₂ ∈ Icc a₁
 
 end OrderClosedTopology
 
-/-!
-## The Lebesgue dominated convergence theorem for interval integrals
-As an application, we show continuity of parametric integrals.
--/
-section DominatedConvergence
-
-variable {a b c d : ℝ} {f g : ℝ → E} {μ : Measure ℝ}
-
-/-- Lebesgue dominated convergence theorem for filters with a countable basis -/
-nonrec theorem tendsto_integral_filter_of_dominated_convergence {ι} {l : Filter ι}
-    [l.IsCountablyGenerated] {F : ι → ℝ → E} (bound : ℝ → ℝ)
-    (hF_meas : ∀ᶠ n in l, AEStronglyMeasurable (F n) (μ.restrict (Ι a b)))
-    (h_bound : ∀ᶠ n in l, ∀ᵐ x ∂μ, x ∈ Ι a b → ‖F n x‖ ≤ bound x)
-    (bound_integrable : IntervalIntegrable bound μ a b)
-    (h_lim : ∀ᵐ x ∂μ, x ∈ Ι a b → Tendsto (fun n => F n x) l (𝓝 (f x))) :
-    Tendsto (fun n => ∫ x in a..b, F n x ∂μ) l (𝓝 <| ∫ x in a..b, f x ∂μ) := by
-  simp only [intervalIntegrable_iff, intervalIntegral_eq_integral_uIoc,
-    ← ae_restrict_iff' (α := ℝ) (μ := μ) measurableSet_uIoc] at *
-  exact tendsto_const_nhds.smul <|
-    tendsto_integral_filter_of_dominated_convergence bound hF_meas h_bound bound_integrable h_lim
-#align interval_integral.tendsto_integral_filter_of_dominated_convergence intervalIntegral.tendsto_integral_filter_of_dominated_convergence
-
-/-- Lebesgue dominated convergence theorem for series. -/
-nonrec theorem hasSum_integral_of_dominated_convergence {ι} [Countable ι] {F : ι → ℝ → E}
-    (bound : ι → ℝ → ℝ) (hF_meas : ∀ n, AEStronglyMeasurable (F n) (μ.restrict (Ι a b)))
-    (h_bound : ∀ n, ∀ᵐ t ∂μ, t ∈ Ι a b → ‖F n t‖ ≤ bound n t)
-    (bound_summable : ∀ᵐ t ∂μ, t ∈ Ι a b → Summable fun n => bound n t)
-    (bound_integrable : IntervalIntegrable (fun t => ∑' n, bound n t) μ a b)
-    (h_lim : ∀ᵐ t ∂μ, t ∈ Ι a b → HasSum (fun n => F n t) (f t)) :
-    HasSum (fun n => ∫ t in a..b, F n t ∂μ) (∫ t in a..b, f t ∂μ) := by
-  simp only [intervalIntegrable_iff, intervalIntegral_eq_integral_uIoc, ←
-    ae_restrict_iff' (α := ℝ) (μ := μ) measurableSet_uIoc] at *
-  exact
-    (hasSum_integral_of_dominated_convergence bound hF_meas h_bound bound_summable bound_integrable
-          h_lim).const_smul
-      _
-#align interval_integral.has_sum_integral_of_dominated_convergence intervalIntegral.hasSum_integral_of_dominated_convergence
-
-open TopologicalSpace
-
-/-- Interval integrals commute with countable sums, when the supremum norms are summable (a
-special case of the dominated convergence theorem). -/
-theorem hasSum_intervalIntegral_of_summable_norm [Countable ι] {f : ι → C(ℝ, E)}
-    (hf_sum : Summable fun i : ι => ‖(f i).restrict (⟨uIcc a b, isCompact_uIcc⟩ : Compacts ℝ)‖) :
-    HasSum (fun i : ι => ∫ x in a..b, f i x) (∫ x in a..b, ∑' i : ι, f i x) := by
-  apply hasSum_integral_of_dominated_convergence
-    (fun i (x : ℝ) => ‖(f i).restrict ↑(⟨uIcc a b, isCompact_uIcc⟩ : Compacts ℝ)‖)
-    (fun i => (map_continuous <| f i).aestronglyMeasurable)
-  · refine fun i => ae_of_all _ fun x hx => ?_
-    apply ContinuousMap.norm_coe_le_norm ((f i).restrict _) ⟨x, _⟩
-    exact ⟨hx.1.le, hx.2⟩
-  · exact ae_of_all _ fun x _ => hf_sum
-  · exact intervalIntegrable_const
-  · refine ae_of_all _ fun x hx => Summable.hasSum ?_
-    let x : (⟨uIcc a b, isCompact_uIcc⟩ : Compacts ℝ) := ⟨x, ?_⟩; swap; exact ⟨hx.1.le, hx.2⟩
-    have := hf_sum.of_norm
-    simpa only [Compacts.coe_mk, ContinuousMap.restrict_apply]
-      using ContinuousMap.summable_apply this x
-#align interval_integral.has_sum_interval_integral_of_summable_norm intervalIntegral.hasSum_intervalIntegral_of_summable_norm
-
-theorem tsum_intervalIntegral_eq_of_summable_norm [Countable ι] {f : ι → C(ℝ, E)}
-    (hf_sum : Summable fun i : ι => ‖(f i).restrict (⟨uIcc a b, isCompact_uIcc⟩ : Compacts ℝ)‖) :
-    ∑' i : ι, ∫ x in a..b, f i x = ∫ x in a..b, ∑' i : ι, f i x :=
-  (hasSum_intervalIntegral_of_summable_norm hf_sum).tsum_eq
-#align interval_integral.tsum_interval_integral_eq_of_summable_norm intervalIntegral.tsum_intervalIntegral_eq_of_summable_norm
-
-variable {X : Type*} [TopologicalSpace X] [FirstCountableTopology X]
-
-/-- Continuity of interval integral with respect to a parameter, at a point within a set.
-  Given `F : X → ℝ → E`, assume `F x` is ae-measurable on `[a, b]` for `x` in a
-  neighborhood of `x₀` within `s` and at `x₀`, and assume it is bounded by a function integrable
-  on `[a, b]` independent of `x` in a neighborhood of `x₀` within `s`. If `(fun x ↦ F x t)`
-  is continuous at `x₀` within `s` for almost every `t` in `[a, b]`
-  then the same holds for `(fun x ↦ ∫ t in a..b, F x t ∂μ) s x₀`. -/
-theorem continuousWithinAt_of_dominated_interval {F : X → ℝ → E} {x₀ : X} {bound : ℝ → ℝ} {a b : ℝ}
-    {s : Set X} (hF_meas : ∀ᶠ x in 𝓝[s] x₀, AEStronglyMeasurable (F x) (μ.restrict <| Ι a b))
-    (h_bound : ∀ᶠ x in 𝓝[s] x₀, ∀ᵐ t ∂μ, t ∈ Ι a b → ‖F x t‖ ≤ bound t)
-    (bound_integrable : IntervalIntegrable bound μ a b)
-    (h_cont : ∀ᵐ t ∂μ, t ∈ Ι a b → ContinuousWithinAt (fun x => F x t) s x₀) :
-    ContinuousWithinAt (fun x => ∫ t in a..b, F x t ∂μ) s x₀ :=
-  tendsto_integral_filter_of_dominated_convergence bound hF_meas h_bound bound_integrable h_cont
-#align interval_integral.continuous_within_at_of_dominated_interval intervalIntegral.continuousWithinAt_of_dominated_interval
-
-/-- Continuity of interval integral with respect to a parameter at a point.
-  Given `F : X → ℝ → E`, assume `F x` is ae-measurable on `[a, b]` for `x` in a
-  neighborhood of `x₀`, and assume it is bounded by a function integrable on
-  `[a, b]` independent of `x` in a neighborhood of `x₀`. If `(fun x ↦ F x t)`
-  is continuous at `x₀` for almost every `t` in `[a, b]`
-  then the same holds for `(fun x ↦ ∫ t in a..b, F x t ∂μ) s x₀`. -/
-theorem continuousAt_of_dominated_interval {F : X → ℝ → E} {x₀ : X} {bound : ℝ → ℝ} {a b : ℝ}
-    (hF_meas : ∀ᶠ x in 𝓝 x₀, AEStronglyMeasurable (F x) (μ.restrict <| Ι a b))
-    (h_bound : ∀ᶠ x in 𝓝 x₀, ∀ᵐ t ∂μ, t ∈ Ι a b → ‖F x t‖ ≤ bound t)
-    (bound_integrable : IntervalIntegrable bound μ a b)
-    (h_cont : ∀ᵐ t ∂μ, t ∈ Ι a b → ContinuousAt (fun x => F x t) x₀) :
-    ContinuousAt (fun x => ∫ t in a..b, F x t ∂μ) x₀ :=
-  tendsto_integral_filter_of_dominated_convergence bound hF_meas h_bound bound_integrable h_cont
-#align interval_integral.continuous_at_of_dominated_interval intervalIntegral.continuousAt_of_dominated_interval
-
-/-- Continuity of interval integral with respect to a parameter.
-  Given `F : X → ℝ → E`, assume each `F x` is ae-measurable on `[a, b]`,
-  and assume it is bounded by a function integrable on `[a, b]` independent of `x`.
-  If `(fun x ↦ F x t)` is continuous for almost every `t` in `[a, b]`
-  then the same holds for `(fun x ↦ ∫ t in a..b, F x t ∂μ) s x₀`. -/
-theorem continuous_of_dominated_interval {F : X → ℝ → E} {bound : ℝ → ℝ} {a b : ℝ}
-    (hF_meas : ∀ x, AEStronglyMeasurable (F x) <| μ.restrict <| Ι a b)
-    (h_bound : ∀ x, ∀ᵐ t ∂μ, t ∈ Ι a b → ‖F x t‖ ≤ bound t)
-    (bound_integrable : IntervalIntegrable bound μ a b)
-    (h_cont : ∀ᵐ t ∂μ, t ∈ Ι a b → Continuous fun x => F x t) :
-    Continuous fun x => ∫ t in a..b, F x t ∂μ :=
-  continuous_iff_continuousAt.mpr fun _ =>
-    continuousAt_of_dominated_interval (eventually_of_forall hF_meas) (eventually_of_forall h_bound)
-        bound_integrable <|
-      h_cont.mono fun _ himp hx => (himp hx).continuousAt
-#align interval_integral.continuous_of_dominated_interval intervalIntegral.continuous_of_dominated_interval
-
-end DominatedConvergence
-
-section ContinuousPrimitive
-
-variable {a b b₀ b₁ b₂ : ℝ} {μ : Measure ℝ} {f g : ℝ → E}
-
-theorem continuousWithinAt_primitive (hb₀ : μ {b₀} = 0)
-    (h_int : IntervalIntegrable f μ (min a b₁) (max a b₂)) :
-    ContinuousWithinAt (fun b => ∫ x in a..b, f x ∂μ) (Icc b₁ b₂) b₀ := by
-  by_cases h₀ : b₀ ∈ Icc b₁ b₂
-  · have h₁₂ : b₁ ≤ b₂ := h₀.1.trans h₀.2
-    have min₁₂ : min b₁ b₂ = b₁ := min_eq_left h₁₂
-    have h_int' : ∀ {x}, x ∈ Icc b₁ b₂ → IntervalIntegrable f μ b₁ x := by
-      rintro x ⟨h₁, h₂⟩
-      apply h_int.mono_set
-      apply uIcc_subset_uIcc
-      · exact ⟨min_le_of_left_le (min_le_right a b₁),
-          h₁.trans (h₂.trans <| le_max_of_le_right <| le_max_right _ _)⟩
-      · exact ⟨min_le_of_left_le <| (min_le_right _ _).trans h₁,
-          le_max_of_le_right <| h₂.trans <| le_max_right _ _⟩
-    have : ∀ b ∈ Icc b₁ b₂,
-        ∫ x in a..b, f x ∂μ = (∫ x in a..b₁, f x ∂μ) + ∫ x in b₁..b, f x ∂μ := by
-      rintro b ⟨h₁, h₂⟩
-      rw [← integral_add_adjacent_intervals _ (h_int' ⟨h₁, h₂⟩)]
-      apply h_int.mono_set
-      apply uIcc_subset_uIcc
-      · exact ⟨min_le_of_left_le (min_le_left a b₁), le_max_of_le_right (le_max_left _ _)⟩
-      · exact ⟨min_le_of_left_le (min_le_right _ _),
-          le_max_of_le_right (h₁.trans <| h₂.trans (le_max_right a b₂))⟩
-    apply ContinuousWithinAt.congr _ this (this _ h₀); clear this
-    refine' continuousWithinAt_const.add _
-    have :
-      (fun b => ∫ x in b₁..b, f x ∂μ) =ᶠ[𝓝[Icc b₁ b₂] b₀] fun b =>
-        ∫ x in b₁..b₂, indicator {x | x ≤ b} f x ∂μ := by
-      apply eventuallyEq_of_mem self_mem_nhdsWithin
-      exact fun b b_in => (integral_indicator b_in).symm
-    apply ContinuousWithinAt.congr_of_eventuallyEq _ this (integral_indicator h₀).symm
-    have : IntervalIntegrable (fun x => ‖f x‖) μ b₁ b₂ :=
-      IntervalIntegrable.norm (h_int' <| right_mem_Icc.mpr h₁₂)
