measure_theory.constructions.prod.integral ⟷ Mathlib.MeasureTheory.Constructions.Prod.Integral

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

@@ -575,15 +575,15 @@ theorem integral_integral_swap ⦃f : α → β → E⦄ (hf : Integrable (uncur
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
-#print MeasureTheory.set_integral_prod /-
+#print MeasureTheory.setIntegral_prod /-
 /-- **Fubini's Theorem** for set integrals. -/
-theorem set_integral_prod (f : α × β → E) {s : Set α} {t : Set β}
+theorem setIntegral_prod (f : α × β → E) {s : Set α} {t : Set β}
     (hf : IntegrableOn f (s ×ˢ t) (μ.Prod ν)) :
     ∫ z in s ×ˢ t, f z ∂μ.Prod ν = ∫ x in s, ∫ y in t, f (x, y) ∂ν ∂μ :=
   by
   simp only [← measure.prod_restrict s t, integrable_on] at hf ⊢
   exact integral_prod f hf
-#align measure_theory.set_integral_prod MeasureTheory.set_integral_prod
+#align measure_theory.set_integral_prod MeasureTheory.setIntegral_prod
 -/
 
 #print MeasureTheory.integral_prod_mul /-
@@ -602,11 +602,11 @@ theorem integral_prod_mul {L : Type _} [RCLike L] (f : α → L) (g : β → L)
 -/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
-#print MeasureTheory.set_integral_prod_mul /-
-theorem set_integral_prod_mul {L : Type _} [RCLike L] (f : α → L) (g : β → L) (s : Set α)
+#print MeasureTheory.setIntegral_prod_mul /-
+theorem setIntegral_prod_mul {L : Type _} [RCLike L] (f : α → L) (g : β → L) (s : Set α)
     (t : Set β) : ∫ z in s ×ˢ t, f z.1 * g z.2 ∂μ.Prod ν = (∫ x in s, f x ∂μ) * ∫ y in t, g y ∂ν :=
   by simp only [← measure.prod_restrict s t, integrable_on, integral_prod_mul]
-#align measure_theory.set_integral_prod_mul MeasureTheory.set_integral_prod_mul
+#align measure_theory.set_integral_prod_mul MeasureTheory.setIntegral_prod_mul
 -/
 
 end MeasureTheory

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

@@ -351,7 +351,7 @@ theorem Integrable.integral_norm_prod_right [SigmaFinite μ] ⦃f : α × β →
 -/
 
 #print MeasureTheory.Integrable.prod_mul /-
-theorem MeasureTheory.Integrable.prod_mul {L : Type _} [IsROrC L] {f : α → L} {g : β → L}
+theorem MeasureTheory.Integrable.prod_mul {L : Type _} [RCLike L] {f : α → L} {g : β → L}
     (hf : Integrable f μ) (hg : Integrable g ν) :
     Integrable (fun z : α × β => f z.1 * g z.2) (μ.Prod ν) :=
   by
@@ -587,7 +587,7 @@ theorem set_integral_prod (f : α × β → E) {s : Set α} {t : Set β}
 -/
 
 #print MeasureTheory.integral_prod_mul /-
-theorem integral_prod_mul {L : Type _} [IsROrC L] (f : α → L) (g : β → L) :
+theorem integral_prod_mul {L : Type _} [RCLike L] (f : α → L) (g : β → L) :
     ∫ z, f z.1 * g z.2 ∂μ.Prod ν = (∫ x, f x ∂μ) * ∫ y, g y ∂ν :=
   by
   by_cases h : integrable (fun z : α × β => f z.1 * g z.2) (μ.prod ν)
@@ -603,7 +603,7 @@ theorem integral_prod_mul {L : Type _} [IsROrC L] (f : α → L) (g : β → L)
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 #print MeasureTheory.set_integral_prod_mul /-
-theorem set_integral_prod_mul {L : Type _} [IsROrC L] (f : α → L) (g : β → L) (s : Set α)
+theorem set_integral_prod_mul {L : Type _} [RCLike L] (f : α → L) (g : β → L) (s : Set α)
     (t : Set β) : ∫ z in s ×ˢ t, f z.1 * g z.2 ∂μ.Prod ν = (∫ x in s, f x ∂μ) * ∫ y in t, g y ∂ν :=
   by simp only [← measure.prod_restrict s t, integrable_on, integral_prod_mul]
 #align measure_theory.set_integral_prod_mul MeasureTheory.set_integral_prod_mul

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

@@ -131,7 +131,7 @@ theorem MeasureTheory.StronglyMeasurable.integral_prod_right [SigmaFinite ν] 
   Fubini's theorem is measurable. -/
 theorem MeasureTheory.StronglyMeasurable.integral_prod_right' [SigmaFinite ν] ⦃f : α × β → E⦄
     (hf : StronglyMeasurable f) : StronglyMeasurable fun x => ∫ y, f (x, y) ∂ν := by
-  rw [← uncurry_curry f] at hf ; exact hf.integral_prod_right
+  rw [← uncurry_curry f] at hf; exact hf.integral_prod_right
 #align measure_theory.strongly_measurable.integral_prod_right' MeasureTheory.StronglyMeasurable.integral_prod_right'
 -/
 
@@ -173,7 +173,7 @@ theorem integrable_measure_prod_mk_left {s : Set (α × β)} (hs : MeasurableSet
   simp_rw [has_finite_integral, ennnorm_eq_of_real to_real_nonneg]
   convert h2s.lt_top using 1; simp_rw [prod_apply hs]; apply lintegral_congr_ae
   refine' (ae_measure_lt_top hs h2s).mp _; apply eventually_of_forall; intro x hx
-  rw [lt_top_iff_ne_top] at hx ; simp [of_real_to_real, hx]
+  rw [lt_top_iff_ne_top] at hx; simp [of_real_to_real, hx]
 #align measure_theory.measure.integrable_measure_prod_mk_left MeasureTheory.Measure.integrable_measure_prod_mk_left
 -/
 
@@ -190,7 +190,7 @@ section
 #print MeasureTheory.AEStronglyMeasurable.prod_swap /-
 theorem MeasureTheory.AEStronglyMeasurable.prod_swap {γ : Type _} [TopologicalSpace γ]
     [SigmaFinite μ] [SigmaFinite ν] {f : β × α → γ} (hf : AEStronglyMeasurable f (ν.Prod μ)) :
-    AEStronglyMeasurable (fun z : α × β => f z.symm) (μ.Prod ν) := by rw [← prod_swap] at hf ;
+    AEStronglyMeasurable (fun z : α × β => f z.symm) (μ.Prod ν) := by rw [← prod_swap] at hf;
   exact hf.comp_measurable measurable_swap
 #align measure_theory.ae_strongly_measurable.prod_swap MeasureTheory.AEStronglyMeasurable.prod_swap
 -/
@@ -394,7 +394,7 @@ variable [SigmaFinite μ]
 theorem integral_prod_swap (f : α × β → E) (hf : AEStronglyMeasurable f (μ.Prod ν)) :
     ∫ z, f z.symm ∂ν.Prod μ = ∫ z, f z ∂μ.Prod ν :=
   by
-  rw [← prod_swap] at hf 
+  rw [← prod_swap] at hf
   rw [← integral_map measurable_swap.ae_measurable hf, prod_swap]
 #align measure_theory.integral_prod_swap MeasureTheory.integral_prod_swap
 -/

mathlib commit https://github.com/leanprover-community/mathlib/commit/19c869efa56bbb8b500f2724c0b77261edbfa28c

@@ -350,15 +350,16 @@ theorem Integrable.integral_norm_prod_right [SigmaFinite μ] ⦃f : α × β →
 #align measure_theory.integrable.integral_norm_prod_right MeasureTheory.Integrable.integral_norm_prod_right
 -/
 
-#print MeasureTheory.integrable_prod_mul /-
-theorem integrable_prod_mul {L : Type _} [IsROrC L] {f : α → L} {g : β → L} (hf : Integrable f μ)
-    (hg : Integrable g ν) : Integrable (fun z : α × β => f z.1 * g z.2) (μ.Prod ν) :=
+#print MeasureTheory.Integrable.prod_mul /-
+theorem MeasureTheory.Integrable.prod_mul {L : Type _} [IsROrC L] {f : α → L} {g : β → L}
+    (hf : Integrable f μ) (hg : Integrable g ν) :
+    Integrable (fun z : α × β => f z.1 * g z.2) (μ.Prod ν) :=
   by
   refine' (integrable_prod_iff _).2 ⟨_, _⟩
   · exact hf.1.fst.mul hg.1.snd
   · exact eventually_of_forall fun x => hg.const_mul (f x)
   · simpa only [norm_mul, integral_mul_left] using hf.norm.mul_const _
-#align measure_theory.integrable_prod_mul MeasureTheory.integrable_prod_mul
+#align measure_theory.integrable_prod_mul MeasureTheory.Integrable.prod_mul
 -/
 
 end

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

@@ -3,8 +3,8 @@ Copyright (c) 2020 Floris van Doorn. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Floris van Doorn
 -/
-import Mathbin.MeasureTheory.Constructions.Prod.Basic
-import Mathbin.MeasureTheory.Integral.SetIntegral
+import MeasureTheory.Constructions.Prod.Basic
+import MeasureTheory.Integral.SetIntegral
 
 #align_import measure_theory.constructions.prod.integral from "leanprover-community/mathlib"@"c20927220ef87bb4962ba08bf6da2ce3cf50a6dd"
 

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

@@ -505,7 +505,7 @@ theorem continuous_integral_integral :
   simp_rw [← lintegral_prod_of_measurable _ (this _), ← L1.of_real_norm_sub_eq_lintegral, ←
     of_real_zero]
   refine' (continuous_of_real.tendsto 0).comp _
-  rw [← tendsto_iff_norm_tendsto_zero]; exact tendsto_id
+  rw [← tendsto_iff_norm_sub_tendsto_zero]; exact tendsto_id
 #align measure_theory.continuous_integral_integral MeasureTheory.continuous_integral_integral
 -/
 

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

@@ -2,15 +2,12 @@
 Copyright (c) 2020 Floris van Doorn. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Floris van Doorn
-
-! This file was ported from Lean 3 source module measure_theory.constructions.prod.integral
-! leanprover-community/mathlib commit c20927220ef87bb4962ba08bf6da2ce3cf50a6dd
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.MeasureTheory.Constructions.Prod.Basic
 import Mathbin.MeasureTheory.Integral.SetIntegral
 