-    refine' continuousWithinAt_of_dominated_interval _ _ this _ <;> clear this
-    · apply Eventually.mono self_mem_nhdsWithin
-      intro x hx
-      erw [aestronglyMeasurable_indicator_iff, Measure.restrict_restrict, Iic_inter_Ioc_of_le]
-      · rw [min₁₂]
-        exact (h_int' hx).1.aestronglyMeasurable
-      · exact le_max_of_le_right hx.2
-      exacts [measurableSet_Iic, measurableSet_Iic]
-    · refine' eventually_of_forall fun x => eventually_of_forall fun t => _
-      dsimp [indicator]
-      split_ifs <;> simp
-    · have : ∀ᵐ t ∂μ, t < b₀ ∨ b₀ < t := by
-        apply Eventually.mono (compl_mem_ae_iff.mpr hb₀)
-        intro x hx
-        exact Ne.lt_or_lt hx
-      apply this.mono
-      rintro x₀ (hx₀ | hx₀) -
-      · have : ∀ᶠ x in 𝓝[Icc b₁ b₂] b₀, {t : ℝ | t ≤ x}.indicator f x₀ = f x₀ := by
-          apply mem_nhdsWithin_of_mem_nhds
-          apply Eventually.mono (Ioi_mem_nhds hx₀)
-          intro x hx
-          simp [hx.le]
-        apply continuousWithinAt_const.congr_of_eventuallyEq this
-        simp [hx₀.le]
-      · have : ∀ᶠ x in 𝓝[Icc b₁ b₂] b₀, {t : ℝ | t ≤ x}.indicator f x₀ = 0 := by
-          apply mem_nhdsWithin_of_mem_nhds
-          apply Eventually.mono (Iio_mem_nhds hx₀)
-          intro x hx
-          simp [hx]
-        apply continuousWithinAt_const.congr_of_eventuallyEq this
-        simp [hx₀]
-  · apply continuousWithinAt_of_not_mem_closure
-    rwa [closure_Icc]
-#align interval_integral.continuous_within_at_primitive intervalIntegral.continuousWithinAt_primitive
-
-variable {X : Type*} [TopologicalSpace X] [FirstCountableTopology X]
-  {E : Type*} [NormedAddCommGroup E] [NormedSpace ℝ E] [CompleteSpace E]
-
-theorem continuousAt_parametric_primitive_of_dominated {F : X → ℝ → E} (bound : ℝ → ℝ) (a b : ℝ)
-    {a₀ b₀ : ℝ} {x₀ : X} (hF_meas : ∀ x, AEStronglyMeasurable (F x) (μ.restrict <| Ι a b))
-    (h_bound : ∀ᶠ x in 𝓝 x₀, ∀ᵐ t ∂μ.restrict <| Ι a b, ‖F x t‖ ≤ bound t)
-    (bound_integrable : IntervalIntegrable bound μ a b)
-    (h_cont : ∀ᵐ t ∂μ.restrict <| Ι a b, ContinuousAt (fun x ↦ F x t) x₀) (ha₀ : a₀ ∈ Ioo a b)
-    (hb₀ : b₀ ∈ Ioo a b) (hμb₀ : μ {b₀} = 0) :
-    ContinuousAt (fun p : X × ℝ ↦ ∫ t : ℝ in a₀..p.2, F p.1 t ∂μ) (x₀, b₀) := by
-  have hsub : ∀ {a₀ b₀}, a₀ ∈ Ioo a b → b₀ ∈ Ioo a b → Ι a₀ b₀ ⊆ Ι a b := fun ha₀ hb₀ ↦
-    (ordConnected_Ioo.uIoc_subset ha₀ hb₀).trans (Ioo_subset_Ioc_self.trans Ioc_subset_uIoc)
-  have Ioo_nhds : Ioo a b ∈ 𝓝 b₀ := Ioo_mem_nhds hb₀.1 hb₀.2
-  have Icc_nhds : Icc a b ∈ 𝓝 b₀ := Icc_mem_nhds hb₀.1 hb₀.2
-  have hx₀ : ∀ᵐ t : ℝ ∂μ.restrict (Ι a b), ‖F x₀ t‖ ≤ bound t := h_bound.self_of_nhds
-  have : ∀ᶠ p : X × ℝ in 𝓝 (x₀, b₀),
-      ∫ s in a₀..p.2, F p.1 s ∂μ =
-        ∫ s in a₀..b₀, F p.1 s ∂μ + ∫ s in b₀..p.2, F x₀ s ∂μ +
-          ∫ s in b₀..p.2, F p.1 s - F x₀ s ∂μ := by
-    rw [nhds_prod_eq]
-    refine (h_bound.prod_mk Ioo_nhds).mono ?_
-    rintro ⟨x, t⟩ ⟨hx : ∀ᵐ t : ℝ ∂μ.restrict (Ι a b), ‖F x t‖ ≤ bound t, ht : t ∈ Ioo a b⟩
-    dsimp (config := { eta := false })
-    have hiF : ∀ {x a₀ b₀},
-        (∀ᵐ t : ℝ ∂μ.restrict (Ι a b), ‖F x t‖ ≤ bound t) → a₀ ∈ Ioo a b → b₀ ∈ Ioo a b →
-          IntervalIntegrable (F x) μ a₀ b₀ := fun {x a₀ b₀} hx ha₀ hb₀ ↦
-      (bound_integrable.mono_set_ae <| eventually_of_forall <| hsub ha₀ hb₀).mono_fun'
-        ((hF_meas x).mono_set <| hsub ha₀ hb₀)
-        (ae_restrict_of_ae_restrict_of_subset (hsub ha₀ hb₀) hx)
-    rw [intervalIntegral.integral_sub, add_assoc, add_sub_cancel'_right,
-      intervalIntegral.integral_add_adjacent_intervals]
-    · exact hiF hx ha₀ hb₀
-    · exact hiF hx hb₀ ht
-    · exact hiF hx hb₀ ht
-    · exact hiF hx₀ hb₀ ht
-  rw [continuousAt_congr this]; clear this
-  refine (ContinuousAt.add ?_ ?_).add ?_
-  · exact (intervalIntegral.continuousAt_of_dominated_interval
-        (eventually_of_forall fun x ↦ (hF_meas x).mono_set <| hsub ha₀ hb₀)
-          (h_bound.mono fun x hx ↦
-            ae_imp_of_ae_restrict <| ae_restrict_of_ae_restrict_of_subset (hsub ha₀ hb₀) hx)
-          (bound_integrable.mono_set_ae <| eventually_of_forall <| hsub ha₀ hb₀) <|
-          ae_imp_of_ae_restrict <| ae_restrict_of_ae_restrict_of_subset (hsub ha₀ hb₀) h_cont).fst'
-  · refine (?_ : ContinuousAt (fun t ↦ ∫ s in b₀..t, F x₀ s ∂μ) b₀).snd'
-    apply ContinuousWithinAt.continuousAt _ (Icc_mem_nhds hb₀.1 hb₀.2)
-    apply intervalIntegral.continuousWithinAt_primitive hμb₀
-    rw [min_eq_right hb₀.1.le, max_eq_right hb₀.2.le]
-    exact bound_integrable.mono_fun' (hF_meas x₀) hx₀
-  · suffices Tendsto (fun x : X × ℝ ↦ ∫ s in b₀..x.2, F x.1 s - F x₀ s ∂μ) (𝓝 (x₀, b₀)) (𝓝 0) by
-      simpa [ContinuousAt]
-    have : ∀ᶠ p : X × ℝ in 𝓝 (x₀, b₀),
-        ‖∫ s in b₀..p.2, F p.1 s - F x₀ s ∂μ‖ ≤ |∫ s in b₀..p.2, 2 * bound s ∂μ| := by
-      rw [nhds_prod_eq]
-      refine (h_bound.prod_mk Ioo_nhds).mono ?_
-      rintro ⟨x, t⟩ ⟨hx : ∀ᵐ t ∂μ.restrict (Ι a b), ‖F x t‖ ≤ bound t, ht : t ∈ Ioo a b⟩
-      have H : ∀ᵐ t : ℝ ∂μ.restrict (Ι b₀ t), ‖F x t - F x₀ t‖ ≤ 2 * bound t := by
-        apply (ae_restrict_of_ae_restrict_of_subset (hsub hb₀ ht) (hx.and hx₀)).mono
-        rintro s ⟨hs₁, hs₂⟩
-        calc
-          ‖F x s - F x₀ s‖ ≤ ‖F x s‖ + ‖F x₀ s‖ := norm_sub_le _ _
-          _ ≤ 2 * bound s := by linarith only [hs₁, hs₂]
-      exact intervalIntegral.norm_integral_le_of_norm_le H
-        ((bound_integrable.mono_set' <| hsub hb₀ ht).const_mul 2)
-    apply squeeze_zero_norm' this
-    have : Tendsto (fun t ↦ ∫ s in b₀..t, 2 * bound s ∂μ) (𝓝 b₀) (𝓝 0) := by
-      suffices ContinuousAt (fun t ↦ ∫ s in b₀..t, 2 * bound s ∂μ) b₀ by
-        simpa [ContinuousAt] using this
-      apply ContinuousWithinAt.continuousAt _ Icc_nhds
-      apply intervalIntegral.continuousWithinAt_primitive hμb₀
-      apply IntervalIntegrable.const_mul
-      apply bound_integrable.mono_set'
-      rw [min_eq_right hb₀.1.le, max_eq_right hb₀.2.le]
-    rw [nhds_prod_eq]
-    exact (continuous_abs.tendsto' _ _ abs_zero).comp (this.comp tendsto_snd)
-
-variable [NoAtoms μ]
-
-theorem continuousOn_primitive (h_int : IntegrableOn f (Icc a b) μ) :
-    ContinuousOn (fun x => ∫ t in Ioc a x, f t ∂μ) (Icc a b) := by
-  by_cases h : a ≤ b
-  · have : ∀ x ∈ Icc a b, ∫ t in Ioc a x, f t ∂μ = ∫ t in a..x, f t ∂μ := by
-      intro x x_in
-      simp_rw [integral_of_le x_in.1]
-    rw [continuousOn_congr this]
-    intro x₀ _
-    refine' continuousWithinAt_primitive (measure_singleton x₀) _
-    simp only [intervalIntegrable_iff_integrableOn_Ioc_of_le, min_eq_left, max_eq_right, h,
-      min_self]
-    exact h_int.mono Ioc_subset_Icc_self le_rfl
-  · rw [Icc_eq_empty h]
-    exact continuousOn_empty _
-#align interval_integral.continuous_on_primitive intervalIntegral.continuousOn_primitive
-
-theorem continuousOn_primitive_Icc (h_int : IntegrableOn f (Icc a b) μ) :
-    ContinuousOn (fun x => ∫ t in Icc a x, f t ∂μ) (Icc a b) := by
-  have aux : (fun x => ∫ t in Icc a x, f t ∂μ) = fun x => ∫ t in Ioc a x, f t ∂μ := by
-    ext x
-    exact integral_Icc_eq_integral_Ioc
-  rw [aux]
-  exact continuousOn_primitive h_int
-#align interval_integral.continuous_on_primitive_Icc intervalIntegral.continuousOn_primitive_Icc
-
-/-- Note: this assumes that `f` is `IntervalIntegrable`, in contrast to some other lemmas here. -/
-theorem continuousOn_primitive_interval' (h_int : IntervalIntegrable f μ b₁ b₂)
-    (ha : a ∈ [[b₁, b₂]]) : ContinuousOn (fun b => ∫ x in a..b, f x ∂μ) [[b₁, b₂]] := fun _ _ ↦ by
-  refine continuousWithinAt_primitive (measure_singleton _) ?_
-  rw [min_eq_right ha.1, max_eq_right ha.2]
-  simpa [intervalIntegrable_iff, uIoc] using h_int
-#align interval_integral.continuous_on_primitive_interval' intervalIntegral.continuousOn_primitive_interval'
-
-theorem continuousOn_primitive_interval (h_int : IntegrableOn f (uIcc a b) μ) :
-    ContinuousOn (fun x => ∫ t in a..x, f t ∂μ) (uIcc a b) :=
-  continuousOn_primitive_interval' h_int.intervalIntegrable left_mem_uIcc
-#align interval_integral.continuous_on_primitive_interval intervalIntegral.continuousOn_primitive_interval
-
-theorem continuousOn_primitive_interval_left (h_int : IntegrableOn f (uIcc a b) μ) :
-    ContinuousOn (fun x => ∫ t in x..b, f t ∂μ) (uIcc a b) := by
-  rw [uIcc_comm a b] at h_int ⊢
-  simp only [integral_symm b]
-  exact (continuousOn_primitive_interval h_int).neg
-#align interval_integral.continuous_on_primitive_interval_left intervalIntegral.continuousOn_primitive_interval_left
-
-theorem continuous_primitive (h_int : ∀ a b, IntervalIntegrable f μ a b) (a : ℝ) :
-    Continuous fun b => ∫ x in a..b, f x ∂μ := by
-  rw [continuous_iff_continuousAt]
-  intro b₀
-  cases' exists_lt b₀ with b₁ hb₁
-  cases' exists_gt b₀ with b₂ hb₂
-  apply ContinuousWithinAt.continuousAt _ (Icc_mem_nhds hb₁ hb₂)
-  exact continuousWithinAt_primitive (measure_singleton b₀) (h_int _ _)
-#align interval_integral.continuous_primitive intervalIntegral.continuous_primitive
-
-nonrec theorem _root_.MeasureTheory.Integrable.continuous_primitive (h_int : Integrable f μ)
-    (a : ℝ) : Continuous fun b => ∫ x in a..b, f x ∂μ :=
-  continuous_primitive (fun _ _ => h_int.intervalIntegrable) a
-#align measure_theory.integrable.continuous_primitive MeasureTheory.Integrable.continuous_primitive
-
-end ContinuousPrimitive
-
 section
 
 variable {f g : ℝ → ℝ} {a b : ℝ} {μ : Measure ℝ}

Homogenises porting notes via capitalisation and addition of whitespace.