+#align_import measure_theory.constructions.prod.integral from "leanprover-community/mathlib"@"c20927220ef87bb4962ba08bf6da2ce3cf50a6dd"
+
 /-!
 # Integration with respect to the product measure
 

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

@@ -67,17 +67,20 @@ along one of the variables (using either the Lebesgue or Bochner integral) is me
 -/
 
 
+#print measurableSet_integrable /-
 theorem measurableSet_integrable [SigmaFinite ν] ⦃f : α → β → E⦄
     (hf : StronglyMeasurable (uncurry f)) : MeasurableSet {x | Integrable (f x) ν} :=
   by
   simp_rw [integrable, hf.of_uncurry_left.ae_strongly_measurable, true_and_iff]
   exact measurableSet_lt (Measurable.lintegral_prod_right hf.ennnorm) measurable_const
 #align measurable_set_integrable measurableSet_integrable
+-/
 
 section
 
 variable [NormedSpace ℝ E] [CompleteSpace E]
 
+#print MeasureTheory.StronglyMeasurable.integral_prod_right /-
 /-- The Bochner integral is measurable. This shows that the integrand of (the right-hand-side of)
   Fubini's theorem is measurable.
   This version has `f` in curried form. -/
@@ -124,14 +127,18 @@ theorem MeasureTheory.StronglyMeasurable.integral_prod_right [SigmaFinite ν] 
     · simp [f', hfx, integral_undef]
   exact stronglyMeasurable_of_tendsto _ hf' h2f'
 #align measure_theory.strongly_measurable.integral_prod_right MeasureTheory.StronglyMeasurable.integral_prod_right
+-/
 
+#print MeasureTheory.StronglyMeasurable.integral_prod_right' /-
 /-- The Bochner integral is measurable. This shows that the integrand of (the right-hand-side of)
   Fubini's theorem is measurable. -/
 theorem MeasureTheory.StronglyMeasurable.integral_prod_right' [SigmaFinite ν] ⦃f : α × β → E⦄
     (hf : StronglyMeasurable f) : StronglyMeasurable fun x => ∫ y, f (x, y) ∂ν := by
   rw [← uncurry_curry f] at hf ; exact hf.integral_prod_right
 #align measure_theory.strongly_measurable.integral_prod_right' MeasureTheory.StronglyMeasurable.integral_prod_right'
+-/
 
+#print MeasureTheory.StronglyMeasurable.integral_prod_left /-
 /-- The Bochner integral is measurable. This shows that the integrand of (the right-hand-side of)
   the symmetric version of Fubini's theorem is measurable.
   This version has `f` in curried form. -/
@@ -139,13 +146,16 @@ theorem MeasureTheory.StronglyMeasurable.integral_prod_left [SigmaFinite μ] ⦃
     (hf : StronglyMeasurable (uncurry f)) : StronglyMeasurable fun y => ∫ x, f x y ∂μ :=
   (hf.comp_measurable measurable_swap).integral_prod_right'
 #align measure_theory.strongly_measurable.integral_prod_left MeasureTheory.StronglyMeasurable.integral_prod_left
+-/
 
+#print MeasureTheory.StronglyMeasurable.integral_prod_left' /-
 /-- The Bochner integral is measurable. This shows that the integrand of (the right-hand-side of)
   the symmetric version of Fubini's theorem is measurable. -/
 theorem MeasureTheory.StronglyMeasurable.integral_prod_left' [SigmaFinite μ] ⦃f : α × β → E⦄
     (hf : StronglyMeasurable f) : StronglyMeasurable fun y => ∫ x, f (x, y) ∂μ :=
   (hf.comp_measurable measurable_swap).integral_prod_right'
 #align measure_theory.strongly_measurable.integral_prod_left' MeasureTheory.StronglyMeasurable.integral_prod_left'
+-/
 
 end
 
@@ -158,6 +168,7 @@ namespace Measure
 
 variable [SigmaFinite ν]
 
+#print MeasureTheory.Measure.integrable_measure_prod_mk_left /-
 theorem integrable_measure_prod_mk_left {s : Set (α × β)} (hs : MeasurableSet s)
     (h2s : (μ.Prod ν) s ≠ ∞) : Integrable (fun x => (ν (Prod.mk x ⁻¹' s)).toReal) μ :=
   by
@@ -167,6 +178,7 @@ theorem integrable_measure_prod_mk_left {s : Set (α × β)} (hs : MeasurableSet
   refine' (ae_measure_lt_top hs h2s).mp _; apply eventually_of_forall; intro x hx
   rw [lt_top_iff_ne_top] at hx ; simp [of_real_to_real, hx]
 #align measure_theory.measure.integrable_measure_prod_mk_left MeasureTheory.Measure.integrable_measure_prod_mk_left
+-/
 
 end Measure
 
@@ -178,11 +190,13 @@ open MeasureTheory.Measure
 
 section
 
+#print MeasureTheory.AEStronglyMeasurable.prod_swap /-
 theorem MeasureTheory.AEStronglyMeasurable.prod_swap {γ : Type _} [TopologicalSpace γ]
     [SigmaFinite μ] [SigmaFinite ν] {f : β × α → γ} (hf : AEStronglyMeasurable f (ν.Prod μ)) :
     AEStronglyMeasurable (fun z : α × β => f z.symm) (μ.Prod ν) := by rw [← prod_swap] at hf ;
   exact hf.comp_measurable measurable_swap
 #align measure_theory.ae_strongly_measurable.prod_swap MeasureTheory.AEStronglyMeasurable.prod_swap
+-/
 
 #print MeasureTheory.AEStronglyMeasurable.fst /-
 theorem MeasureTheory.AEStronglyMeasurable.fst {γ} [TopologicalSpace γ] [SigmaFinite ν] {f : α → γ}
@@ -198,6 +212,7 @@ theorem MeasureTheory.AEStronglyMeasurable.snd {γ} [TopologicalSpace γ] [Sigma
 #align measure_theory.ae_strongly_measurable.snd MeasureTheory.AEStronglyMeasurable.snd
 -/
 
+#print MeasureTheory.AEStronglyMeasurable.integral_prod_right' /-
 /-- The Bochner integral is a.e.-measurable.
   This shows that the integrand of (the right-hand-side of) Fubini's theorem is a.e.-measurable. -/
 theorem MeasureTheory.AEStronglyMeasurable.integral_prod_right' [SigmaFinite ν] [NormedSpace ℝ E]
@@ -206,6 +221,7 @@ theorem MeasureTheory.AEStronglyMeasurable.integral_prod_right' [SigmaFinite ν]
   ⟨fun x => ∫ y, hf.mk f (x, y) ∂ν, hf.stronglyMeasurable_mk.integral_prod_right', by
     filter_upwards [ae_ae_of_ae_prod hf.ae_eq_mk] with _ hx using integral_congr_ae hx⟩
 #align measure_theory.ae_strongly_measurable.integral_prod_right' MeasureTheory.AEStronglyMeasurable.integral_prod_right'
+-/
 
 #print MeasureTheory.AEStronglyMeasurable.prod_mk_left /-
 theorem MeasureTheory.AEStronglyMeasurable.prod_mk_left {γ : Type _} [SigmaFinite ν]
@@ -229,17 +245,22 @@ variable [SigmaFinite ν]
 
 section
 
+#print MeasureTheory.Integrable.swap /-
 theorem Integrable.swap [SigmaFinite μ] ⦃f : α × β → E⦄ (hf : Integrable f (μ.Prod ν)) :
     Integrable (f ∘ Prod.swap) (ν.Prod μ) :=
   ⟨hf.AEStronglyMeasurable.prod_swap,
     (lintegral_prod_swap _ hf.AEStronglyMeasurable.ennnorm : _).le.trans_lt hf.HasFiniteIntegral⟩
 #align measure_theory.integrable.swap MeasureTheory.Integrable.swap
+-/
 
+#print MeasureTheory.integrable_swap_iff /-
 theorem integrable_swap_iff [SigmaFinite μ] ⦃f : α × β → E⦄ :
     Integrable (f ∘ Prod.swap) (ν.Prod μ) ↔ Integrable f (μ.Prod ν) :=
   ⟨fun hf => by convert hf.swap; ext ⟨x, y⟩; rfl, fun hf => hf.symm⟩
 #align measure_theory.integrable_swap_iff MeasureTheory.integrable_swap_iff
+-/
 
+#print MeasureTheory.hasFiniteIntegral_prod_iff /-
 theorem hasFiniteIntegral_prod_iff ⦃f : α × β → E⦄ (h1f : StronglyMeasurable f) :
     HasFiniteIntegral f (μ.Prod ν) ↔
       (∀ᵐ x ∂μ, HasFiniteIntegral (fun y => f (x, y)) ν) ∧
@@ -259,7 +280,9 @@ theorem hasFiniteIntegral_prod_iff ⦃f : α × β → E⦄ (h1f : StronglyMeasu
     rw [of_real_to_real]; rw [← lt_top_iff_ne_top]; exact hx
   · intro h2f; refine' ae_lt_top _ h2f.ne; exact h1f.ennnorm.lintegral_prod_right'
 #align measure_theory.has_finite_integral_prod_iff MeasureTheory.hasFiniteIntegral_prod_iff
+-/
 
+#print MeasureTheory.hasFiniteIntegral_prod_iff' /-
 theorem hasFiniteIntegral_prod_iff' ⦃f : α × β → E⦄ (h1f : AEStronglyMeasurable f (μ.Prod ν)) :
     HasFiniteIntegral f (μ.Prod ν) ↔
       (∀ᵐ x ∂μ, HasFiniteIntegral (fun y => f (x, y)) ν) ∧
@@ -277,7 +300,9 @@ theorem hasFiniteIntegral_prod_iff' ⦃f : α × β → E⦄ (h1f : AEStronglyMe
       integral_congr_ae (eventually_eq.fun_comp hx _)
   · infer_instance
 #align measure_theory.has_finite_integral_prod_iff' MeasureTheory.hasFiniteIntegral_prod_iff'
+-/
 