It makes the following changes:

• converts "--porting note" into "-- Porting note";
• converts "porting note" into "Porting note".

@@ -156,7 +156,7 @@ nonrec theorem symm (h : IntervalIntegrable f μ a b) : IntervalIntegrable f μ
   h.symm
 #align interval_integrable.symm IntervalIntegrable.symm
 
-@[refl, simp] -- porting note: added `simp`
+@[refl, simp] -- Porting note: added `simp`
 theorem refl : IntervalIntegrable f μ a a := by constructor <;> simp
 #align interval_integrable.refl IntervalIntegrable.refl
 
@@ -318,7 +318,7 @@ theorem comp_mul_left (hf : IntervalIntegrable f volume a b) (c : ℝ) :
   · rw [preimage_mul_const_uIcc (inv_ne_zero hc)]; field_simp [hc]
 #align interval_integrable.comp_mul_left IntervalIntegrable.comp_mul_left
 
--- porting note: new lemma
+-- Porting note: new lemma
 theorem comp_mul_left_iff {c : ℝ} (hc : c ≠ 0) :
     IntervalIntegrable (fun x ↦ f (c * x)) volume (a / c) (b / c) ↔
       IntervalIntegrable f volume a b :=
@@ -669,7 +669,7 @@ nonrec theorem integral_smul_measure (c : ℝ≥0∞) :
 
 end Basic
 
--- porting note: TODO: add `Complex.ofReal` version of `_root_.integral_ofReal`
+-- Porting note: TODO: add `Complex.ofReal` version of `_root_.integral_ofReal`
 nonrec theorem _root_.IsROrC.interval_integral_ofReal {𝕜 : Type*} [IsROrC 𝕜] {a b : ℝ}
     {μ : Measure ℝ} {f : ℝ → ℝ} : (∫ x in a..b, (f x : 𝕜) ∂μ) = ↑(∫ x in a..b, f x ∂μ) := by
   simp only [intervalIntegral, integral_ofReal, IsROrC.ofReal_sub]

if it is bounded by an integrable function: by the dominated convergence theorem.

From the sphere-eversion project. The first two commits are preliminary clean-up; happy to split these into a separate PR.

@@ -69,6 +69,9 @@ def IntervalIntegrable (f : ℝ → E) (μ : Measure ℝ) (a b : ℝ) : Prop :=
   IntegrableOn f (Ioc a b) μ ∧ IntegrableOn f (Ioc b a) μ
 #align interval_integrable IntervalIntegrable
 
+/-!
+## Basic iff's for `IntervalIntegrable`
+-/
 section
 
 variable {f : ℝ → E} {a b : ℝ} {μ : Measure ℝ}
@@ -135,6 +138,13 @@ theorem intervalIntegrable_const [IsLocallyFiniteMeasure μ] {c : E} :
 
 end
 
+/-!
+## Basic properties of interval integrability
+- interval integrability is symmetric, reflexive, transitive
+- monotonicity and strong measurability of the interval integral
+- if `f` is interval integrable, so are its absolute value and norm
+- arithmetic properties
+-/
 namespace IntervalIntegrable
 
 section
@@ -353,6 +363,9 @@ theorem comp_sub_left (hf : IntervalIntegrable f volume a b) (c : ℝ) :
 
 end IntervalIntegrable
 
+/-!
+## Continuous functions are interval integrable
+-/
 section
 
 variable {μ : Measure ℝ} [IsLocallyFiniteMeasure μ]
@@ -376,6 +389,9 @@ theorem Continuous.intervalIntegrable {u : ℝ → E} (hu : Continuous u) (a b :
 
 end
 
+/-!
+## Monotone and antitone functions are integral integrable
+-/
 section
 
 variable {μ : Measure ℝ} [IsLocallyFiniteMeasure μ] [ConditionallyCompleteLinearOrder E]
@@ -686,6 +702,10 @@ theorem _root_.ContinuousLinearMap.intervalIntegral_comp_comm (L : E →L[𝕜]
 
 end ContinuousLinearMap
 
+/-!
+## Basic arithmetic
+Includes addition, scalar multiplication and affine transformations.
+-/
 section Comp
 
 variable {a b c d : ℝ} (f : ℝ → E)
@@ -874,8 +894,8 @@ end Comp
 In this section we prove that `∫ x in a..b, f x ∂μ + ∫ x in b..c, f x ∂μ = ∫ x in a..c, f x ∂μ`
 as well as a few other identities trivially equivalent to this one. We also prove that
 `∫ x in a..b, f x ∂μ = ∫ x, f x ∂μ` provided that `support f ⊆ Ioc a b`.
--/
 
+-/
 
 section OrderClosedTopology
 
@@ -1025,6 +1045,16 @@ nonrec theorem integral_indicator {a₁ a₂ a₃ : ℝ} (h : a₂ ∈ Icc a₁
   all_goals apply measurableSet_Iic
 #align interval_integral.integral_indicator intervalIntegral.integral_indicator
 
+end OrderClosedTopology
+
+/-!
+## The Lebesgue dominated convergence theorem for interval integrals
+As an application, we show continuity of parametric integrals.
+-/
+section DominatedConvergence
+
+variable {a b c d : ℝ} {f g : ℝ → E} {μ : Measure ℝ}
+
 /-- Lebesgue dominated convergence theorem for filters with a countable basis -/
 nonrec theorem tendsto_integral_filter_of_dominated_convergence {ι} {l : Filter ι}
     [l.IsCountablyGenerated] {F : ι → ℝ → E} (bound : ℝ → ℝ)
@@ -1132,12 +1162,10 @@ theorem continuous_of_dominated_interval {F : X → ℝ → E} {bound : ℝ →
       h_cont.mono fun _ himp hx => (himp hx).continuousAt
 #align interval_integral.continuous_of_dominated_interval intervalIntegral.continuous_of_dominated_interval
 
-end OrderClosedTopology
+end DominatedConvergence
 
 section ContinuousPrimitive
 
-open TopologicalSpace
-
 variable {a b b₀ b₁ b₂ : ℝ} {μ : Measure ℝ} {f g : ℝ → E}
 
 theorem continuousWithinAt_primitive (hb₀ : μ {b₀} = 0)
@@ -1208,7 +1236,84 @@ theorem continuousWithinAt_primitive (hb₀ : μ {b₀} = 0)
     rwa [closure_Icc]
 #align interval_integral.continuous_within_at_primitive intervalIntegral.continuousWithinAt_primitive
 
-theorem continuousOn_primitive [NoAtoms μ] (h_int : IntegrableOn f (Icc a b) μ) :
+variable {X : Type*} [TopologicalSpace X] [FirstCountableTopology X]
+  {E : Type*} [NormedAddCommGroup E] [NormedSpace ℝ E] [CompleteSpace E]
+
+theorem continuousAt_parametric_primitive_of_dominated {F : X → ℝ → E} (bound : ℝ → ℝ) (a b : ℝ)
+    {a₀ b₀ : ℝ} {x₀ : X} (hF_meas : ∀ x, AEStronglyMeasurable (F x) (μ.restrict <| Ι a b))
+    (h_bound : ∀ᶠ x in 𝓝 x₀, ∀ᵐ t ∂μ.restrict <| Ι a b, ‖F x t‖ ≤ bound t)
+    (bound_integrable : IntervalIntegrable bound μ a b)
+    (h_cont : ∀ᵐ t ∂μ.restrict <| Ι a b, ContinuousAt (fun x ↦ F x t) x₀) (ha₀ : a₀ ∈ Ioo a b)
+    (hb₀ : b₀ ∈ Ioo a b) (hμb₀ : μ {b₀} = 0) :
+    ContinuousAt (fun p : X × ℝ ↦ ∫ t : ℝ in a₀..p.2, F p.1 t ∂μ) (x₀, b₀) := by
+  have hsub : ∀ {a₀ b₀}, a₀ ∈ Ioo a b → b₀ ∈ Ioo a b → Ι a₀ b₀ ⊆ Ι a b := fun ha₀ hb₀ ↦
+    (ordConnected_Ioo.uIoc_subset ha₀ hb₀).trans (Ioo_subset_Ioc_self.trans Ioc_subset_uIoc)
+  have Ioo_nhds : Ioo a b ∈ 𝓝 b₀ := Ioo_mem_nhds hb₀.1 hb₀.2
+  have Icc_nhds : Icc a b ∈ 𝓝 b₀ := Icc_mem_nhds hb₀.1 hb₀.2
+  have hx₀ : ∀ᵐ t : ℝ ∂μ.restrict (Ι a b), ‖F x₀ t‖ ≤ bound t := h_bound.self_of_nhds
+  have : ∀ᶠ p : X × ℝ in 𝓝 (x₀, b₀),
+      ∫ s in a₀..p.2, F p.1 s ∂μ =
+        ∫ s in a₀..b₀, F p.1 s ∂μ + ∫ s in b₀..p.2, F x₀ s ∂μ +
+          ∫ s in b₀..p.2, F p.1 s - F x₀ s ∂μ := by
+    rw [nhds_prod_eq]
+    refine (h_bound.prod_mk Ioo_nhds).mono ?_
+    rintro ⟨x, t⟩ ⟨hx : ∀ᵐ t : ℝ ∂μ.restrict (Ι a b), ‖F x t‖ ≤ bound t, ht : t ∈ Ioo a b⟩
+    dsimp (config := { eta := false })
+    have hiF : ∀ {x a₀ b₀},
+        (∀ᵐ t : ℝ ∂μ.restrict (Ι a b), ‖F x t‖ ≤ bound t) → a₀ ∈ Ioo a b → b₀ ∈ Ioo a b →
+          IntervalIntegrable (F x) μ a₀ b₀ := fun {x a₀ b₀} hx ha₀ hb₀ ↦
+      (bound_integrable.mono_set_ae <| eventually_of_forall <| hsub ha₀ hb₀).mono_fun'
+        ((hF_meas x).mono_set <| hsub ha₀ hb₀)
+        (ae_restrict_of_ae_restrict_of_subset (hsub ha₀ hb₀) hx)
+    rw [intervalIntegral.integral_sub, add_assoc, add_sub_cancel'_right,
+      intervalIntegral.integral_add_adjacent_intervals]
+    · exact hiF hx ha₀ hb₀
+    · exact hiF hx hb₀ ht
+    · exact hiF hx hb₀ ht
+    · exact hiF hx₀ hb₀ ht
+  rw [continuousAt_congr this]; clear this
+  refine (ContinuousAt.add ?_ ?_).add ?_
+  · exact (intervalIntegral.continuousAt_of_dominated_interval
+        (eventually_of_forall fun x ↦ (hF_meas x).mono_set <| hsub ha₀ hb₀)
+          (h_bound.mono fun x hx ↦
+            ae_imp_of_ae_restrict <| ae_restrict_of_ae_restrict_of_subset (hsub ha₀ hb₀) hx)
+          (bound_integrable.mono_set_ae <| eventually_of_forall <| hsub ha₀ hb₀) <|
+          ae_imp_of_ae_restrict <| ae_restrict_of_ae_restrict_of_subset (hsub ha₀ hb₀) h_cont).fst'
+  · refine (?_ : ContinuousAt (fun t ↦ ∫ s in b₀..t, F x₀ s ∂μ) b₀).snd'
+    apply ContinuousWithinAt.continuousAt _ (Icc_mem_nhds hb₀.1 hb₀.2)
+    apply intervalIntegral.continuousWithinAt_primitive hμb₀
+    rw [min_eq_right hb₀.1.le, max_eq_right hb₀.2.le]
+    exact bound_integrable.mono_fun' (hF_meas x₀) hx₀
+  · suffices Tendsto (fun x : X × ℝ ↦ ∫ s in b₀..x.2, F x.1 s - F x₀ s ∂μ) (𝓝 (x₀, b₀)) (𝓝 0) by
+      simpa [ContinuousAt]
+    have : ∀ᶠ p : X × ℝ in 𝓝 (x₀, b₀),
+        ‖∫ s in b₀..p.2, F p.1 s - F x₀ s ∂μ‖ ≤ |∫ s in b₀..p.2, 2 * bound s ∂μ| := by
+      rw [nhds_prod_eq]
+      refine (h_bound.prod_mk Ioo_nhds).mono ?_
+      rintro ⟨x, t⟩ ⟨hx : ∀ᵐ t ∂μ.restrict (Ι a b), ‖F x t‖ ≤ bound t, ht : t ∈ Ioo a b⟩
+      have H : ∀ᵐ t : ℝ ∂μ.restrict (Ι b₀ t), ‖F x t - F x₀ t‖ ≤ 2 * bound t := by
+        apply (ae_restrict_of_ae_restrict_of_subset (hsub hb₀ ht) (hx.and hx₀)).mono
+        rintro s ⟨hs₁, hs₂⟩
+        calc
+          ‖F x s - F x₀ s‖ ≤ ‖F x s‖ + ‖F x₀ s‖ := norm_sub_le _ _
+          _ ≤ 2 * bound s := by linarith only [hs₁, hs₂]
+      exact intervalIntegral.norm_integral_le_of_norm_le H
+        ((bound_integrable.mono_set' <| hsub hb₀ ht).const_mul 2)
+    apply squeeze_zero_norm' this
+    have : Tendsto (fun t ↦ ∫ s in b₀..t, 2 * bound s ∂μ) (𝓝 b₀) (𝓝 0) := by
+      suffices ContinuousAt (fun t ↦ ∫ s in b₀..t, 2 * bound s ∂μ) b₀ by
+        simpa [ContinuousAt] using this
+      apply ContinuousWithinAt.continuousAt _ Icc_nhds
+      apply intervalIntegral.continuousWithinAt_primitive hμb₀
+      apply IntervalIntegrable.const_mul
+      apply bound_integrable.mono_set'
+      rw [min_eq_right hb₀.1.le, max_eq_right hb₀.2.le]
+    rw [nhds_prod_eq]
+    exact (continuous_abs.tendsto' _ _ abs_zero).comp (this.comp tendsto_snd)
+
+variable [NoAtoms μ]
+
+theorem continuousOn_primitive (h_int : IntegrableOn f (Icc a b) μ) :
     ContinuousOn (fun x => ∫ t in Ioc a x, f t ∂μ) (Icc a b) := by
   by_cases h : a ≤ b
   · have : ∀ x ∈ Icc a b, ∫ t in Ioc a x, f t ∂μ = ∫ t in a..x, f t ∂μ := by
@@ -1224,7 +1329,7 @@ theorem continuousOn_primitive [NoAtoms μ] (h_int : IntegrableOn f (Icc a b) μ
     exact continuousOn_empty _
 #align interval_integral.continuous_on_primitive intervalIntegral.continuousOn_primitive
 