+#print MeasureTheory.integrable_prod_iff /-
 /-- A binary function is integrable if the function `y ↦ f (x, y)` is integrable for almost every
   `x` and the function `x ↦ ∫ ‖f (x, y)‖ dy` is integrable. -/
 theorem integrable_prod_iff ⦃f : α × β → E⦄ (h1f : AEStronglyMeasurable f (μ.Prod ν)) :
@@ -287,7 +312,9 @@ theorem integrable_prod_iff ⦃f : α × β → E⦄ (h1f : AEStronglyMeasurable
   simp [integrable, h1f, has_finite_integral_prod_iff', h1f.norm.integral_prod_right',
     h1f.prod_mk_left]
 #align measure_theory.integrable_prod_iff MeasureTheory.integrable_prod_iff
+-/
 
+#print MeasureTheory.integrable_prod_iff' /-
 /-- A binary function is integrable if the function `x ↦ f (x, y)` is integrable for almost every
   `y` and the function `y ↦ ∫ ‖f (x, y)‖ dx` is integrable. -/
 theorem integrable_prod_iff' [SigmaFinite μ] ⦃f : α × β → E⦄
@@ -296,27 +323,37 @@ theorem integrable_prod_iff' [SigmaFinite μ] ⦃f : α × β → E⦄
       (∀ᵐ y ∂ν, Integrable (fun x => f (x, y)) μ) ∧ Integrable (fun y => ∫ x, ‖f (x, y)‖ ∂μ) ν :=
   by convert integrable_prod_iff h1f.prod_swap using 1; rw [integrable_swap_iff]
 #align measure_theory.integrable_prod_iff' MeasureTheory.integrable_prod_iff'
+-/
 
+#print MeasureTheory.Integrable.prod_left_ae /-
 theorem Integrable.prod_left_ae [SigmaFinite μ] ⦃f : α × β → E⦄ (hf : Integrable f (μ.Prod ν)) :
     ∀ᵐ y ∂ν, Integrable (fun x => f (x, y)) μ :=
   ((integrable_prod_iff' hf.AEStronglyMeasurable).mp hf).1
 #align measure_theory.integrable.prod_left_ae MeasureTheory.Integrable.prod_left_ae
+-/
 
+#print MeasureTheory.Integrable.prod_right_ae /-
 theorem Integrable.prod_right_ae [SigmaFinite μ] ⦃f : α × β → E⦄ (hf : Integrable f (μ.Prod ν)) :
     ∀ᵐ x ∂μ, Integrable (fun y => f (x, y)) ν :=
   hf.symm.prod_left_ae
 #align measure_theory.integrable.prod_right_ae MeasureTheory.Integrable.prod_right_ae
+-/
 
+#print MeasureTheory.Integrable.integral_norm_prod_left /-
 theorem Integrable.integral_norm_prod_left ⦃f : α × β → E⦄ (hf : Integrable f (μ.Prod ν)) :
     Integrable (fun x => ∫ y, ‖f (x, y)‖ ∂ν) μ :=
   ((integrable_prod_iff hf.AEStronglyMeasurable).mp hf).2
 #align measure_theory.integrable.integral_norm_prod_left MeasureTheory.Integrable.integral_norm_prod_left
+-/
 
+#print MeasureTheory.Integrable.integral_norm_prod_right /-
 theorem Integrable.integral_norm_prod_right [SigmaFinite μ] ⦃f : α × β → E⦄
     (hf : Integrable f (μ.Prod ν)) : Integrable (fun y => ∫ x, ‖f (x, y)‖ ∂μ) ν :=
   hf.symm.integral_norm_prod_left
 #align measure_theory.integrable.integral_norm_prod_right MeasureTheory.Integrable.integral_norm_prod_right
+-/
 
+#print MeasureTheory.integrable_prod_mul /-
 theorem integrable_prod_mul {L : Type _} [IsROrC L] {f : α → L} {g : β → L} (hf : Integrable f μ)
     (hg : Integrable g ν) : Integrable (fun z : α × β => f z.1 * g z.2) (μ.Prod ν) :=
   by
@@ -325,11 +362,13 @@ theorem integrable_prod_mul {L : Type _} [IsROrC L] {f : α → L} {g : β → L
   · exact eventually_of_forall fun x => hg.const_mul (f x)
   · simpa only [norm_mul, integral_mul_left] using hf.norm.mul_const _
 #align measure_theory.integrable_prod_mul MeasureTheory.integrable_prod_mul
+-/
 
 end
 
 variable [NormedSpace ℝ E] [CompleteSpace E]
 
+#print MeasureTheory.Integrable.integral_prod_left /-
 theorem Integrable.integral_prod_left ⦃f : α × β → E⦄ (hf : Integrable f (μ.Prod ν)) :
     Integrable (fun x => ∫ y, f (x, y) ∂ν) μ :=
   Integrable.mono hf.integral_norm_prod_left hf.AEStronglyMeasurable.integral_prod_right' <|
@@ -339,23 +378,28 @@ theorem Integrable.integral_prod_left ⦃f : α × β → E⦄ (hf : Integrable
             integral_nonneg_of_ae <|
               eventually_of_forall fun y => (norm_nonneg (f (x, y)) : _)).symm
 #align measure_theory.integrable.integral_prod_left MeasureTheory.Integrable.integral_prod_left
+-/
 
+#print MeasureTheory.Integrable.integral_prod_right /-
 theorem Integrable.integral_prod_right [SigmaFinite μ] ⦃f : α × β → E⦄
     (hf : Integrable f (μ.Prod ν)) : Integrable (fun y => ∫ x, f (x, y) ∂μ) ν :=
   hf.symm.integral_prod_left
 #align measure_theory.integrable.integral_prod_right MeasureTheory.Integrable.integral_prod_right
+-/
 
 /-! ### The Bochner integral on a product -/
 
 
 variable [SigmaFinite μ]
 
+#print MeasureTheory.integral_prod_swap /-
 theorem integral_prod_swap (f : α × β → E) (hf : AEStronglyMeasurable f (μ.Prod ν)) :
     ∫ z, f z.symm ∂ν.Prod μ = ∫ z, f z ∂μ.Prod ν :=
   by
   rw [← prod_swap] at hf 
   rw [← integral_map measurable_swap.ae_measurable hf, prod_swap]
 #align measure_theory.integral_prod_swap MeasureTheory.integral_prod_swap
+-/
 
 variable {E' : Type _} [NormedAddCommGroup E'] [CompleteSpace E'] [NormedSpace ℝ E']
 
@@ -363,6 +407,7 @@ variable {E' : Type _} [NormedAddCommGroup E'] [CompleteSpace E'] [NormedSpace 
   we separate them out as separate lemmas, because they involve quite some steps. -/
 
 
+#print MeasureTheory.integral_fn_integral_add /-
 /-- Integrals commute with addition inside another integral. `F` can be any function. -/
 theorem integral_fn_integral_add ⦃f g : α × β → E⦄ (F : E → E') (hf : Integrable f (μ.Prod ν))
     (hg : Integrable g (μ.Prod ν)) :
@@ -372,7 +417,9 @@ theorem integral_fn_integral_add ⦃f g : α × β → E⦄ (F : E → E') (hf :
   filter_upwards [hf.prod_right_ae, hg.prod_right_ae] with _ h2f h2g
   simp [integral_add h2f h2g]
 #align measure_theory.integral_fn_integral_add MeasureTheory.integral_fn_integral_add
+-/
 
+#print MeasureTheory.integral_fn_integral_sub /-
 /-- Integrals commute with subtraction inside another integral.
   `F` can be any measurable function. -/
 theorem integral_fn_integral_sub ⦃f g : α × β → E⦄ (F : E → E') (hf : Integrable f (μ.Prod ν))
@@ -383,7 +430,9 @@ theorem integral_fn_integral_sub ⦃f g : α × β → E⦄ (F : E → E') (hf :
   filter_upwards [hf.prod_right_ae, hg.prod_right_ae] with _ h2f h2g
   simp [integral_sub h2f h2g]
 #align measure_theory.integral_fn_integral_sub MeasureTheory.integral_fn_integral_sub
+-/
 
+#print MeasureTheory.lintegral_fn_integral_sub /-
 /-- Integrals commute with subtraction inside a lower Lebesgue integral.
   `F` can be any function. -/
 theorem lintegral_fn_integral_sub ⦃f g : α × β → E⦄ (F : E → ℝ≥0∞) (hf : Integrable f (μ.Prod ν))
@@ -394,7 +443,9 @@ theorem lintegral_fn_integral_sub ⦃f g : α × β → E⦄ (F : E → ℝ≥0
   filter_upwards [hf.prod_right_ae, hg.prod_right_ae] with _ h2f h2g
   simp [integral_sub h2f h2g]
 #align measure_theory.lintegral_fn_integral_sub MeasureTheory.lintegral_fn_integral_sub
+-/
 
+#print MeasureTheory.integral_integral_add /-
 /-- Double integrals commute with addition. -/
 theorem integral_integral_add ⦃f g : α × β → E⦄ (hf : Integrable f (μ.Prod ν))
     (hg : Integrable g (μ.Prod ν)) :
@@ -402,7 +453,9 @@ theorem integral_integral_add ⦃f g : α × β → E⦄ (hf : Integrable f (μ.
   (integral_fn_integral_add id hf hg).trans <|
     integral_add hf.integral_prod_left hg.integral_prod_left
 #align measure_theory.integral_integral_add MeasureTheory.integral_integral_add
+-/
 
+#print MeasureTheory.integral_integral_add' /-
 /-- Double integrals commute with addition. This is the version with `(f + g) (x, y)`
   (instead of `f (x, y) + g (x, y)`) in the LHS. -/
 theorem integral_integral_add' ⦃f g : α × β → E⦄ (hf : Integrable f (μ.Prod ν))
@@ -410,7 +463,9 @@ theorem integral_integral_add' ⦃f g : α × β → E⦄ (hf : Integrable f (μ
     ∫ x, ∫ y, (f + g) (x, y) ∂ν ∂μ = ∫ x, ∫ y, f (x, y) ∂ν ∂μ + ∫ x, ∫ y, g (x, y) ∂ν ∂μ :=
   integral_integral_add hf hg
 #align measure_theory.integral_integral_add' MeasureTheory.integral_integral_add'
+-/
 
+#print MeasureTheory.integral_integral_sub /-
 /-- Double integrals commute with subtraction. -/
 theorem integral_integral_sub ⦃f g : α × β → E⦄ (hf : Integrable f (μ.Prod ν))
     (hg : Integrable g (μ.Prod ν)) :
@@ -418,7 +473,9 @@ theorem integral_integral_sub ⦃f g : α × β → E⦄ (hf : Integrable f (μ.
   (integral_fn_integral_sub id hf hg).trans <|
     integral_sub hf.integral_prod_left hg.integral_prod_left
 #align measure_theory.integral_integral_sub MeasureTheory.integral_integral_sub
+-/
 
+#print MeasureTheory.integral_integral_sub' /-
 /-- Double integrals commute with subtraction. This is the version with `(f - g) (x, y)`
   (instead of `f (x, y) - g (x, y)`) in the LHS. -/
 theorem integral_integral_sub' ⦃f g : α × β → E⦄ (hf : Integrable f (μ.Prod ν))
@@ -426,7 +483,9 @@ theorem integral_integral_sub' ⦃f g : α × β → E⦄ (hf : Integrable f (μ
     ∫ x, ∫ y, (f - g) (x, y) ∂ν ∂μ = ∫ x, ∫ y, f (x, y) ∂ν ∂μ - ∫ x, ∫ y, g (x, y) ∂ν ∂μ :=
   integral_integral_sub hf hg
 #align measure_theory.integral_integral_sub' MeasureTheory.integral_integral_sub'
+-/
 
+#print MeasureTheory.continuous_integral_integral /-
 /-- The map that sends an L¹-function `f : α × β → E` to `∫∫f` is continuous. -/
 theorem continuous_integral_integral :
     Continuous fun f : α × β →₁[μ.Prod ν] E => ∫ x, ∫ y, f (x, y) ∂ν ∂μ :=
@@ -451,7 +510,9 @@ theorem continuous_integral_integral :
   refine' (continuous_of_real.tendsto 0).comp _
   rw [← tendsto_iff_norm_tendsto_zero]; exact tendsto_id
 #align measure_theory.continuous_integral_integral MeasureTheory.continuous_integral_integral
+-/
 
+#print MeasureTheory.integral_prod /-
 /-- **Fubini's Theorem**: For integrable functions on `α × β`,
   the Bochner integral of `f` is equal to the iterated Bochner integral.
   `integrable_prod_iff` can be useful to show that the function in question in integrable.
@@ -478,7 +539,9 @@ theorem integral_prod :
       apply eventually_of_forall; intro x hfgx
       exact integral_congr_ae (ae_eq_symm hfgx)
 #align measure_theory.integral_prod MeasureTheory.integral_prod
+-/
 
+#print MeasureTheory.integral_prod_symm /-
 /-- Symmetric version of **Fubini's Theorem**: For integrable functions on `α × β`,
   the Bochner integral of `f` is equal to the iterated Bochner integral.
   This version has the integrals on the right-hand side in the other order. -/
@@ -486,6 +549,7 @@ theorem integral_prod_symm (f : α × β → E) (hf : Integrable f (μ.Prod ν))
     ∫ z, f z ∂μ.Prod ν = ∫ y, ∫ x, f (x, y) ∂μ ∂ν := by
   simp_rw [← integral_prod_swap f hf.ae_strongly_measurable]; exact integral_prod _ hf.swap
 #align measure_theory.integral_prod_symm MeasureTheory.integral_prod_symm
+-/
 
 #print MeasureTheory.integral_integral /-
 /-- Reversed version of **Fubini's Theorem**. -/
@@ -513,6 +577,7 @@ theorem integral_integral_swap ⦃f : α → β → E⦄ (hf : Integrable (uncur
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print MeasureTheory.set_integral_prod /-
 /-- **Fubini's Theorem** for set integrals. -/
 theorem set_integral_prod (f : α × β → E) {s : Set α} {t : Set β}
     (hf : IntegrableOn f (s ×ˢ t) (μ.Prod ν)) :
@@ -521,7 +586,9 @@ theorem set_integral_prod (f : α × β → E) {s : Set α} {t : Set β}
   simp only [← measure.prod_restrict s t, integrable_on] at hf ⊢
   exact integral_prod f hf
 #align measure_theory.set_integral_prod MeasureTheory.set_integral_prod
+-/
 
+#print MeasureTheory.integral_prod_mul /-
 theorem integral_prod_mul {L : Type _} [IsROrC L] (f : α → L) (g : β → L) :
     ∫ z, f z.1 * g z.2 ∂μ.Prod ν = (∫ x, f x ∂μ) * ∫ y, g y ∂ν :=
   by
@@ -534,12 +601,15 @@ theorem integral_prod_mul {L : Type _} [IsROrC L] (f : α → L) (g : β → L)
     exact integrable_prod_mul h.1 h.2
   cases H <;> simp [integral_undef h, integral_undef H]
 #align measure_theory.integral_prod_mul MeasureTheory.integral_prod_mul
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print MeasureTheory.set_integral_prod_mul /-
 theorem set_integral_prod_mul {L : Type _} [IsROrC L] (f : α → L) (g : β → L) (s : Set α)
     (t : Set β) : ∫ z in s ×ˢ t, f z.1 * g z.2 ∂μ.Prod ν = (∫ x in s, f x ∂μ) * ∫ y in t, g y ∂ν :=
   by simp only [← measure.prod_restrict s t, integrable_on, integral_prod_mul]
 #align measure_theory.set_integral_prod_mul MeasureTheory.set_integral_prod_mul
+-/
 
 end MeasureTheory
 

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

@@ -351,7 +351,7 @@ theorem Integrable.integral_prod_right [SigmaFinite μ] ⦃f : α × β → E⦄
 variable [SigmaFinite μ]
 
 theorem integral_prod_swap (f : α × β → E) (hf : AEStronglyMeasurable f (μ.Prod ν)) :
-    (∫ z, f z.symm ∂ν.Prod μ) = ∫ z, f z ∂μ.Prod ν :=
+    ∫ z, f z.symm ∂ν.Prod μ = ∫ z, f z ∂μ.Prod ν :=
   by
   rw [← prod_swap] at hf 
   rw [← integral_map measurable_swap.ae_measurable hf, prod_swap]
@@ -366,7 +366,7 @@ variable {E' : Type _} [NormedAddCommGroup E'] [CompleteSpace E'] [NormedSpace 
 /-- Integrals commute with addition inside another integral. `F` can be any function. -/
 theorem integral_fn_integral_add ⦃f g : α × β → E⦄ (F : E → E') (hf : Integrable f (μ.Prod ν))
     (hg : Integrable g (μ.Prod ν)) :
-    (∫ x, F (∫ y, f (x, y) + g (x, y) ∂ν) ∂μ) = ∫ x, F ((∫ y, f (x, y) ∂ν) + ∫ y, g (x, y) ∂ν) ∂μ :=
+    ∫ x, F (∫ y, f (x, y) + g (x, y) ∂ν) ∂μ = ∫ x, F (∫ y, f (x, y) ∂ν + ∫ y, g (x, y) ∂ν) ∂μ :=
   by
   refine' integral_congr_ae _
   filter_upwards [hf.prod_right_ae, hg.prod_right_ae] with _ h2f h2g
@@ -377,7 +377,7 @@ theorem integral_fn_integral_add ⦃f g : α × β → E⦄ (F : E → E') (hf :
   `F` can be any measurable function. -/
 theorem integral_fn_integral_sub ⦃f g : α × β → E⦄ (F : E → E') (hf : Integrable f (μ.Prod ν))
     (hg : Integrable g (μ.Prod ν)) :
-    (∫ x, F (∫ y, f (x, y) - g (x, y) ∂ν) ∂μ) = ∫ x, F ((∫ y, f (x, y) ∂ν) - ∫ y, g (x, y) ∂ν) ∂μ :=
+    ∫ x, F (∫ y, f (x, y) - g (x, y) ∂ν) ∂μ = ∫ x, F (∫ y, f (x, y) ∂ν - ∫ y, g (x, y) ∂ν) ∂μ :=
   by
   refine' integral_congr_ae _
   filter_upwards [hf.prod_right_ae, hg.prod_right_ae] with _ h2f h2g
@@ -388,8 +388,7 @@ theorem integral_fn_integral_sub ⦃f g : α × β → E⦄ (F : E → E') (hf :
   `F` can be any function. -/
 theorem lintegral_fn_integral_sub ⦃f g : α × β → E⦄ (F : E → ℝ≥0∞) (hf : Integrable f (μ.Prod ν))
     (hg : Integrable g (μ.Prod ν)) :
-    (∫⁻ x, F (∫ y, f (x, y) - g (x, y) ∂ν) ∂μ) =
-      ∫⁻ x, F ((∫ y, f (x, y) ∂ν) - ∫ y, g (x, y) ∂ν) ∂μ :=
+    ∫⁻ x, F (∫ y, f (x, y) - g (x, y) ∂ν) ∂μ = ∫⁻ x, F (∫ y, f (x, y) ∂ν - ∫ y, g (x, y) ∂ν) ∂μ :=
   by
   refine' lintegral_congr_ae _
   filter_upwards [hf.prod_right_ae, hg.prod_right_ae] with _ h2f h2g
@@ -399,7 +398,7 @@ theorem lintegral_fn_integral_sub ⦃f g : α × β → E⦄ (F : E → ℝ≥0
 /-- Double integrals commute with addition. -/
 theorem integral_integral_add ⦃f g : α × β → E⦄ (hf : Integrable f (μ.Prod ν))
     (hg : Integrable g (μ.Prod ν)) :
-    (∫ x, ∫ y, f (x, y) + g (x, y) ∂ν ∂μ) = (∫ x, ∫ y, f (x, y) ∂ν ∂μ) + ∫ x, ∫ y, g (x, y) ∂ν ∂μ :=
+    ∫ x, ∫ y, f (x, y) + g (x, y) ∂ν ∂μ = ∫ x, ∫ y, f (x, y) ∂ν ∂μ + ∫ x, ∫ y, g (x, y) ∂ν ∂μ :=
   (integral_fn_integral_add id hf hg).trans <|
     integral_add hf.integral_prod_left hg.integral_prod_left
 #align measure_theory.integral_integral_add MeasureTheory.integral_integral_add
@@ -408,14 +407,14 @@ theorem integral_integral_add ⦃f g : α × β → E⦄ (hf : Integrable f (μ.
   (instead of `f (x, y) + g (x, y)`) in the LHS. -/
 theorem integral_integral_add' ⦃f g : α × β → E⦄ (hf : Integrable f (μ.Prod ν))
     (hg : Integrable g (μ.Prod ν)) :
-    (∫ x, ∫ y, (f + g) (x, y) ∂ν ∂μ) = (∫ x, ∫ y, f (x, y) ∂ν ∂μ) + ∫ x, ∫ y, g (x, y) ∂ν ∂μ :=
+    ∫ x, ∫ y, (f + g) (x, y) ∂ν ∂μ = ∫ x, ∫ y, f (x, y) ∂ν ∂μ + ∫ x, ∫ y, g (x, y) ∂ν ∂μ :=
   integral_integral_add hf hg
 #align measure_theory.integral_integral_add' MeasureTheory.integral_integral_add'
 