-theorem continuousOn_primitive_Icc [NoAtoms μ] (h_int : IntegrableOn f (Icc a b) μ) :
+theorem continuousOn_primitive_Icc (h_int : IntegrableOn f (Icc a b) μ) :
     ContinuousOn (fun x => ∫ t in Icc a x, f t ∂μ) (Icc a b) := by
   have aux : (fun x => ∫ t in Icc a x, f t ∂μ) = fun x => ∫ t in Ioc a x, f t ∂μ := by
     ext x
@@ -1234,27 +1339,25 @@ theorem continuousOn_primitive_Icc [NoAtoms μ] (h_int : IntegrableOn f (Icc a b
 #align interval_integral.continuous_on_primitive_Icc intervalIntegral.continuousOn_primitive_Icc
 
 /-- Note: this assumes that `f` is `IntervalIntegrable`, in contrast to some other lemmas here. -/
-theorem continuousOn_primitive_interval' [NoAtoms μ] (h_int : IntervalIntegrable f μ b₁ b₂)
+theorem continuousOn_primitive_interval' (h_int : IntervalIntegrable f μ b₁ b₂)
     (ha : a ∈ [[b₁, b₂]]) : ContinuousOn (fun b => ∫ x in a..b, f x ∂μ) [[b₁, b₂]] := fun _ _ ↦ by
   refine continuousWithinAt_primitive (measure_singleton _) ?_
   rw [min_eq_right ha.1, max_eq_right ha.2]
   simpa [intervalIntegrable_iff, uIoc] using h_int
 #align interval_integral.continuous_on_primitive_interval' intervalIntegral.continuousOn_primitive_interval'
 
-theorem continuousOn_primitive_interval [NoAtoms μ] (h_int : IntegrableOn f (uIcc a b) μ) :
+theorem continuousOn_primitive_interval (h_int : IntegrableOn f (uIcc a b) μ) :
     ContinuousOn (fun x => ∫ t in a..x, f t ∂μ) (uIcc a b) :=
   continuousOn_primitive_interval' h_int.intervalIntegrable left_mem_uIcc
 #align interval_integral.continuous_on_primitive_interval intervalIntegral.continuousOn_primitive_interval
 
-theorem continuousOn_primitive_interval_left [NoAtoms μ] (h_int : IntegrableOn f (uIcc a b) μ) :
+theorem continuousOn_primitive_interval_left (h_int : IntegrableOn f (uIcc a b) μ) :
     ContinuousOn (fun x => ∫ t in x..b, f t ∂μ) (uIcc a b) := by
   rw [uIcc_comm a b] at h_int ⊢
   simp only [integral_symm b]
   exact (continuousOn_primitive_interval h_int).neg
 #align interval_integral.continuous_on_primitive_interval_left intervalIntegral.continuousOn_primitive_interval_left
 
-variable [NoAtoms μ]
-
 theorem continuous_primitive (h_int : ∀ a b, IntervalIntegrable f μ a b) (a : ℝ) :
     Continuous fun b => ∫ x in a..b, f x ∂μ := by
   rw [continuous_iff_continuousAt]

Classify by adding issue number (#10618) to porting notes claiming anything semantically equivalent to

• "simp can prove this"
• "simp can simplify this`"
• "was @[simp], now can be proved by simp"
• "was @[simp], but simp can prove it"
• "removed simp attribute as the equality can already be obtained by simp"
• "simp can already prove this"
• "simp already proves this"
• "simp can prove these"

@@ -695,7 +695,7 @@ Porting note: some `@[simp]` attributes in this section were removed to make the
 happy. TODO: find out if these lemmas are actually good or bad `simp` lemmas.
 -/
 
--- porting note: was @[simp]
+-- Porting note (#10618): was @[simp]
 theorem integral_comp_mul_right (hc : c ≠ 0) :
     (∫ x in a..b, f (x * c)) = c⁻¹ • ∫ x in a * c..b * c, f x := by
   have A : MeasurableEmbedding fun x => x * c :=
@@ -709,35 +709,35 @@ theorem integral_comp_mul_right (hc : c ≠ 0) :
   · simp [h, mul_div_cancel, hc, abs_of_pos]
 #align interval_integral.integral_comp_mul_right intervalIntegral.integral_comp_mul_right
 
--- porting note: was @[simp]
+-- Porting note (#10618): was @[simp]
 theorem smul_integral_comp_mul_right (c) :
     (c • ∫ x in a..b, f (x * c)) = ∫ x in a * c..b * c, f x := by
   by_cases hc : c = 0 <;> simp [hc, integral_comp_mul_right]
 #align interval_integral.smul_integral_comp_mul_right intervalIntegral.smul_integral_comp_mul_right
 
--- porting note: was @[simp]
+-- Porting note (#10618): was @[simp]
 theorem integral_comp_mul_left (hc : c ≠ 0) :
     (∫ x in a..b, f (c * x)) = c⁻¹ • ∫ x in c * a..c * b, f x := by
   simpa only [mul_comm c] using integral_comp_mul_right f hc
 #align interval_integral.integral_comp_mul_left intervalIntegral.integral_comp_mul_left
 
--- porting note: was @[simp]
+-- Porting note (#10618): was @[simp]
 theorem smul_integral_comp_mul_left (c) : (c • ∫ x in a..b, f (c * x)) = ∫ x in c * a..c * b, f x :=
   by by_cases hc : c = 0 <;> simp [hc, integral_comp_mul_left]
 #align interval_integral.smul_integral_comp_mul_left intervalIntegral.smul_integral_comp_mul_left
 
--- porting note: was @[simp]
+-- Porting note (#10618): was @[simp]
 theorem integral_comp_div (hc : c ≠ 0) : (∫ x in a..b, f (x / c)) = c • ∫ x in a / c..b / c, f x :=
   by simpa only [inv_inv] using integral_comp_mul_right f (inv_ne_zero hc)
 #align interval_integral.integral_comp_div intervalIntegral.integral_comp_div
 
--- porting note: was @[simp]
+-- Porting note (#10618): was @[simp]
 theorem inv_smul_integral_comp_div (c) :
     (c⁻¹ • ∫ x in a..b, f (x / c)) = ∫ x in a / c..b / c, f x := by
   by_cases hc : c = 0 <;> simp [hc, integral_comp_div]
 #align interval_integral.inv_smul_integral_comp_div intervalIntegral.inv_smul_integral_comp_div
 
--- porting note: was @[simp]
+-- Porting note (#10618): was @[simp]
 theorem integral_comp_add_right (d) : (∫ x in a..b, f (x + d)) = ∫ x in a + d..b + d, f x :=
   have A : MeasurableEmbedding fun x => x + d :=
     (Homeomorph.addRight d).closedEmbedding.measurableEmbedding
@@ -747,73 +747,73 @@ theorem integral_comp_add_right (d) : (∫ x in a..b, f (x + d)) = ∫ x in a +
     _ = ∫ x in a + d..b + d, f x := by rw [map_add_right_eq_self]
 #align interval_integral.integral_comp_add_right intervalIntegral.integral_comp_add_right
 
--- porting note: was @[simp]
+-- Porting note (#10618): was @[simp]
 nonrec theorem integral_comp_add_left (d) :
     (∫ x in a..b, f (d + x)) = ∫ x in d + a..d + b, f x := by
   simpa only [add_comm d] using integral_comp_add_right f d
 #align interval_integral.integral_comp_add_left intervalIntegral.integral_comp_add_left
 
--- porting note: was @[simp]
+-- Porting note (#10618): was @[simp]
 theorem integral_comp_mul_add (hc : c ≠ 0) (d) :
     (∫ x in a..b, f (c * x + d)) = c⁻¹ • ∫ x in c * a + d..c * b + d, f x := by
   rw [← integral_comp_add_right, ← integral_comp_mul_left _ hc]
 #align interval_integral.integral_comp_mul_add intervalIntegral.integral_comp_mul_add
 
--- porting note: was @[simp]
+-- Porting note (#10618): was @[simp]
 theorem smul_integral_comp_mul_add (c d) :
     (c • ∫ x in a..b, f (c * x + d)) = ∫ x in c * a + d..c * b + d, f x := by
   by_cases hc : c = 0 <;> simp [hc, integral_comp_mul_add]
 #align interval_integral.smul_integral_comp_mul_add intervalIntegral.smul_integral_comp_mul_add
 
--- porting note: was @[simp]
+-- Porting note (#10618): was @[simp]
 theorem integral_comp_add_mul (hc : c ≠ 0) (d) :
     (∫ x in a..b, f (d + c * x)) = c⁻¹ • ∫ x in d + c * a..d + c * b, f x := by
   rw [← integral_comp_add_left, ← integral_comp_mul_left _ hc]
 #align interval_integral.integral_comp_add_mul intervalIntegral.integral_comp_add_mul
 
--- porting note: was @[simp]
+-- Porting note (#10618): was @[simp]
 theorem smul_integral_comp_add_mul (c d) :
     (c • ∫ x in a..b, f (d + c * x)) = ∫ x in d + c * a..d + c * b, f x := by
   by_cases hc : c = 0 <;> simp [hc, integral_comp_add_mul]
 #align interval_integral.smul_integral_comp_add_mul intervalIntegral.smul_integral_comp_add_mul
 
--- porting note: was @[simp]
+-- Porting note (#10618): was @[simp]
 theorem integral_comp_div_add (hc : c ≠ 0) (d) :
     (∫ x in a..b, f (x / c + d)) = c • ∫ x in a / c + d..b / c + d, f x := by
   simpa only [div_eq_inv_mul, inv_inv] using integral_comp_mul_add f (inv_ne_zero hc) d
 #align interval_integral.integral_comp_div_add intervalIntegral.integral_comp_div_add
 
--- porting note: was @[simp]
+-- Porting note (#10618): was @[simp]
 theorem inv_smul_integral_comp_div_add (c d) :
     (c⁻¹ • ∫ x in a..b, f (x / c + d)) = ∫ x in a / c + d..b / c + d, f x := by
   by_cases hc : c = 0 <;> simp [hc, integral_comp_div_add]
 #align interval_integral.inv_smul_integral_comp_div_add intervalIntegral.inv_smul_integral_comp_div_add
 
--- porting note: was @[simp]
+-- Porting note (#10618): was @[simp]
 theorem integral_comp_add_div (hc : c ≠ 0) (d) :
     (∫ x in a..b, f (d + x / c)) = c • ∫ x in d + a / c..d + b / c, f x := by
   simpa only [div_eq_inv_mul, inv_inv] using integral_comp_add_mul f (inv_ne_zero hc) d
 #align interval_integral.integral_comp_add_div intervalIntegral.integral_comp_add_div
 
--- porting note: was @[simp]
+-- Porting note (#10618): was @[simp]
 theorem inv_smul_integral_comp_add_div (c d) :
     (c⁻¹ • ∫ x in a..b, f (d + x / c)) = ∫ x in d + a / c..d + b / c, f x := by
   by_cases hc : c = 0 <;> simp [hc, integral_comp_add_div]
 #align interval_integral.inv_smul_integral_comp_add_div intervalIntegral.inv_smul_integral_comp_add_div
 
--- porting note: was @[simp]
+-- Porting note (#10618): was @[simp]
 theorem integral_comp_mul_sub (hc : c ≠ 0) (d) :
     (∫ x in a..b, f (c * x - d)) = c⁻¹ • ∫ x in c * a - d..c * b - d, f x := by
   simpa only [sub_eq_add_neg] using integral_comp_mul_add f hc (-d)
 #align interval_integral.integral_comp_mul_sub intervalIntegral.integral_comp_mul_sub
 
--- porting note: was @[simp]
+-- Porting note (#10618): was @[simp]
 theorem smul_integral_comp_mul_sub (c d) :
     (c • ∫ x in a..b, f (c * x - d)) = ∫ x in c * a - d..c * b - d, f x := by
   by_cases hc : c = 0 <;> simp [hc, integral_comp_mul_sub]
 #align interval_integral.smul_integral_comp_mul_sub intervalIntegral.smul_integral_comp_mul_sub
 
--- porting note: was @[simp]
+-- Porting note (#10618): was @[simp]
 theorem integral_comp_sub_mul (hc : c ≠ 0) (d) :
     (∫ x in a..b, f (d - c * x)) = c⁻¹ • ∫ x in d - c * b..d - c * a, f x := by
   simp only [sub_eq_add_neg, neg_mul_eq_neg_mul]
@@ -821,47 +821,47 @@ theorem integral_comp_sub_mul (hc : c ≠ 0) (d) :
   simp only [inv_neg, smul_neg, neg_neg, neg_smul]
 #align interval_integral.integral_comp_sub_mul intervalIntegral.integral_comp_sub_mul
 
--- porting note: was @[simp]
+-- Porting note (#10618): was @[simp]
 theorem smul_integral_comp_sub_mul (c d) :
     (c • ∫ x in a..b, f (d - c * x)) = ∫ x in d - c * b..d - c * a, f x := by
   by_cases hc : c = 0 <;> simp [hc, integral_comp_sub_mul]
 #align interval_integral.smul_integral_comp_sub_mul intervalIntegral.smul_integral_comp_sub_mul
 
--- porting note: was @[simp]
+-- Porting note (#10618): was @[simp]
 theorem integral_comp_div_sub (hc : c ≠ 0) (d) :
     (∫ x in a..b, f (x / c - d)) = c • ∫ x in a / c - d..b / c - d, f x := by
   simpa only [div_eq_inv_mul, inv_inv] using integral_comp_mul_sub f (inv_ne_zero hc) d
 #align interval_integral.integral_comp_div_sub intervalIntegral.integral_comp_div_sub
 
--- porting note: was @[simp]
+-- Porting note (#10618): was @[simp]
 theorem inv_smul_integral_comp_div_sub (c d) :
     (c⁻¹ • ∫ x in a..b, f (x / c - d)) = ∫ x in a / c - d..b / c - d, f x := by
   by_cases hc : c = 0 <;> simp [hc, integral_comp_div_sub]
 #align interval_integral.inv_smul_integral_comp_div_sub intervalIntegral.inv_smul_integral_comp_div_sub
 
--- porting note: was @[simp]
+-- Porting note (#10618): was @[simp]
 theorem integral_comp_sub_div (hc : c ≠ 0) (d) :
     (∫ x in a..b, f (d - x / c)) = c • ∫ x in d - b / c..d - a / c, f x := by
   simpa only [div_eq_inv_mul, inv_inv] using integral_comp_sub_mul f (inv_ne_zero hc) d
 #align interval_integral.integral_comp_sub_div intervalIntegral.integral_comp_sub_div
 
--- porting note: was @[simp]
+-- Porting note (#10618): was @[simp]
 theorem inv_smul_integral_comp_sub_div (c d) :
     (c⁻¹ • ∫ x in a..b, f (d - x / c)) = ∫ x in d - b / c..d - a / c, f x := by
   by_cases hc : c = 0 <;> simp [hc, integral_comp_sub_div]
 #align interval_integral.inv_smul_integral_comp_sub_div intervalIntegral.inv_smul_integral_comp_sub_div
 
--- porting note: was @[simp]
+-- Porting note (#10618): was @[simp]
 theorem integral_comp_sub_right (d) : (∫ x in a..b, f (x - d)) = ∫ x in a - d..b - d, f x := by
   simpa only [sub_eq_add_neg] using integral_comp_add_right f (-d)
 #align interval_integral.integral_comp_sub_right intervalIntegral.integral_comp_sub_right
 
--- porting note: was @[simp]
+-- Porting note (#10618): was @[simp]
 theorem integral_comp_sub_left (d) : (∫ x in a..b, f (d - x)) = ∫ x in d - b..d - a, f x := by
   simpa only [one_mul, one_smul, inv_one] using integral_comp_sub_mul f one_ne_zero d
 #align interval_integral.integral_comp_sub_left intervalIntegral.integral_comp_sub_left
 
--- porting note: was @[simp]
+-- Porting note (#10618): was @[simp]
 theorem integral_comp_neg : (∫ x in a..b, f (-x)) = ∫ x in -b..-a, f x := by
   simpa only [zero_sub] using integral_comp_sub_left f 0
 #align interval_integral.integral_comp_neg intervalIntegral.integral_comp_neg

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

@@ -971,6 +971,18 @@ theorem integral_Iic_sub_Iic (ha : IntegrableOn f (Iic a) μ) (hb : IntegrableOn
   exacts [measurableSet_Ioc, ha, hb.mono_set fun _ => And.right]
 #align interval_integral.integral_Iic_sub_Iic intervalIntegral.integral_Iic_sub_Iic
 
+theorem integral_Iic_add_Ioi (h_left : IntegrableOn f (Iic b) μ)
+    (h_right : IntegrableOn f (Ioi b) μ) :
+    (∫ x in Iic b, f x ∂μ) + (∫ x in Ioi b, f x ∂μ) = ∫ (x : ℝ), f x ∂μ := by
+  convert (integral_union (Iic_disjoint_Ioi <| Eq.le rfl) measurableSet_Ioi h_left h_right).symm
+  rw [Iic_union_Ioi, Measure.restrict_univ]
+
+theorem integral_Iio_add_Ici (h_left : IntegrableOn f (Iio b) μ)
+    (h_right : IntegrableOn f (Ici b) μ) :
+    (∫ x in Iio b, f x ∂μ) + (∫ x in Ici b, f x ∂μ) = ∫ (x : ℝ), f x ∂μ := by
+  convert (integral_union (Iio_disjoint_Ici <| Eq.le rfl) measurableSet_Ici h_left h_right).symm
+  rw [Iio_union_Ici, Measure.restrict_univ]
+
 /-- If `μ` is a finite measure then `∫ x in a..b, c ∂μ = (μ (Iic b) - μ (Iic a)) • c`. -/
 theorem integral_const_of_cdf [IsFiniteMeasure μ] (c : E) :
     ∫ _ in a..b, c ∂μ = ((μ (Iic b)).toReal - (μ (Iic a)).toReal) • c := by

I literally went through and regex'd some uses of cases', replacing them with rcases; this is meant to be a low effort PR as I hope that tools can do this in the future.

rcases is an easier replacement than cases, though with better tools we could in future do a second pass converting simple rcases added here (and existing ones) to cases.

@@ -884,7 +884,7 @@ variable {a b c d : ℝ} {f g : ℝ → E} {μ : Measure ℝ}
 /-- If two functions are equal in the relevant interval, their interval integrals are also equal. -/
 theorem integral_congr {a b : ℝ} (h : EqOn f g [[a, b]]) :
     ∫ x in a..b, f x ∂μ = ∫ x in a..b, g x ∂μ := by
-  cases' le_total a b with hab hab <;>
+  rcases le_total a b with hab | hab <;>
     simpa [hab, integral_of_le, integral_of_ge] using
       set_integral_congr measurableSet_Ioc (h.mono Ioc_subset_Icc_self)
 #align interval_integral.integral_congr intervalIntegral.integral_congr
@@ -981,7 +981,7 @@ theorem integral_const_of_cdf [IsFiniteMeasure μ] (c : E) :
 
 theorem integral_eq_integral_of_support_subset {a b} (h : support f ⊆ Ioc a b) :
     ∫ x in a..b, f x ∂μ = ∫ x, f x ∂μ := by
-  cases' le_total a b with hab hab
+  rcases le_total a b with hab | hab
   · rw [integral_of_le hab, ← integral_indicator measurableSet_Ioc, indicator_eq_self.2 h]
   · rw [Ioc_eq_empty hab.not_lt, subset_empty_iff, support_eq_empty_iff] at h
     simp [h]
@@ -1272,7 +1272,7 @@ theorem integral_eq_zero_iff_of_le_of_nonneg_ae (hab : a ≤ b) (hf : 0 ≤ᵐ[
 theorem integral_eq_zero_iff_of_nonneg_ae (hf : 0 ≤ᵐ[μ.restrict (Ioc a b ∪ Ioc b a)] f)
     (hfi : IntervalIntegrable f μ a b) :
     ∫ x in a..b, f x ∂μ = 0 ↔ f =ᵐ[μ.restrict (Ioc a b ∪ Ioc b a)] 0 := by
-  cases' le_total a b with hab hab <;>
+  rcases le_total a b with hab | hab <;>
     simp only [Ioc_eq_empty hab.not_lt, empty_union, union_empty] at hf ⊢
   · exact integral_eq_zero_iff_of_le_of_nonneg_ae hab hf hfi
   · rw [integral_symm, neg_eq_zero, integral_eq_zero_iff_of_le_of_nonneg_ae hab hf hfi.symm]

We have in the library the lemma not_intervalIntegrable_of_tendsto_norm_atTop_of_deriv_isBigO_filter, saying that if a function tends to infinity at a point in an interval [a, b], then its derivative is not interval-integrable on [a, b]. We generalize this result to allow for any set instead of [a, b], and apply it to half-infinite intervals.

In particular, we characterize integrability of x^s on [a, +oo), and deduce that x^s is never integrable on [0, +oo). This makes it possible to remove one assumption in Lemma mellin_comp_rpow on the Mellin transform.

@@ -86,20 +86,28 @@ theorem IntervalIntegrable.def (h : IntervalIntegrable f μ a b) : IntegrableOn
   intervalIntegrable_iff.mp h
 #align interval_integrable.def IntervalIntegrable.def
 
-theorem intervalIntegrable_iff_integrable_Ioc_of_le (hab : a ≤ b) :
+theorem intervalIntegrable_iff_integrableOn_Ioc_of_le (hab : a ≤ b) :
     IntervalIntegrable f μ a b ↔ IntegrableOn f (Ioc a b) μ := by
   rw [intervalIntegrable_iff, uIoc_of_le hab]
-#align interval_integrable_iff_integrable_Ioc_of_le intervalIntegrable_iff_integrable_Ioc_of_le
+#align interval_integrable_iff_integrable_Ioc_of_le intervalIntegrable_iff_integrableOn_Ioc_of_le
 
 theorem intervalIntegrable_iff' [NoAtoms μ] :
     IntervalIntegrable f μ a b ↔ IntegrableOn f (uIcc a b) μ := by
   rw [intervalIntegrable_iff, ← Icc_min_max, uIoc, integrableOn_Icc_iff_integrableOn_Ioc]
 #align interval_integrable_iff' intervalIntegrable_iff'
 
-theorem intervalIntegrable_iff_integrable_Icc_of_le {f : ℝ → E} {a b : ℝ} (hab : a ≤ b)
+theorem intervalIntegrable_iff_integrableOn_Icc_of_le {f : ℝ → E} {a b : ℝ} (hab : a ≤ b)
     {μ : Measure ℝ} [NoAtoms μ] : IntervalIntegrable f μ a b ↔ IntegrableOn f (Icc a b) μ := by
-  rw [intervalIntegrable_iff_integrable_Ioc_of_le hab, integrableOn_Icc_iff_integrableOn_Ioc]
-#align interval_integrable_iff_integrable_Icc_of_le intervalIntegrable_iff_integrable_Icc_of_le
+  rw [intervalIntegrable_iff_integrableOn_Ioc_of_le hab, integrableOn_Icc_iff_integrableOn_Ioc]
+#align interval_integrable_iff_integrable_Icc_of_le intervalIntegrable_iff_integrableOn_Icc_of_le
+
+theorem intervalIntegrable_iff_integrableOn_Ico_of_le [NoAtoms μ] (hab : a ≤ b) :
+    IntervalIntegrable f μ a b ↔ IntegrableOn f (Ico a b) μ := by
+  rw [intervalIntegrable_iff_integrableOn_Icc_of_le hab, integrableOn_Icc_iff_integrableOn_Ico]
+
+theorem intervalIntegrable_iff_integrableOn_Ioo_of_le [NoAtoms μ] (hab : a ≤ b) :
+    IntervalIntegrable f μ a b ↔ IntegrableOn f (Ioo a b) μ := by
+  rw [intervalIntegrable_iff_integrableOn_Icc_of_le hab, integrableOn_Icc_iff_integrableOn_Ioo]
 
 /-- If a function is integrable with respect to a given measure `μ` then it is interval integrable
   with respect to `μ` on `uIcc a b`. -/
@@ -1197,7 +1205,8 @@ theorem continuousOn_primitive [NoAtoms μ] (h_int : IntegrableOn f (Icc a b) μ
     rw [continuousOn_congr this]
     intro x₀ _
     refine' continuousWithinAt_primitive (measure_singleton x₀) _
-    simp only [intervalIntegrable_iff_integrable_Ioc_of_le, min_eq_left, max_eq_right, h, min_self]
+    simp only [intervalIntegrable_iff_integrableOn_Ioc_of_le, min_eq_left, max_eq_right, h,
+      min_self]
     exact h_int.mono Ioc_subset_Icc_self le_rfl
   · rw [Icc_eq_empty h]
     exact continuousOn_empty _

Rename

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

New lemmas

• Summable.of_norm_bounded_eventually_nat
• Summable.norm

Misc changes

• Golf a few proofs.