 /-- Double integrals commute with subtraction. -/
 theorem integral_integral_sub ⦃f g : α × β → E⦄ (hf : Integrable f (μ.Prod ν))
     (hg : Integrable g (μ.Prod ν)) :
-    (∫ x, ∫ y, f (x, y) - g (x, y) ∂ν ∂μ) = (∫ x, ∫ y, f (x, y) ∂ν ∂μ) - ∫ x, ∫ y, g (x, y) ∂ν ∂μ :=
+    ∫ x, ∫ y, f (x, y) - g (x, y) ∂ν ∂μ = ∫ x, ∫ y, f (x, y) ∂ν ∂μ - ∫ x, ∫ y, g (x, y) ∂ν ∂μ :=
   (integral_fn_integral_sub id hf hg).trans <|
     integral_sub hf.integral_prod_left hg.integral_prod_left
 #align measure_theory.integral_integral_sub MeasureTheory.integral_integral_sub
@@ -424,7 +423,7 @@ theorem integral_integral_sub ⦃f g : α × β → E⦄ (hf : Integrable f (μ.
   (instead of `f (x, y) - g (x, y)`) in the LHS. -/
 theorem integral_integral_sub' ⦃f g : α × β → E⦄ (hf : Integrable f (μ.Prod ν))
     (hg : Integrable g (μ.Prod ν)) :
-    (∫ x, ∫ y, (f - g) (x, y) ∂ν ∂μ) = (∫ x, ∫ y, f (x, y) ∂ν ∂μ) - ∫ x, ∫ y, g (x, y) ∂ν ∂μ :=
+    ∫ x, ∫ y, (f - g) (x, y) ∂ν ∂μ = ∫ x, ∫ y, f (x, y) ∂ν ∂μ - ∫ x, ∫ y, g (x, y) ∂ν ∂μ :=
   integral_integral_sub hf hg
 #align measure_theory.integral_integral_sub' MeasureTheory.integral_integral_sub'
 
@@ -460,7 +459,7 @@ theorem continuous_integral_integral :
   of the right-hand side is integrable. -/
 theorem integral_prod :
     ∀ (f : α × β → E) (hf : Integrable f (μ.Prod ν)),
-      (∫ z, f z ∂μ.Prod ν) = ∫ x, ∫ y, f (x, y) ∂ν ∂μ :=
+      ∫ z, f z ∂μ.Prod ν = ∫ x, ∫ y, f (x, y) ∂ν ∂μ :=
   by
   apply integrable.induction
   · intro c s hs h2s
@@ -484,14 +483,14 @@ theorem integral_prod :
   the Bochner integral of `f` is equal to the iterated Bochner integral.
   This version has the integrals on the right-hand side in the other order. -/
 theorem integral_prod_symm (f : α × β → E) (hf : Integrable f (μ.Prod ν)) :
-    (∫ z, f z ∂μ.Prod ν) = ∫ y, ∫ x, f (x, y) ∂μ ∂ν := by
+    ∫ z, f z ∂μ.Prod ν = ∫ y, ∫ x, f (x, y) ∂μ ∂ν := by
   simp_rw [← integral_prod_swap f hf.ae_strongly_measurable]; exact integral_prod _ hf.swap
 #align measure_theory.integral_prod_symm MeasureTheory.integral_prod_symm
 
 #print MeasureTheory.integral_integral /-
 /-- Reversed version of **Fubini's Theorem**. -/
 theorem integral_integral {f : α → β → E} (hf : Integrable (uncurry f) (μ.Prod ν)) :
-    (∫ x, ∫ y, f x y ∂ν ∂μ) = ∫ z, f z.1 z.2 ∂μ.Prod ν :=
+    ∫ x, ∫ y, f x y ∂ν ∂μ = ∫ z, f z.1 z.2 ∂μ.Prod ν :=
   (integral_prod _ hf).symm
 #align measure_theory.integral_integral MeasureTheory.integral_integral
 -/
@@ -499,7 +498,7 @@ theorem integral_integral {f : α → β → E} (hf : Integrable (uncurry f) (μ
 #print MeasureTheory.integral_integral_symm /-
 /-- Reversed version of **Fubini's Theorem** (symmetric version). -/
 theorem integral_integral_symm {f : α → β → E} (hf : Integrable (uncurry f) (μ.Prod ν)) :
-    (∫ x, ∫ y, f x y ∂ν ∂μ) = ∫ z, f z.2 z.1 ∂ν.Prod μ :=
+    ∫ x, ∫ y, f x y ∂ν ∂μ = ∫ z, f z.2 z.1 ∂ν.Prod μ :=
   (integral_prod_symm _ hf.symm).symm
 #align measure_theory.integral_integral_symm MeasureTheory.integral_integral_symm
 -/
@@ -507,7 +506,7 @@ theorem integral_integral_symm {f : α → β → E} (hf : Integrable (uncurry f
 #print MeasureTheory.integral_integral_swap /-
 /-- Change the order of Bochner integration. -/
 theorem integral_integral_swap ⦃f : α → β → E⦄ (hf : Integrable (uncurry f) (μ.Prod ν)) :
-    (∫ x, ∫ y, f x y ∂ν ∂μ) = ∫ y, ∫ x, f x y ∂μ ∂ν :=
+    ∫ x, ∫ y, f x y ∂ν ∂μ = ∫ y, ∫ x, f x y ∂μ ∂ν :=
   (integral_integral hf).trans (integral_prod_symm _ hf)
 #align measure_theory.integral_integral_swap MeasureTheory.integral_integral_swap
 -/
@@ -517,14 +516,14 @@ theorem integral_integral_swap ⦃f : α → β → E⦄ (hf : Integrable (uncur
 /-- **Fubini's Theorem** for set integrals. -/
 theorem set_integral_prod (f : α × β → E) {s : Set α} {t : Set β}
     (hf : IntegrableOn f (s ×ˢ t) (μ.Prod ν)) :
-    (∫ z in s ×ˢ t, f z ∂μ.Prod ν) = ∫ x in s, ∫ y in t, f (x, y) ∂ν ∂μ :=
+    ∫ z in s ×ˢ t, f z ∂μ.Prod ν = ∫ x in s, ∫ y in t, f (x, y) ∂ν ∂μ :=
   by
   simp only [← measure.prod_restrict s t, integrable_on] at hf ⊢
   exact integral_prod f hf
 #align measure_theory.set_integral_prod MeasureTheory.set_integral_prod
 
 theorem integral_prod_mul {L : Type _} [IsROrC L] (f : α → L) (g : β → L) :
-    (∫ z, f z.1 * g z.2 ∂μ.Prod ν) = (∫ x, f x ∂μ) * ∫ y, g y ∂ν :=
+    ∫ z, f z.1 * g z.2 ∂μ.Prod ν = (∫ x, f x ∂μ) * ∫ y, g y ∂ν :=
   by
   by_cases h : integrable (fun z : α × β => f z.1 * g z.2) (μ.prod ν)
   · rw [integral_prod _ h]
@@ -538,9 +537,8 @@ theorem integral_prod_mul {L : Type _} [IsROrC L] (f : α → L) (g : β → L)
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 theorem set_integral_prod_mul {L : Type _} [IsROrC L] (f : α → L) (g : β → L) (s : Set α)
-    (t : Set β) :
-    (∫ z in s ×ˢ t, f z.1 * g z.2 ∂μ.Prod ν) = (∫ x in s, f x ∂μ) * ∫ y in t, g y ∂ν := by
-  simp only [← measure.prod_restrict s t, integrable_on, integral_prod_mul]
+    (t : Set β) : ∫ z in s ×ˢ t, f z.1 * g z.2 ∂μ.Prod ν = (∫ x in s, f x ∂μ) * ∫ y in t, g y ∂ν :=
+  by simp only [← measure.prod_restrict s t, integrable_on, integral_prod_mul]
 #align measure_theory.set_integral_prod_mul MeasureTheory.set_integral_prod_mul
 
 end MeasureTheory

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

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Floris van Doorn
 
 ! This file was ported from Lean 3 source module measure_theory.constructions.prod.integral
-! leanprover-community/mathlib commit fd5edc43dc4f10b85abfe544b88f82cf13c5f844
+! leanprover-community/mathlib commit c20927220ef87bb4962ba08bf6da2ce3cf50a6dd
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -14,6 +14,9 @@ import Mathbin.MeasureTheory.Integral.SetIntegral
 /-!
 # Integration with respect to the product measure
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 In this file we prove Fubini's theorem.
 