@@ -1052,7 +1052,7 @@ theorem hasSum_intervalIntegral_of_summable_norm [Countable ι] {f : ι → C(
   · exact intervalIntegrable_const
   · refine ae_of_all _ fun x hx => Summable.hasSum ?_
     let x : (⟨uIcc a b, isCompact_uIcc⟩ : Compacts ℝ) := ⟨x, ?_⟩; swap; exact ⟨hx.1.le, hx.2⟩
-    have := summable_of_summable_norm hf_sum
+    have := hf_sum.of_norm
     simpa only [Compacts.coe_mk, ContinuousMap.restrict_apply]
       using ContinuousMap.summable_apply this x
 #align interval_integral.has_sum_interval_integral_of_summable_norm intervalIntegral.hasSum_intervalIntegral_of_summable_norm

All the other properties of topological spaces like T0Space or RegularSpace are in the root namespace. Many files were opening TopologicalSpace just for the sake of shortening TopologicalSpace.SecondCountableTopology...

@@ -50,8 +50,6 @@ integral
 
 noncomputable section
 
-open TopologicalSpace (SecondCountableTopology)
-
 open MeasureTheory Set Classical Filter Function
 
 open scoped Classical Topology Filter ENNReal BigOperators Interval NNReal

@@ -227,10 +227,10 @@ protected theorem aestronglyMeasurable (h : IntervalIntegrable f μ a b) :
   h.1.aestronglyMeasurable
 #align interval_integrable.ae_strongly_measurable IntervalIntegrable.aestronglyMeasurable
 
-protected theorem ae_strongly_measurable' (h : IntervalIntegrable f μ a b) :
+protected theorem aestronglyMeasurable' (h : IntervalIntegrable f μ a b) :
     AEStronglyMeasurable f (μ.restrict (Ioc b a)) :=
   h.2.aestronglyMeasurable
-#align interval_integrable.ae_strongly_measurable' IntervalIntegrable.ae_strongly_measurable'
+#align interval_integrable.ae_strongly_measurable' IntervalIntegrable.aestronglyMeasurable'
 
 end
 
@@ -405,8 +405,8 @@ Suppose that `f : ℝ → E` has a finite limit at `l' ⊓ μ.ae`. Then `f` is i
 `u..v` provided that both `u` and `v` tend to `l`.
 
 Typeclass instances allow Lean to find `l'` based on `l` but not vice versa, so
-`apply tendsto.eventually_interval_integrable_ae` will generate goals `Filter ℝ` and
-`tendsto_Ixx_class Ioc ?m_1 l'`. -/
+`apply Tendsto.eventually_intervalIntegrable_ae` will generate goals `Filter ℝ` and
+`TendstoIxxClass Ioc ?m_1 l'`. -/
 theorem Filter.Tendsto.eventually_intervalIntegrable_ae {f : ℝ → E} {μ : Measure ℝ}
     {l l' : Filter ℝ} (hfm : StronglyMeasurableAtFilter f l' μ) [TendstoIxxClass Ioc l l']
     [IsMeasurablyGenerated l'] (hμ : μ.FiniteAtFilter l') {c : E} (hf : Tendsto f (l' ⊓ μ.ae) (𝓝 c))
@@ -423,8 +423,8 @@ Suppose that `f : ℝ → E` has a finite limit at `l`. Then `f` is interval int
 provided that both `u` and `v` tend to `l`.
 
 Typeclass instances allow Lean to find `l'` based on `l` but not vice versa, so
-`apply tendsto.eventually_interval_integrable_ae` will generate goals `Filter ℝ` and
-`tendsto_Ixx_class Ioc ?m_1 l'`. -/
+`apply Tendsto.eventually_intervalIntegrable` will generate goals `Filter ℝ` and
+`TendstoIxxClass Ioc ?m_1 l'`. -/
 theorem Filter.Tendsto.eventually_intervalIntegrable {f : ℝ → E} {μ : Measure ℝ} {l l' : Filter ℝ}
     (hfm : StronglyMeasurableAtFilter f l' μ) [TendstoIxxClass Ioc l l'] [IsMeasurablyGenerated l']
     (hμ : μ.FiniteAtFilter l') {c : E} (hf : Tendsto f l' (𝓝 c)) {u v : ι → ℝ} {lt : Filter ι}

Co-authored-by: Eric Wieser <wieser.eric@gmail.com>

@@ -1195,7 +1195,7 @@ theorem continuousOn_primitive [NoAtoms μ] (h_int : IntegrableOn f (Icc a b) μ
   by_cases h : a ≤ b
   · have : ∀ x ∈ Icc a b, ∫ t in Ioc a x, f t ∂μ = ∫ t in a..x, f t ∂μ := by
       intro x x_in
-      simp_rw [← uIoc_of_le h, integral_of_le x_in.1]
+      simp_rw [integral_of_le x_in.1]
     rw [continuousOn_congr this]
     intro x₀ _
     refine' continuousWithinAt_primitive (measure_singleton x₀) _

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

This has nice performance benefits.

@@ -56,7 +56,7 @@ open MeasureTheory Set Classical Filter Function
 
 open scoped Classical Topology Filter ENNReal BigOperators Interval NNReal
 
-variable {ι 𝕜 E F A : Type _} [NormedAddCommGroup E]
+variable {ι 𝕜 E F A : Type*} [NormedAddCommGroup E]
 
 /-!
 ### Integrability on an interval
@@ -283,7 +283,7 @@ theorem mul_const {f : ℝ → A} (hf : IntervalIntegrable f μ a b) (c : A) :
 #align interval_integrable.mul_const IntervalIntegrable.mul_const
 
 @[simp]
-theorem div_const {𝕜 : Type _} {f : ℝ → 𝕜} [NormedField 𝕜] (h : IntervalIntegrable f μ a b)
+theorem div_const {𝕜 : Type*} {f : ℝ → 𝕜} [NormedField 𝕜] (h : IntervalIntegrable f μ a b)
     (c : 𝕜) : IntervalIntegrable (fun x => f x / c) μ a b := by
   simpa only [div_eq_mul_inv] using mul_const h c⁻¹
 #align interval_integrable.div_const IntervalIntegrable.div_const
@@ -599,32 +599,32 @@ theorem integral_sub (hf : IntervalIntegrable f μ a b) (hg : IntervalIntegrable
 #align interval_integral.integral_sub intervalIntegral.integral_sub
 
 @[simp]
-nonrec theorem integral_smul {𝕜 : Type _} [NontriviallyNormedField 𝕜] [NormedSpace 𝕜 E]
+nonrec theorem integral_smul {𝕜 : Type*} [NontriviallyNormedField 𝕜] [NormedSpace 𝕜 E]
     [SMulCommClass ℝ 𝕜 E] (r : 𝕜) (f : ℝ → E) :
     ∫ x in a..b, r • f x ∂μ = r • ∫ x in a..b, f x ∂μ := by
   simp only [intervalIntegral, integral_smul, smul_sub]
 #align interval_integral.integral_smul intervalIntegral.integral_smul
 
 @[simp]
-nonrec theorem integral_smul_const {𝕜 : Type _} [IsROrC 𝕜] [NormedSpace 𝕜 E] (f : ℝ → 𝕜) (c : E) :
+nonrec theorem integral_smul_const {𝕜 : Type*} [IsROrC 𝕜] [NormedSpace 𝕜 E] (f : ℝ → 𝕜) (c : E) :
     ∫ x in a..b, f x • c ∂μ = (∫ x in a..b, f x ∂μ) • c := by
   simp only [intervalIntegral_eq_integral_uIoc, integral_smul_const, smul_assoc]
 #align interval_integral.integral_smul_const intervalIntegral.integral_smul_const
 
 @[simp]
-theorem integral_const_mul {𝕜 : Type _} [IsROrC 𝕜] (r : 𝕜) (f : ℝ → 𝕜) :
+theorem integral_const_mul {𝕜 : Type*} [IsROrC 𝕜] (r : 𝕜) (f : ℝ → 𝕜) :
     ∫ x in a..b, r * f x ∂μ = r * ∫ x in a..b, f x ∂μ :=
   integral_smul r f
 #align interval_integral.integral_const_mul intervalIntegral.integral_const_mul
 
 @[simp]
-theorem integral_mul_const {𝕜 : Type _} [IsROrC 𝕜] (r : 𝕜) (f : ℝ → 𝕜) :
+theorem integral_mul_const {𝕜 : Type*} [IsROrC 𝕜] (r : 𝕜) (f : ℝ → 𝕜) :
     ∫ x in a..b, f x * r ∂μ = (∫ x in a..b, f x ∂μ) * r := by
   simpa only [mul_comm r] using integral_const_mul r f
 #align interval_integral.integral_mul_const intervalIntegral.integral_mul_const
 
 @[simp]
-theorem integral_div {𝕜 : Type _} [IsROrC 𝕜] (r : 𝕜) (f : ℝ → 𝕜) :
+theorem integral_div {𝕜 : Type*} [IsROrC 𝕜] (r : 𝕜) (f : ℝ → 𝕜) :
     ∫ x in a..b, f x / r ∂μ = (∫ x in a..b, f x ∂μ) / r := by
   simpa only [div_eq_mul_inv] using integral_mul_const r⁻¹ f
 #align interval_integral.integral_div intervalIntegral.integral_div
@@ -648,7 +648,7 @@ nonrec theorem integral_smul_measure (c : ℝ≥0∞) :
 end Basic
 
 -- porting note: TODO: add `Complex.ofReal` version of `_root_.integral_ofReal`
-nonrec theorem _root_.IsROrC.interval_integral_ofReal {𝕜 : Type _} [IsROrC 𝕜] {a b : ℝ}
+nonrec theorem _root_.IsROrC.interval_integral_ofReal {𝕜 : Type*} [IsROrC 𝕜] {a b : ℝ}
     {μ : Measure ℝ} {f : ℝ → ℝ} : (∫ x in a..b, (f x : 𝕜) ∂μ) = ↑(∫ x in a..b, f x ∂μ) := by
   simp only [intervalIntegral, integral_ofReal, IsROrC.ofReal_sub]
 
@@ -1065,7 +1065,7 @@ theorem tsum_intervalIntegral_eq_of_summable_norm [Countable ι] {f : ι → C(
   (hasSum_intervalIntegral_of_summable_norm hf_sum).tsum_eq
 #align interval_integral.tsum_interval_integral_eq_of_summable_norm intervalIntegral.tsum_intervalIntegral_eq_of_summable_norm
 
-variable {X : Type _} [TopologicalSpace X] [FirstCountableTopology X]
+variable {X : Type*} [TopologicalSpace X] [FirstCountableTopology X]
 
 /-- Continuity of interval integral with respect to a parameter, at a point within a set.
   Given `F : X → ℝ → E`, assume `F x` is ae-measurable on `[a, b]` for `x` in a

• depends on: #5966

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

@@ -2,16 +2,13 @@
 Copyright (c) 2020 Yury G. Kudryashov. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury G. Kudryashov, Patrick Massot, Sébastien Gouëzel
-
-! This file was ported from Lean 3 source module measure_theory.integral.interval_integral
-! leanprover-community/mathlib commit fd5edc43dc4f10b85abfe544b88f82cf13c5f844
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Data.Set.Intervals.Disjoint
 import Mathlib.MeasureTheory.Integral.SetIntegral
 import Mathlib.MeasureTheory.Measure.Lebesgue.Basic
 
+#align_import measure_theory.integral.interval_integral from "leanprover-community/mathlib"@"fd5edc43dc4f10b85abfe544b88f82cf13c5f844"
+
 /-!
 # Integral over an interval
 

@@ -298,7 +298,7 @@ theorem comp_mul_left (hf : IntervalIntegrable f volume a b) (c : ℝ) :
   have A : MeasurableEmbedding fun x => x * c⁻¹ :=
     (Homeomorph.mulRight₀ _ (inv_ne_zero hc)).closedEmbedding.measurableEmbedding
   rw [← Real.smul_map_volume_mul_right (inv_ne_zero hc), IntegrableOn, Measure.restrict_smul,
-    integrable_smul_measure (by simpa : ENNReal.ofReal (|c⁻¹|) ≠ 0) ENNReal.ofReal_ne_top,
+    integrable_smul_measure (by simpa : ENNReal.ofReal |c⁻¹| ≠ 0) ENNReal.ofReal_ne_top,
     ← IntegrableOn, MeasurableEmbedding.integrableOn_map_iff A]
   convert hf using 1
   · ext; simp only [comp_apply]; congr 1; field_simp; ring

• Also remove most superfluous parentheses around big operators (∑, ∏ and variants).
• roughly the used regex: ([^a-zA-Zα-ωΑ-Ω'𝓝ℳ₀𝕂ₛ)]) \(([∑∏][^()∑∏]*,[^()∑∏:]*)\) ([⊂⊆=<≤]) replaced by $1 $2 $3