 ## Main results

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

@@ -181,15 +181,19 @@ theorem MeasureTheory.AEStronglyMeasurable.prod_swap {γ : Type _} [TopologicalS
   exact hf.comp_measurable measurable_swap
 #align measure_theory.ae_strongly_measurable.prod_swap MeasureTheory.AEStronglyMeasurable.prod_swap
 
+#print MeasureTheory.AEStronglyMeasurable.fst /-
 theorem MeasureTheory.AEStronglyMeasurable.fst {γ} [TopologicalSpace γ] [SigmaFinite ν] {f : α → γ}
     (hf : AEStronglyMeasurable f μ) : AEStronglyMeasurable (fun z : α × β => f z.1) (μ.Prod ν) :=
   hf.comp_quasiMeasurePreserving quasiMeasurePreserving_fst
 #align measure_theory.ae_strongly_measurable.fst MeasureTheory.AEStronglyMeasurable.fst
+-/
 
+#print MeasureTheory.AEStronglyMeasurable.snd /-
 theorem MeasureTheory.AEStronglyMeasurable.snd {γ} [TopologicalSpace γ] [SigmaFinite ν] {f : β → γ}
     (hf : AEStronglyMeasurable f ν) : AEStronglyMeasurable (fun z : α × β => f z.2) (μ.Prod ν) :=
   hf.comp_quasiMeasurePreserving quasiMeasurePreserving_snd
 #align measure_theory.ae_strongly_measurable.snd MeasureTheory.AEStronglyMeasurable.snd
+-/
 
 /-- The Bochner integral is a.e.-measurable.
   This shows that the integrand of (the right-hand-side of) Fubini's theorem is a.e.-measurable. -/
@@ -200,6 +204,7 @@ theorem MeasureTheory.AEStronglyMeasurable.integral_prod_right' [SigmaFinite ν]
     filter_upwards [ae_ae_of_ae_prod hf.ae_eq_mk] with _ hx using integral_congr_ae hx⟩
 #align measure_theory.ae_strongly_measurable.integral_prod_right' MeasureTheory.AEStronglyMeasurable.integral_prod_right'
 
+#print MeasureTheory.AEStronglyMeasurable.prod_mk_left /-
 theorem MeasureTheory.AEStronglyMeasurable.prod_mk_left {γ : Type _} [SigmaFinite ν]
     [TopologicalSpace γ] {f : α × β → γ} (hf : AEStronglyMeasurable f (μ.Prod ν)) :
     ∀ᵐ x ∂μ, AEStronglyMeasurable (fun y => f (x, y)) ν :=
@@ -208,6 +213,7 @@ theorem MeasureTheory.AEStronglyMeasurable.prod_mk_left {γ : Type _} [SigmaFini
   exact
     ⟨fun y => hf.mk f (x, y), hf.strongly_measurable_mk.comp_measurable measurable_prod_mk_left, hx⟩
 #align measure_theory.ae_strongly_measurable.prod_mk_left MeasureTheory.AEStronglyMeasurable.prod_mk_left
+-/
 
 end
 
@@ -479,23 +485,29 @@ theorem integral_prod_symm (f : α × β → E) (hf : Integrable f (μ.Prod ν))
   simp_rw [← integral_prod_swap f hf.ae_strongly_measurable]; exact integral_prod _ hf.swap
 #align measure_theory.integral_prod_symm MeasureTheory.integral_prod_symm
 
+#print MeasureTheory.integral_integral /-
 /-- Reversed version of **Fubini's Theorem**. -/
 theorem integral_integral {f : α → β → E} (hf : Integrable (uncurry f) (μ.Prod ν)) :
     (∫ x, ∫ y, f x y ∂ν ∂μ) = ∫ z, f z.1 z.2 ∂μ.Prod ν :=
   (integral_prod _ hf).symm
 #align measure_theory.integral_integral MeasureTheory.integral_integral
+-/
 
+#print MeasureTheory.integral_integral_symm /-
 /-- Reversed version of **Fubini's Theorem** (symmetric version). -/
 theorem integral_integral_symm {f : α → β → E} (hf : Integrable (uncurry f) (μ.Prod ν)) :
     (∫ x, ∫ y, f x y ∂ν ∂μ) = ∫ z, f z.2 z.1 ∂ν.Prod μ :=
   (integral_prod_symm _ hf.symm).symm
 #align measure_theory.integral_integral_symm MeasureTheory.integral_integral_symm
+-/
 
+#print MeasureTheory.integral_integral_swap /-
 /-- Change the order of Bochner integration. -/
 theorem integral_integral_swap ⦃f : α → β → E⦄ (hf : Integrable (uncurry f) (μ.Prod ν)) :
     (∫ x, ∫ y, f x y ∂ν ∂μ) = ∫ y, ∫ x, f x y ∂μ ∂ν :=
   (integral_integral hf).trans (integral_prod_symm _ hf)
 #align measure_theory.integral_integral_swap MeasureTheory.integral_integral_swap
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/

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

@@ -65,7 +65,7 @@ along one of the variables (using either the Lebesgue or Bochner integral) is me
 
 
 theorem measurableSet_integrable [SigmaFinite ν] ⦃f : α → β → E⦄
-    (hf : StronglyMeasurable (uncurry f)) : MeasurableSet { x | Integrable (f x) ν } :=
+    (hf : StronglyMeasurable (uncurry f)) : MeasurableSet {x | Integrable (f x) ν} :=
   by
   simp_rw [integrable, hf.of_uncurry_left.ae_strongly_measurable, true_and_iff]
   exact measurableSet_lt (Measurable.lintegral_prod_right hf.ennnorm) measurable_const
@@ -87,7 +87,7 @@ theorem MeasureTheory.StronglyMeasurable.integral_prod_right [SigmaFinite ν] 
   let s : ℕ → simple_func (α × β) E :=
     simple_func.approx_on _ hf.measurable (range (uncurry f) ∪ {0}) 0 (by simp)
   let s' : ℕ → α → simple_func β E := fun n x => (s n).comp (Prod.mk x) measurable_prod_mk_left
-  let f' : ℕ → α → E := fun n => { x | integrable (f x) ν }.indicator fun x => (s' n x).integral ν
+  let f' : ℕ → α → E := fun n => {x | integrable (f x) ν}.indicator fun x => (s' n x).integral ν
   have hf' : ∀ n, strongly_measurable (f' n) :=
     by
     intro n; refine' strongly_measurable.indicator _ (measurableSet_integrable hf)
@@ -197,14 +197,14 @@ theorem MeasureTheory.AEStronglyMeasurable.integral_prod_right' [SigmaFinite ν]
     [CompleteSpace E] ⦃f : α × β → E⦄ (hf : AEStronglyMeasurable f (μ.Prod ν)) :
     AEStronglyMeasurable (fun x => ∫ y, f (x, y) ∂ν) μ :=
   ⟨fun x => ∫ y, hf.mk f (x, y) ∂ν, hf.stronglyMeasurable_mk.integral_prod_right', by
-    filter_upwards [ae_ae_of_ae_prod hf.ae_eq_mk]with _ hx using integral_congr_ae hx⟩
+    filter_upwards [ae_ae_of_ae_prod hf.ae_eq_mk] with _ hx using integral_congr_ae hx⟩
 #align measure_theory.ae_strongly_measurable.integral_prod_right' MeasureTheory.AEStronglyMeasurable.integral_prod_right'
 
 theorem MeasureTheory.AEStronglyMeasurable.prod_mk_left {γ : Type _} [SigmaFinite ν]
     [TopologicalSpace γ] {f : α × β → γ} (hf : AEStronglyMeasurable f (μ.Prod ν)) :
     ∀ᵐ x ∂μ, AEStronglyMeasurable (fun y => f (x, y)) ν :=
   by
-  filter_upwards [ae_ae_of_ae_prod hf.ae_eq_mk]with x hx
+  filter_upwards [ae_ae_of_ae_prod hf.ae_eq_mk] with x hx
   exact
     ⟨fun y => hf.mk f (x, y), hf.strongly_measurable_mk.comp_measurable measurable_prod_mk_left, hx⟩
 #align measure_theory.ae_strongly_measurable.prod_mk_left MeasureTheory.AEStronglyMeasurable.prod_mk_left
@@ -264,8 +264,8 @@ theorem hasFiniteIntegral_prod_iff' ⦃f : α × β → E⦄ (h1f : AEStronglyMe
     intro x hx
     exact has_finite_integral_congr hx
   · apply has_finite_integral_congr
-    filter_upwards [ae_ae_of_ae_prod
-        h1f.ae_eq_mk.symm]with _ hx using integral_congr_ae (eventually_eq.fun_comp hx _)
+    filter_upwards [ae_ae_of_ae_prod h1f.ae_eq_mk.symm] with _ hx using
+      integral_congr_ae (eventually_eq.fun_comp hx _)
   · infer_instance
 #align measure_theory.has_finite_integral_prod_iff' MeasureTheory.hasFiniteIntegral_prod_iff'
 
@@ -360,7 +360,7 @@ theorem integral_fn_integral_add ⦃f g : α × β → E⦄ (F : E → E') (hf :
     (∫ x, F (∫ y, f (x, y) + g (x, y) ∂ν) ∂μ) = ∫ x, F ((∫ y, f (x, y) ∂ν) + ∫ y, g (x, y) ∂ν) ∂μ :=
   by
   refine' integral_congr_ae _
-  filter_upwards [hf.prod_right_ae, hg.prod_right_ae]with _ h2f h2g
+  filter_upwards [hf.prod_right_ae, hg.prod_right_ae] with _ h2f h2g
   simp [integral_add h2f h2g]
 #align measure_theory.integral_fn_integral_add MeasureTheory.integral_fn_integral_add
 
@@ -371,7 +371,7 @@ theorem integral_fn_integral_sub ⦃f g : α × β → E⦄ (F : E → E') (hf :
     (∫ x, F (∫ y, f (x, y) - g (x, y) ∂ν) ∂μ) = ∫ x, F ((∫ y, f (x, y) ∂ν) - ∫ y, g (x, y) ∂ν) ∂μ :=
   by
   refine' integral_congr_ae _
-  filter_upwards [hf.prod_right_ae, hg.prod_right_ae]with _ h2f h2g
+  filter_upwards [hf.prod_right_ae, hg.prod_right_ae] with _ h2f h2g
   simp [integral_sub h2f h2g]
 #align measure_theory.integral_fn_integral_sub MeasureTheory.integral_fn_integral_sub
 
@@ -383,7 +383,7 @@ theorem lintegral_fn_integral_sub ⦃f g : α × β → E⦄ (F : E → ℝ≥0
       ∫⁻ x, F ((∫ y, f (x, y) ∂ν) - ∫ y, g (x, y) ∂ν) ∂μ :=
   by
   refine' lintegral_congr_ae _
-  filter_upwards [hf.prod_right_ae, hg.prod_right_ae]with _ h2f h2g
+  filter_upwards [hf.prod_right_ae, hg.prod_right_ae] with _ h2f h2g
   simp [integral_sub h2f h2g]
 #align measure_theory.lintegral_fn_integral_sub MeasureTheory.lintegral_fn_integral_sub
 

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

@@ -126,7 +126,7 @@ theorem MeasureTheory.StronglyMeasurable.integral_prod_right [SigmaFinite ν] 
   Fubini's theorem is measurable. -/
 theorem MeasureTheory.StronglyMeasurable.integral_prod_right' [SigmaFinite ν] ⦃f : α × β → E⦄
     (hf : StronglyMeasurable f) : StronglyMeasurable fun x => ∫ y, f (x, y) ∂ν := by
-  rw [← uncurry_curry f] at hf; exact hf.integral_prod_right
+  rw [← uncurry_curry f] at hf ; exact hf.integral_prod_right
 #align measure_theory.strongly_measurable.integral_prod_right' MeasureTheory.StronglyMeasurable.integral_prod_right'
 