@@ -908,7 +908,7 @@ theorem integral_add_adjacent_intervals (hab : IntervalIntegrable f μ a b)
 
 theorem sum_integral_adjacent_intervals_Ico {a : ℕ → ℝ} {m n : ℕ} (hmn : m ≤ n)
     (hint : ∀ k ∈ Ico m n, IntervalIntegrable f μ (a k) (a <| k + 1)) :
-    (∑ k : ℕ in Finset.Ico m n, ∫ x in a k..a <| k + 1, f x ∂μ) = ∫ x in a m..a n, f x ∂μ := by
+    ∑ k : ℕ in Finset.Ico m n, ∫ x in a k..a <| k + 1, f x ∂μ = ∫ x in a m..a n, f x ∂μ := by
   revert hint
   refine' Nat.le_induction _ _ n hmn
   · simp
@@ -924,7 +924,7 @@ theorem sum_integral_adjacent_intervals_Ico {a : ℕ → ℝ} {m n : ℕ} (hmn :
 
 theorem sum_integral_adjacent_intervals {a : ℕ → ℝ} {n : ℕ}
     (hint : ∀ k < n, IntervalIntegrable f μ (a k) (a <| k + 1)) :
-    (∑ k : ℕ in Finset.range n, ∫ x in a k..a <| k + 1, f x ∂μ) = ∫ x in (a 0)..(a n), f x ∂μ := by
+    ∑ k : ℕ in Finset.range n, ∫ x in a k..a <| k + 1, f x ∂μ = ∫ x in (a 0)..(a n), f x ∂μ := by
   rw [← Nat.Ico_zero_eq_range]
   exact sum_integral_adjacent_intervals_Ico (zero_le n) fun k hk => hint k hk.2
 #align interval_integral.sum_integral_adjacent_intervals intervalIntegral.sum_integral_adjacent_intervals
@@ -1064,7 +1064,7 @@ theorem hasSum_intervalIntegral_of_summable_norm [Countable ι] {f : ι → C(
 
 theorem tsum_intervalIntegral_eq_of_summable_norm [Countable ι] {f : ι → C(ℝ, E)}
     (hf_sum : Summable fun i : ι => ‖(f i).restrict (⟨uIcc a b, isCompact_uIcc⟩ : Compacts ℝ)‖) :
-    (∑' i : ι, ∫ x in a..b, f i x) = ∫ x in a..b, ∑' i : ι, f i x :=
+    ∑' i : ι, ∫ x in a..b, f i x = ∫ x in a..b, ∑' i : ι, f i x :=
   (hasSum_intervalIntegral_of_summable_norm hf_sum).tsum_eq
 #align interval_integral.tsum_interval_integral_eq_of_summable_norm intervalIntegral.tsum_intervalIntegral_eq_of_summable_norm
 

@@ -465,25 +465,25 @@ variable {a b : ℝ} {f g : ℝ → E} {μ : Measure ℝ}
 theorem integral_zero : (∫ _ in a..b, (0 : E) ∂μ) = 0 := by simp [intervalIntegral]
 #align interval_integral.integral_zero intervalIntegral.integral_zero
 
-theorem integral_of_le (h : a ≤ b) : (∫ x in a..b, f x ∂μ) = ∫ x in Ioc a b, f x ∂μ := by
+theorem integral_of_le (h : a ≤ b) : ∫ x in a..b, f x ∂μ = ∫ x in Ioc a b, f x ∂μ := by
   simp [intervalIntegral, h]
 #align interval_integral.integral_of_le intervalIntegral.integral_of_le
 
 @[simp]
-theorem integral_same : (∫ x in a..a, f x ∂μ) = 0 :=
+theorem integral_same : ∫ x in a..a, f x ∂μ = 0 :=
   sub_self _
 #align interval_integral.integral_same intervalIntegral.integral_same
 
-theorem integral_symm (a b) : (∫ x in b..a, f x ∂μ) = -∫ x in a..b, f x ∂μ := by
+theorem integral_symm (a b) : ∫ x in b..a, f x ∂μ = -∫ x in a..b, f x ∂μ := by
   simp only [intervalIntegral, neg_sub]
 #align interval_integral.integral_symm intervalIntegral.integral_symm
 
-theorem integral_of_ge (h : b ≤ a) : (∫ x in a..b, f x ∂μ) = -∫ x in Ioc b a, f x ∂μ := by
+theorem integral_of_ge (h : b ≤ a) : ∫ x in a..b, f x ∂μ = -∫ x in Ioc b a, f x ∂μ := by
   simp only [integral_symm b, integral_of_le h]
 #align interval_integral.integral_of_ge intervalIntegral.integral_of_ge
 
 theorem intervalIntegral_eq_integral_uIoc (f : ℝ → E) (a b : ℝ) (μ : Measure ℝ) :
-    (∫ x in a..b, f x ∂μ) = (if a ≤ b then 1 else -1 : ℝ) • ∫ x in Ι a b, f x ∂μ := by
+    ∫ x in a..b, f x ∂μ = (if a ≤ b then 1 else -1 : ℝ) • ∫ x in Ι a b, f x ∂μ := by
   split_ifs with h
   · simp only [integral_of_le h, uIoc_of_le h, one_smul]
   · simp only [integral_of_ge (not_le.1 h).le, uIoc_of_lt (not_le.1 h), neg_one_smul]
@@ -505,7 +505,7 @@ theorem integral_cases (f : ℝ → E) (a b) :
   rw [intervalIntegral_eq_integral_uIoc]; split_ifs <;> simp
 #align interval_integral.integral_cases intervalIntegral.integral_cases
 
-nonrec theorem integral_undef (h : ¬IntervalIntegrable f μ a b) : (∫ x in a..b, f x ∂μ) = 0 := by
+nonrec theorem integral_undef (h : ¬IntervalIntegrable f μ a b) : ∫ x in a..b, f x ∂μ = 0 := by
   rw [intervalIntegrable_iff] at h
   rw [intervalIntegral_eq_integral_uIoc, integral_undef h, smul_zero]
 #align interval_integral.integral_undef intervalIntegral.integral_undef
@@ -517,12 +517,12 @@ theorem intervalIntegrable_of_integral_ne_zero {a b : ℝ} {f : ℝ → E} {μ :
 
 nonrec theorem integral_non_aestronglyMeasurable
     (hf : ¬AEStronglyMeasurable f (μ.restrict (Ι a b))) :
-    (∫ x in a..b, f x ∂μ) = 0 := by
+    ∫ x in a..b, f x ∂μ = 0 := by
   rw [intervalIntegral_eq_integral_uIoc, integral_non_aestronglyMeasurable hf, smul_zero]
 #align interval_integral.integral_non_ae_strongly_measurable intervalIntegral.integral_non_aestronglyMeasurable
 
 theorem integral_non_aestronglyMeasurable_of_le (h : a ≤ b)
-    (hf : ¬AEStronglyMeasurable f (μ.restrict (Ioc a b))) : (∫ x in a..b, f x ∂μ) = 0 :=
+    (hf : ¬AEStronglyMeasurable f (μ.restrict (Ioc a b))) : ∫ x in a..b, f x ∂μ = 0 :=
   integral_non_aestronglyMeasurable <| by rwa [uIoc_of_le h]
 #align interval_integral.integral_non_ae_strongly_measurable_of_le intervalIntegral.integral_non_aestronglyMeasurable_of_le
 
@@ -579,72 +579,72 @@ theorem norm_integral_le_of_norm_le_const {a b C : ℝ} {f : ℝ → E} (h : ∀
 
 @[simp]
 nonrec theorem integral_add (hf : IntervalIntegrable f μ a b) (hg : IntervalIntegrable g μ a b) :
-    (∫ x in a..b, f x + g x ∂μ) = (∫ x in a..b, f x ∂μ) + ∫ x in a..b, g x ∂μ := by
+    ∫ x in a..b, f x + g x ∂μ = (∫ x in a..b, f x ∂μ) + ∫ x in a..b, g x ∂μ := by
   simp only [intervalIntegral_eq_integral_uIoc, integral_add hf.def hg.def, smul_add]
 #align interval_integral.integral_add intervalIntegral.integral_add
 
 nonrec theorem integral_finset_sum {ι} {s : Finset ι} {f : ι → ℝ → E}
     (h : ∀ i ∈ s, IntervalIntegrable (f i) μ a b) :
-    (∫ x in a..b, ∑ i in s, f i x ∂μ) = ∑ i in s, ∫ x in a..b, f i x ∂μ := by
+    ∫ x in a..b, ∑ i in s, f i x ∂μ = ∑ i in s, ∫ x in a..b, f i x ∂μ := by
   simp only [intervalIntegral_eq_integral_uIoc, integral_finset_sum s fun i hi => (h i hi).def,
     Finset.smul_sum]
 #align interval_integral.integral_finset_sum intervalIntegral.integral_finset_sum
 
 @[simp]
-nonrec theorem integral_neg : (∫ x in a..b, -f x ∂μ) = -∫ x in a..b, f x ∂μ := by
+nonrec theorem integral_neg : ∫ x in a..b, -f x ∂μ = -∫ x in a..b, f x ∂μ := by
   simp only [intervalIntegral, integral_neg]; abel
 #align interval_integral.integral_neg intervalIntegral.integral_neg
 
 @[simp]
 theorem integral_sub (hf : IntervalIntegrable f μ a b) (hg : IntervalIntegrable g μ a b) :
-    (∫ x in a..b, f x - g x ∂μ) = (∫ x in a..b, f x ∂μ) - ∫ x in a..b, g x ∂μ := by
+    ∫ x in a..b, f x - g x ∂μ = (∫ x in a..b, f x ∂μ) - ∫ x in a..b, g x ∂μ := by
   simpa only [sub_eq_add_neg] using (integral_add hf hg.neg).trans (congr_arg _ integral_neg)
 #align interval_integral.integral_sub intervalIntegral.integral_sub
 
 @[simp]
 nonrec theorem integral_smul {𝕜 : Type _} [NontriviallyNormedField 𝕜] [NormedSpace 𝕜 E]
     [SMulCommClass ℝ 𝕜 E] (r : 𝕜) (f : ℝ → E) :
-    (∫ x in a..b, r • f x ∂μ) = r • ∫ x in a..b, f x ∂μ := by
+    ∫ x in a..b, r • f x ∂μ = r • ∫ x in a..b, f x ∂μ := by
   simp only [intervalIntegral, integral_smul, smul_sub]
 #align interval_integral.integral_smul intervalIntegral.integral_smul
 
 @[simp]
 nonrec theorem integral_smul_const {𝕜 : Type _} [IsROrC 𝕜] [NormedSpace 𝕜 E] (f : ℝ → 𝕜) (c : E) :
-    (∫ x in a..b, f x • c ∂μ) = (∫ x in a..b, f x ∂μ) • c := by
+    ∫ x in a..b, f x • c ∂μ = (∫ x in a..b, f x ∂μ) • c := by
   simp only [intervalIntegral_eq_integral_uIoc, integral_smul_const, smul_assoc]
 #align interval_integral.integral_smul_const intervalIntegral.integral_smul_const
 
 @[simp]
 theorem integral_const_mul {𝕜 : Type _} [IsROrC 𝕜] (r : 𝕜) (f : ℝ → 𝕜) :
-    (∫ x in a..b, r * f x ∂μ) = r * ∫ x in a..b, f x ∂μ :=
+    ∫ x in a..b, r * f x ∂μ = r * ∫ x in a..b, f x ∂μ :=
   integral_smul r f
 #align interval_integral.integral_const_mul intervalIntegral.integral_const_mul
 
 @[simp]
 theorem integral_mul_const {𝕜 : Type _} [IsROrC 𝕜] (r : 𝕜) (f : ℝ → 𝕜) :
-    (∫ x in a..b, f x * r ∂μ) = (∫ x in a..b, f x ∂μ) * r := by
+    ∫ x in a..b, f x * r ∂μ = (∫ x in a..b, f x ∂μ) * r := by
   simpa only [mul_comm r] using integral_const_mul r f
 #align interval_integral.integral_mul_const intervalIntegral.integral_mul_const
 
 @[simp]
 theorem integral_div {𝕜 : Type _} [IsROrC 𝕜] (r : 𝕜) (f : ℝ → 𝕜) :
-    (∫ x in a..b, f x / r ∂μ) = (∫ x in a..b, f x ∂μ) / r := by
+    ∫ x in a..b, f x / r ∂μ = (∫ x in a..b, f x ∂μ) / r := by
   simpa only [div_eq_mul_inv] using integral_mul_const r⁻¹ f
 #align interval_integral.integral_div intervalIntegral.integral_div
 
 theorem integral_const' (c : E) :
-    (∫ _ in a..b, c ∂μ) = ((μ <| Ioc a b).toReal - (μ <| Ioc b a).toReal) • c := by
+    ∫ _ in a..b, c ∂μ = ((μ <| Ioc a b).toReal - (μ <| Ioc b a).toReal) • c := by
   simp only [intervalIntegral, set_integral_const, sub_smul]
 #align interval_integral.integral_const' intervalIntegral.integral_const'
 
 @[simp]
-theorem integral_const (c : E) : (∫ _ in a..b, c) = (b - a) • c := by
+theorem integral_const (c : E) : ∫ _ in a..b, c = (b - a) • c := by
   simp only [integral_const', Real.volume_Ioc, ENNReal.toReal_ofReal', ← neg_sub b,
     max_zero_sub_eq_self]
 #align interval_integral.integral_const intervalIntegral.integral_const
 
 nonrec theorem integral_smul_measure (c : ℝ≥0∞) :
-    (∫ x in a..b, f x ∂c • μ) = c.toReal • ∫ x in a..b, f x ∂μ := by
+    ∫ x in a..b, f x ∂c • μ = c.toReal • ∫ x in a..b, f x ∂μ := by
   simp only [intervalIntegral, Measure.restrict_smul, integral_smul_measure, smul_sub]
 #align interval_integral.integral_smul_measure intervalIntegral.integral_smul_measure
 