 /-- The Bochner integral is measurable. This shows that the integrand of (the right-hand-side of)
@@ -162,7 +162,7 @@ theorem integrable_measure_prod_mk_left {s : Set (α × β)} (hs : MeasurableSet
   simp_rw [has_finite_integral, ennnorm_eq_of_real to_real_nonneg]
   convert h2s.lt_top using 1; simp_rw [prod_apply hs]; apply lintegral_congr_ae
   refine' (ae_measure_lt_top hs h2s).mp _; apply eventually_of_forall; intro x hx
-  rw [lt_top_iff_ne_top] at hx; simp [of_real_to_real, hx]
+  rw [lt_top_iff_ne_top] at hx ; simp [of_real_to_real, hx]
 #align measure_theory.measure.integrable_measure_prod_mk_left MeasureTheory.Measure.integrable_measure_prod_mk_left
 
 end Measure
@@ -177,7 +177,7 @@ section
 
 theorem MeasureTheory.AEStronglyMeasurable.prod_swap {γ : Type _} [TopologicalSpace γ]
     [SigmaFinite μ] [SigmaFinite ν] {f : β × α → γ} (hf : AEStronglyMeasurable f (ν.Prod μ)) :
-    AEStronglyMeasurable (fun z : α × β => f z.symm) (μ.Prod ν) := by rw [← prod_swap] at hf;
+    AEStronglyMeasurable (fun z : α × β => f z.symm) (μ.Prod ν) := by rw [← prod_swap] at hf ;
   exact hf.comp_measurable measurable_swap
 #align measure_theory.ae_strongly_measurable.prod_swap MeasureTheory.AEStronglyMeasurable.prod_swap
 
@@ -344,7 +344,7 @@ variable [SigmaFinite μ]
 theorem integral_prod_swap (f : α × β → E) (hf : AEStronglyMeasurable f (μ.Prod ν)) :
     (∫ z, f z.symm ∂ν.Prod μ) = ∫ z, f z ∂μ.Prod ν :=
   by
-  rw [← prod_swap] at hf
+  rw [← prod_swap] at hf 
   rw [← integral_map measurable_swap.ae_measurable hf, prod_swap]
 #align measure_theory.integral_prod_swap MeasureTheory.integral_prod_swap
 
@@ -504,7 +504,7 @@ theorem set_integral_prod (f : α × β → E) {s : Set α} {t : Set β}
     (hf : IntegrableOn f (s ×ˢ t) (μ.Prod ν)) :
     (∫ z in s ×ˢ t, f z ∂μ.Prod ν) = ∫ x in s, ∫ y in t, f (x, y) ∂ν ∂μ :=
   by
-  simp only [← measure.prod_restrict s t, integrable_on] at hf⊢
+  simp only [← measure.prod_restrict s t, integrable_on] at hf ⊢
   exact integral_prod f hf
 #align measure_theory.set_integral_prod MeasureTheory.set_integral_prod
 

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

@@ -36,7 +36,7 @@ product measure, Fubini's theorem, Fubini-Tonelli theorem
 
 noncomputable section
 
-open Classical Topology ENNReal MeasureTheory
+open scoped Classical Topology ENNReal MeasureTheory
 
 open Set Function Real ENNReal
 

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

@@ -90,16 +90,11 @@ theorem MeasureTheory.StronglyMeasurable.integral_prod_right [SigmaFinite ν] 
   let f' : ℕ → α → E := fun n => { x | integrable (f x) ν }.indicator fun x => (s' n x).integral ν
   have hf' : ∀ n, strongly_measurable (f' n) :=
     by
-    intro n
-    refine' strongly_measurable.indicator _ (measurableSet_integrable hf)
+    intro n; refine' strongly_measurable.indicator _ (measurableSet_integrable hf)
     have : ∀ x, ((s' n x).range.filterₓ fun x => x ≠ 0) ⊆ (s n).range :=
       by
-      intro x
-      refine' Finset.Subset.trans (Finset.filter_subset _ _) _
-      intro y
-      simp_rw [simple_func.mem_range]
-      rintro ⟨z, rfl⟩
-      exact ⟨(x, z), rfl⟩
+      intro x; refine' Finset.Subset.trans (Finset.filter_subset _ _) _; intro y
+      simp_rw [simple_func.mem_range]; rintro ⟨z, rfl⟩; exact ⟨(x, z), rfl⟩
     simp only [simple_func.integral_eq_sum_of_subset (this _)]
     refine' Finset.stronglyMeasurable_sum _ fun x _ => _
     refine' (Measurable.ennreal_toReal _).StronglyMeasurable.smul_const _
@@ -108,16 +103,12 @@ theorem MeasureTheory.StronglyMeasurable.integral_prod_right [SigmaFinite ν] 
     exact (s n).measurableSet_fiber x
   have h2f' : tendsto f' at_top (𝓝 fun x : α => ∫ y : β, f x y ∂ν) :=
     by
-    rw [tendsto_pi_nhds]
-    intro x
+    rw [tendsto_pi_nhds]; intro x
     by_cases hfx : integrable (f x) ν
     · have : ∀ n, integrable (s' n x) ν := by
-        intro n
-        apply (hfx.norm.add hfx.norm).mono' (s' n x).AEStronglyMeasurable
-        apply eventually_of_forall
-        intro y
-        simp_rw [s', simple_func.coe_comp]
-        exact simple_func.norm_approx_on_zero_le _ _ (x, y) n
+        intro n; apply (hfx.norm.add hfx.norm).mono' (s' n x).AEStronglyMeasurable
+        apply eventually_of_forall; intro y
+        simp_rw [s', simple_func.coe_comp]; exact simple_func.norm_approx_on_zero_le _ _ (x, y) n
       simp only [f', hfx, simple_func.integral_eq_integral _ (this _), indicator_of_mem,
         mem_set_of_eq]
       refine'
@@ -134,10 +125,8 @@ theorem MeasureTheory.StronglyMeasurable.integral_prod_right [SigmaFinite ν] 
 /-- The Bochner integral is measurable. This shows that the integrand of (the right-hand-side of)
   Fubini's theorem is measurable. -/
 theorem MeasureTheory.StronglyMeasurable.integral_prod_right' [SigmaFinite ν] ⦃f : α × β → E⦄
-    (hf : StronglyMeasurable f) : StronglyMeasurable fun x => ∫ y, f (x, y) ∂ν :=
-  by
-  rw [← uncurry_curry f] at hf
-  exact hf.integral_prod_right
+    (hf : StronglyMeasurable f) : StronglyMeasurable fun x => ∫ y, f (x, y) ∂ν := by
+  rw [← uncurry_curry f] at hf; exact hf.integral_prod_right
 #align measure_theory.strongly_measurable.integral_prod_right' MeasureTheory.StronglyMeasurable.integral_prod_right'
 
 /-- The Bochner integral is measurable. This shows that the integrand of (the right-hand-side of)
@@ -188,9 +177,7 @@ section
 
 theorem MeasureTheory.AEStronglyMeasurable.prod_swap {γ : Type _} [TopologicalSpace γ]
     [SigmaFinite μ] [SigmaFinite ν] {f : β × α → γ} (hf : AEStronglyMeasurable f (ν.Prod μ)) :
-    AEStronglyMeasurable (fun z : α × β => f z.symm) (μ.Prod ν) :=
-  by
-  rw [← prod_swap] at hf
+    AEStronglyMeasurable (fun z : α × β => f z.symm) (μ.Prod ν) := by rw [← prod_swap] at hf;
   exact hf.comp_measurable measurable_swap
 #align measure_theory.ae_strongly_measurable.prod_swap MeasureTheory.AEStronglyMeasurable.prod_swap
 
@@ -241,10 +228,7 @@ theorem Integrable.swap [SigmaFinite μ] ⦃f : α × β → E⦄ (hf : Integrab
 
 theorem integrable_swap_iff [SigmaFinite μ] ⦃f : α × β → E⦄ :
     Integrable (f ∘ Prod.swap) (ν.Prod μ) ↔ Integrable f (μ.Prod ν) :=
-  ⟨fun hf => by
-    convert hf.swap
-    ext ⟨x, y⟩
-    rfl, fun hf => hf.symm⟩
+  ⟨fun hf => by convert hf.swap; ext ⟨x, y⟩; rfl, fun hf => hf.symm⟩
 #align measure_theory.integrable_swap_iff MeasureTheory.integrable_swap_iff
 
 theorem hasFiniteIntegral_prod_iff ⦃f : α × β → E⦄ (h1f : StronglyMeasurable f) :
@@ -261,18 +245,10 @@ theorem hasFiniteIntegral_prod_iff ⦃f : α × β → E⦄ (h1f : StronglyMeasu
   have : ∀ {p q r : Prop} (h1 : r → p), (r ↔ p ∧ q) ↔ p → (r ↔ q) := fun p q r h1 => by
     rw [← and_congr_right_iff, and_iff_right_of_imp h1]
   rw [this]
-  · intro h2f
-    rw [lintegral_congr_ae]
-    refine' h2f.mp _
-    apply eventually_of_forall
-    intro x hx
-    dsimp only
-    rw [of_real_to_real]
-    rw [← lt_top_iff_ne_top]
-    exact hx
-  · intro h2f
-    refine' ae_lt_top _ h2f.ne
-    exact h1f.ennnorm.lintegral_prod_right'
+  · intro h2f; rw [lintegral_congr_ae]
+    refine' h2f.mp _; apply eventually_of_forall; intro x hx; dsimp only
+    rw [of_real_to_real]; rw [← lt_top_iff_ne_top]; exact hx
+  · intro h2f; refine' ae_lt_top _ h2f.ne; exact h1f.ennnorm.lintegral_prod_right'
 #align measure_theory.has_finite_integral_prod_iff MeasureTheory.hasFiniteIntegral_prod_iff
 