@@ -880,7 +880,7 @@ variable {a b c d : ℝ} {f g : ℝ → E} {μ : Measure ℝ}
 
 /-- If two functions are equal in the relevant interval, their interval integrals are also equal. -/
 theorem integral_congr {a b : ℝ} (h : EqOn f g [[a, b]]) :
-    (∫ x in a..b, f x ∂μ) = ∫ x in a..b, g x ∂μ := by
+    ∫ x in a..b, f x ∂μ = ∫ x in a..b, g x ∂μ := by
   cases' le_total a b with hab hab <;>
     simpa [hab, integral_of_le, integral_of_ge] using
       set_integral_congr measurableSet_Ioc (h.mono Ioc_subset_Icc_self)
@@ -970,14 +970,14 @@ theorem integral_Iic_sub_Iic (ha : IntegrableOn f (Iic a) μ) (hb : IntegrableOn
 
 /-- If `μ` is a finite measure then `∫ x in a..b, c ∂μ = (μ (Iic b) - μ (Iic a)) • c`. -/
 theorem integral_const_of_cdf [IsFiniteMeasure μ] (c : E) :
-    (∫ _ in a..b, c ∂μ) = ((μ (Iic b)).toReal - (μ (Iic a)).toReal) • c := by
+    ∫ _ in a..b, c ∂μ = ((μ (Iic b)).toReal - (μ (Iic a)).toReal) • c := by
   simp only [sub_smul, ← set_integral_const]
   refine' (integral_Iic_sub_Iic _ _).symm <;>
     simp only [integrableOn_const, measure_lt_top, or_true_iff]
 #align interval_integral.integral_const_of_cdf intervalIntegral.integral_const_of_cdf
 
 theorem integral_eq_integral_of_support_subset {a b} (h : support f ⊆ Ioc a b) :
-    (∫ x in a..b, f x ∂μ) = ∫ x, f x ∂μ := by
+    ∫ x in a..b, f x ∂μ = ∫ x, f x ∂μ := by
   cases' le_total a b with hab hab
   · rw [integral_of_le hab, ← integral_indicator measurableSet_Ioc, indicator_eq_self.2 h]
   · rw [Ioc_eq_empty hab.not_lt, subset_empty_iff, support_eq_empty_iff] at h
@@ -985,24 +985,24 @@ theorem integral_eq_integral_of_support_subset {a b} (h : support f ⊆ Ioc a b)
 #align interval_integral.integral_eq_integral_of_support_subset intervalIntegral.integral_eq_integral_of_support_subset
 
 theorem integral_congr_ae' (h : ∀ᵐ x ∂μ, x ∈ Ioc a b → f x = g x)
-    (h' : ∀ᵐ x ∂μ, x ∈ Ioc b a → f x = g x) : (∫ x in a..b, f x ∂μ) = ∫ x in a..b, g x ∂μ := by
+    (h' : ∀ᵐ x ∂μ, x ∈ Ioc b a → f x = g x) : ∫ x in a..b, f x ∂μ = ∫ x in a..b, g x ∂μ := by
   simp only [intervalIntegral, set_integral_congr_ae measurableSet_Ioc h,
     set_integral_congr_ae measurableSet_Ioc h']
 #align interval_integral.integral_congr_ae' intervalIntegral.integral_congr_ae'
 
 theorem integral_congr_ae (h : ∀ᵐ x ∂μ, x ∈ Ι a b → f x = g x) :
-    (∫ x in a..b, f x ∂μ) = ∫ x in a..b, g x ∂μ :=
+    ∫ x in a..b, f x ∂μ = ∫ x in a..b, g x ∂μ :=
   integral_congr_ae' (ae_uIoc_iff.mp h).1 (ae_uIoc_iff.mp h).2
 #align interval_integral.integral_congr_ae intervalIntegral.integral_congr_ae
 
-theorem integral_zero_ae (h : ∀ᵐ x ∂μ, x ∈ Ι a b → f x = 0) : (∫ x in a..b, f x ∂μ) = 0 :=
+theorem integral_zero_ae (h : ∀ᵐ x ∂μ, x ∈ Ι a b → f x = 0) : ∫ x in a..b, f x ∂μ = 0 :=
   calc
-    (∫ x in a..b, f x ∂μ) = ∫ _ in a..b, 0 ∂μ := integral_congr_ae h
+    ∫ x in a..b, f x ∂μ = ∫ _ in a..b, 0 ∂μ := integral_congr_ae h
     _ = 0 := integral_zero
 #align interval_integral.integral_zero_ae intervalIntegral.integral_zero_ae
 
 nonrec theorem integral_indicator {a₁ a₂ a₃ : ℝ} (h : a₂ ∈ Icc a₁ a₃) :
-    (∫ x in a₁..a₃, indicator {x | x ≤ a₂} f x ∂μ) = ∫ x in a₁..a₂, f x ∂μ := by
+    ∫ x in a₁..a₃, indicator {x | x ≤ a₂} f x ∂μ = ∫ x in a₁..a₂, f x ∂μ := by
   have : {x | x ≤ a₂} ∩ Ioc a₁ a₃ = Ioc a₁ a₂ := Iic_inter_Ioc_of_le h.2
   rw [integral_of_le h.1, integral_of_le (h.1.trans h.2), integral_indicator,
     Measure.restrict_restrict, this]
@@ -1140,7 +1140,7 @@ theorem continuousWithinAt_primitive (hb₀ : μ {b₀} = 0)
       · exact ⟨min_le_of_left_le <| (min_le_right _ _).trans h₁,
           le_max_of_le_right <| h₂.trans <| le_max_right _ _⟩
     have : ∀ b ∈ Icc b₁ b₂,
-        (∫ x in a..b, f x ∂μ) = (∫ x in a..b₁, f x ∂μ) + ∫ x in b₁..b, f x ∂μ := by
+        ∫ x in a..b, f x ∂μ = (∫ x in a..b₁, f x ∂μ) + ∫ x in b₁..b, f x ∂μ := by
       rintro b ⟨h₁, h₂⟩
       rw [← integral_add_adjacent_intervals _ (h_int' ⟨h₁, h₂⟩)]
       apply h_int.mono_set
@@ -1196,7 +1196,7 @@ theorem continuousWithinAt_primitive (hb₀ : μ {b₀} = 0)
 theorem continuousOn_primitive [NoAtoms μ] (h_int : IntegrableOn f (Icc a b) μ) :
     ContinuousOn (fun x => ∫ t in Ioc a x, f t ∂μ) (Icc a b) := by
   by_cases h : a ≤ b
-  · have : ∀ x ∈ Icc a b, (∫ t in Ioc a x, f t ∂μ) = ∫ t in a..x, f t ∂μ := by
+  · have : ∀ x ∈ Icc a b, ∫ t in Ioc a x, f t ∂μ = ∫ t in a..x, f t ∂μ := by
       intro x x_in
       simp_rw [← uIoc_of_le h, integral_of_le x_in.1]
     rw [continuousOn_congr this]
@@ -1261,13 +1261,13 @@ section
 variable {f g : ℝ → ℝ} {a b : ℝ} {μ : Measure ℝ}
 
 theorem integral_eq_zero_iff_of_le_of_nonneg_ae (hab : a ≤ b) (hf : 0 ≤ᵐ[μ.restrict (Ioc a b)] f)
-    (hfi : IntervalIntegrable f μ a b) : (∫ x in a..b, f x ∂μ) = 0 ↔ f =ᵐ[μ.restrict (Ioc a b)] 0 :=
+    (hfi : IntervalIntegrable f μ a b) : ∫ x in a..b, f x ∂μ = 0 ↔ f =ᵐ[μ.restrict (Ioc a b)] 0 :=
   by rw [integral_of_le hab, integral_eq_zero_iff_of_nonneg_ae hf hfi.1]
 #align interval_integral.integral_eq_zero_iff_of_le_of_nonneg_ae intervalIntegral.integral_eq_zero_iff_of_le_of_nonneg_ae
 
 theorem integral_eq_zero_iff_of_nonneg_ae (hf : 0 ≤ᵐ[μ.restrict (Ioc a b ∪ Ioc b a)] f)
     (hfi : IntervalIntegrable f μ a b) :
-    (∫ x in a..b, f x ∂μ) = 0 ↔ f =ᵐ[μ.restrict (Ioc a b ∪ Ioc b a)] 0 := by
+    ∫ x in a..b, f x ∂μ = 0 ↔ f =ᵐ[μ.restrict (Ioc a b ∪ Ioc b a)] 0 := by
   cases' le_total a b with hab hab <;>
     simp only [Ioc_eq_empty hab.not_lt, empty_union, union_empty] at hf ⊢
   · exact integral_eq_zero_iff_of_le_of_nonneg_ae hab hf hfi

Found with git grep -n "λ [a-zA-Z_ ]*,"

@@ -1073,9 +1073,9 @@ variable {X : Type _} [TopologicalSpace X] [FirstCountableTopology X]
 /-- Continuity of interval integral with respect to a parameter, at a point within a set.
   Given `F : X → ℝ → E`, assume `F x` is ae-measurable on `[a, b]` for `x` in a
   neighborhood of `x₀` within `s` and at `x₀`, and assume it is bounded by a function integrable
-  on `[a, b]` independent of `x` in a neighborhood of `x₀` within `s`. If `(λ x, F x t)`
+  on `[a, b]` independent of `x` in a neighborhood of `x₀` within `s`. If `(fun x ↦ F x t)`
   is continuous at `x₀` within `s` for almost every `t` in `[a, b]`
-  then the same holds for `(λ x, ∫ t in a..b, F x t ∂μ) s x₀`. -/
+  then the same holds for `(fun x ↦ ∫ t in a..b, F x t ∂μ) s x₀`. -/
 theorem continuousWithinAt_of_dominated_interval {F : X → ℝ → E} {x₀ : X} {bound : ℝ → ℝ} {a b : ℝ}
     {s : Set X} (hF_meas : ∀ᶠ x in 𝓝[s] x₀, AEStronglyMeasurable (F x) (μ.restrict <| Ι a b))
     (h_bound : ∀ᶠ x in 𝓝[s] x₀, ∀ᵐ t ∂μ, t ∈ Ι a b → ‖F x t‖ ≤ bound t)
@@ -1088,9 +1088,9 @@ theorem continuousWithinAt_of_dominated_interval {F : X → ℝ → E} {x₀ : X
 /-- Continuity of interval integral with respect to a parameter at a point.
   Given `F : X → ℝ → E`, assume `F x` is ae-measurable on `[a, b]` for `x` in a
   neighborhood of `x₀`, and assume it is bounded by a function integrable on
-  `[a, b]` independent of `x` in a neighborhood of `x₀`. If `(λ x, F x t)`
+  `[a, b]` independent of `x` in a neighborhood of `x₀`. If `(fun x ↦ F x t)`
   is continuous at `x₀` for almost every `t` in `[a, b]`
-  then the same holds for `(λ x, ∫ t in a..b, F x t ∂μ) s x₀`. -/
+  then the same holds for `(fun x ↦ ∫ t in a..b, F x t ∂μ) s x₀`. -/
 theorem continuousAt_of_dominated_interval {F : X → ℝ → E} {x₀ : X} {bound : ℝ → ℝ} {a b : ℝ}
     (hF_meas : ∀ᶠ x in 𝓝 x₀, AEStronglyMeasurable (F x) (μ.restrict <| Ι a b))
     (h_bound : ∀ᶠ x in 𝓝 x₀, ∀ᵐ t ∂μ, t ∈ Ι a b → ‖F x t‖ ≤ bound t)
@@ -1103,8 +1103,8 @@ theorem continuousAt_of_dominated_interval {F : X → ℝ → E} {x₀ : X} {bou
 /-- Continuity of interval integral with respect to a parameter.
   Given `F : X → ℝ → E`, assume each `F x` is ae-measurable on `[a, b]`,
   and assume it is bounded by a function integrable on `[a, b]` independent of `x`.
-  If `(λ x, F x t)` is continuous for almost every `t` in `[a, b]`
-  then the same holds for `(λ x, ∫ t in a..b, F x t ∂μ) s x₀`. -/
+  If `(fun x ↦ F x t)` is continuous for almost every `t` in `[a, b]`
+  then the same holds for `(fun x ↦ ∫ t in a..b, F x t ∂μ) s x₀`. -/
 theorem continuous_of_dominated_interval {F : X → ℝ → E} {bound : ℝ → ℝ} {a b : ℝ}
     (hF_meas : ∀ x, AEStronglyMeasurable (F x) <| μ.restrict <| Ι a b)
     (h_bound : ∀ x, ∀ᵐ t ∂μ, t ∈ Ι a b → ‖F x t‖ ≤ bound t)

Also drop some of the parentheses that are no longer needed.

@@ -451,8 +451,9 @@ def intervalIntegral (f : ℝ → E) (a b : ℝ) (μ : Measure ℝ) : E :=
   (∫ x in Ioc a b, f x ∂μ) - ∫ x in Ioc b a, f x ∂μ
 #align interval_integral intervalIntegral
 
-notation3"∫ "(...)" in "a".."b", "r:(scoped f => f)" ∂"μ => intervalIntegral r a b μ
-notation3"∫ "(...)" in "a".."b", "r:(scoped f => intervalIntegral f a b volume) => r
+notation3"∫ "(...)" in "a".."b", "r:60:(scoped f => f)" ∂"μ:70 => intervalIntegral r a b μ
+
+notation3"∫ "(...)" in "a".."b", "r:60:(scoped f => intervalIntegral f a b volume) => r
 
 namespace intervalIntegral
 

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