 theorem hasFiniteIntegral_prod_iff' ⦃f : α × β → E⦄ (h1f : AEStronglyMeasurable f (μ.Prod ν)) :
@@ -309,9 +285,7 @@ theorem integrable_prod_iff' [SigmaFinite μ] ⦃f : α × β → E⦄
     (h1f : AEStronglyMeasurable f (μ.Prod ν)) :
     Integrable f (μ.Prod ν) ↔
       (∀ᵐ y ∂ν, Integrable (fun x => f (x, y)) μ) ∧ Integrable (fun y => ∫ x, ‖f (x, y)‖ ∂μ) ν :=
-  by
-  convert integrable_prod_iff h1f.prod_swap using 1
-  rw [integrable_swap_iff]
+  by convert integrable_prod_iff h1f.prod_swap using 1; rw [integrable_swap_iff]
 #align measure_theory.integrable_prod_iff' MeasureTheory.integrable_prod_iff'
 
 theorem Integrable.prod_left_ae [SigmaFinite μ] ⦃f : α × β → E⦄ (hf : Integrable f (μ.Prod ν)) :
@@ -489,13 +463,11 @@ theorem integral_prod :
   · intro f g hfg i_f i_g hf hg
     simp_rw [integral_add' i_f i_g, integral_integral_add' i_f i_g, hf, hg]
   · exact isClosed_eq continuous_integral continuous_integral_integral
-  · intro f g hfg i_f hf
-    convert hf using 1
+  · intro f g hfg i_f hf; convert hf using 1
     · exact integral_congr_ae hfg.symm
     · refine' integral_congr_ae _
       refine' (ae_ae_of_ae_prod hfg).mp _
-      apply eventually_of_forall
-      intro x hfgx
+      apply eventually_of_forall; intro x hfgx
       exact integral_congr_ae (ae_eq_symm hfgx)
 #align measure_theory.integral_prod MeasureTheory.integral_prod
 
@@ -503,10 +475,8 @@ theorem integral_prod :
   the Bochner integral of `f` is equal to the iterated Bochner integral.
   This version has the integrals on the right-hand side in the other order. -/
 theorem integral_prod_symm (f : α × β → E) (hf : Integrable f (μ.Prod ν)) :
-    (∫ z, f z ∂μ.Prod ν) = ∫ y, ∫ x, f (x, y) ∂μ ∂ν :=
-  by
-  simp_rw [← integral_prod_swap f hf.ae_strongly_measurable]
-  exact integral_prod _ hf.swap
+    (∫ z, f z ∂μ.Prod ν) = ∫ y, ∫ x, f (x, y) ∂μ ∂ν := by
+  simp_rw [← integral_prod_swap f hf.ae_strongly_measurable]; exact integral_prod _ hf.swap
 #align measure_theory.integral_prod_symm MeasureTheory.integral_prod_symm
 
 /-- Reversed version of **Fubini's Theorem**. -/

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

@@ -113,7 +113,7 @@ theorem MeasureTheory.StronglyMeasurable.integral_prod_right [SigmaFinite ν] 
     by_cases hfx : integrable (f x) ν
     · have : ∀ n, integrable (s' n x) ν := by
         intro n
-        apply (hfx.norm.add hfx.norm).mono' (s' n x).AeStronglyMeasurable
+        apply (hfx.norm.add hfx.norm).mono' (s' n x).AEStronglyMeasurable
         apply eventually_of_forall
         intro y
         simp_rw [s', simple_func.coe_comp]
@@ -122,7 +122,7 @@ theorem MeasureTheory.StronglyMeasurable.integral_prod_right [SigmaFinite ν] 
         mem_set_of_eq]
       refine'
         tendsto_integral_of_dominated_convergence (fun y => ‖f x y‖ + ‖f x y‖)
-          (fun n => (s' n x).AeStronglyMeasurable) (hfx.norm.add hfx.norm) _ _
+          (fun n => (s' n x).AEStronglyMeasurable) (hfx.norm.add hfx.norm) _ _
       · exact fun n => eventually_of_forall fun y => simple_func.norm_approx_on_zero_le _ _ (x, y) n
       · refine' eventually_of_forall fun y => simple_func.tendsto_approx_on _ _ _
         apply subset_closure
@@ -169,7 +169,7 @@ variable [SigmaFinite ν]
 theorem integrable_measure_prod_mk_left {s : Set (α × β)} (hs : MeasurableSet s)
     (h2s : (μ.Prod ν) s ≠ ∞) : Integrable (fun x => (ν (Prod.mk x ⁻¹' s)).toReal) μ :=
   by
-  refine' ⟨(measurable_measure_prod_mk_left hs).ennreal_toReal.AEMeasurable.AeStronglyMeasurable, _⟩
+  refine' ⟨(measurable_measure_prod_mk_left hs).ennreal_toReal.AEMeasurable.AEStronglyMeasurable, _⟩
   simp_rw [has_finite_integral, ennnorm_eq_of_real to_real_nonneg]
   convert h2s.lt_top using 1; simp_rw [prod_apply hs]; apply lintegral_congr_ae
   refine' (ae_measure_lt_top hs h2s).mp _; apply eventually_of_forall; intro x hx
@@ -186,41 +186,41 @@ open MeasureTheory.Measure
 
 section
 
-theorem MeasureTheory.AeStronglyMeasurable.prod_swap {γ : Type _} [TopologicalSpace γ]
-    [SigmaFinite μ] [SigmaFinite ν] {f : β × α → γ} (hf : AeStronglyMeasurable f (ν.Prod μ)) :
-    AeStronglyMeasurable (fun z : α × β => f z.symm) (μ.Prod ν) :=
+theorem MeasureTheory.AEStronglyMeasurable.prod_swap {γ : Type _} [TopologicalSpace γ]
+    [SigmaFinite μ] [SigmaFinite ν] {f : β × α → γ} (hf : AEStronglyMeasurable f (ν.Prod μ)) :
+    AEStronglyMeasurable (fun z : α × β => f z.symm) (μ.Prod ν) :=
   by
   rw [← prod_swap] at hf
   exact hf.comp_measurable measurable_swap
-#align measure_theory.ae_strongly_measurable.prod_swap MeasureTheory.AeStronglyMeasurable.prod_swap
+#align measure_theory.ae_strongly_measurable.prod_swap MeasureTheory.AEStronglyMeasurable.prod_swap
 
-theorem MeasureTheory.AeStronglyMeasurable.fst {γ} [TopologicalSpace γ] [SigmaFinite ν] {f : α → γ}
-    (hf : AeStronglyMeasurable f μ) : AeStronglyMeasurable (fun z : α × β => f z.1) (μ.Prod ν) :=
+theorem MeasureTheory.AEStronglyMeasurable.fst {γ} [TopologicalSpace γ] [SigmaFinite ν] {f : α → γ}
+    (hf : AEStronglyMeasurable f μ) : AEStronglyMeasurable (fun z : α × β => f z.1) (μ.Prod ν) :=
   hf.comp_quasiMeasurePreserving quasiMeasurePreserving_fst
-#align measure_theory.ae_strongly_measurable.fst MeasureTheory.AeStronglyMeasurable.fst
+#align measure_theory.ae_strongly_measurable.fst MeasureTheory.AEStronglyMeasurable.fst
 
-theorem MeasureTheory.AeStronglyMeasurable.snd {γ} [TopologicalSpace γ] [SigmaFinite ν] {f : β → γ}
-    (hf : AeStronglyMeasurable f ν) : AeStronglyMeasurable (fun z : α × β => f z.2) (μ.Prod ν) :=
+theorem MeasureTheory.AEStronglyMeasurable.snd {γ} [TopologicalSpace γ] [SigmaFinite ν] {f : β → γ}
+    (hf : AEStronglyMeasurable f ν) : AEStronglyMeasurable (fun z : α × β => f z.2) (μ.Prod ν) :=
   hf.comp_quasiMeasurePreserving quasiMeasurePreserving_snd
-#align measure_theory.ae_strongly_measurable.snd MeasureTheory.AeStronglyMeasurable.snd
+#align measure_theory.ae_strongly_measurable.snd MeasureTheory.AEStronglyMeasurable.snd
 
 /-- The Bochner integral is a.e.-measurable.
   This shows that the integrand of (the right-hand-side of) Fubini's theorem is a.e.-measurable. -/
-theorem MeasureTheory.AeStronglyMeasurable.integral_prod_right' [SigmaFinite ν] [NormedSpace ℝ E]
-    [CompleteSpace E] ⦃f : α × β → E⦄ (hf : AeStronglyMeasurable f (μ.Prod ν)) :
-    AeStronglyMeasurable (fun x => ∫ y, f (x, y) ∂ν) μ :=
+theorem MeasureTheory.AEStronglyMeasurable.integral_prod_right' [SigmaFinite ν] [NormedSpace ℝ E]
+    [CompleteSpace E] ⦃f : α × β → E⦄ (hf : AEStronglyMeasurable f (μ.Prod ν)) :
+    AEStronglyMeasurable (fun x => ∫ y, f (x, y) ∂ν) μ :=
   ⟨fun x => ∫ y, hf.mk f (x, y) ∂ν, hf.stronglyMeasurable_mk.integral_prod_right', by
     filter_upwards [ae_ae_of_ae_prod hf.ae_eq_mk]with _ hx using integral_congr_ae hx⟩
-#align measure_theory.ae_strongly_measurable.integral_prod_right' MeasureTheory.AeStronglyMeasurable.integral_prod_right'
+#align measure_theory.ae_strongly_measurable.integral_prod_right' MeasureTheory.AEStronglyMeasurable.integral_prod_right'
 
-theorem MeasureTheory.AeStronglyMeasurable.prod_mk_left {γ : Type _} [SigmaFinite ν]
-    [TopologicalSpace γ] {f : α × β → γ} (hf : AeStronglyMeasurable f (μ.Prod ν)) :
-    ∀ᵐ x ∂μ, AeStronglyMeasurable (fun y => f (x, y)) ν :=
+theorem MeasureTheory.AEStronglyMeasurable.prod_mk_left {γ : Type _} [SigmaFinite ν]
+    [TopologicalSpace γ] {f : α × β → γ} (hf : AEStronglyMeasurable f (μ.Prod ν)) :
+    ∀ᵐ x ∂μ, AEStronglyMeasurable (fun y => f (x, y)) ν :=
   by
   filter_upwards [ae_ae_of_ae_prod hf.ae_eq_mk]with x hx
   exact
     ⟨fun y => hf.mk f (x, y), hf.strongly_measurable_mk.comp_measurable measurable_prod_mk_left, hx⟩
-#align measure_theory.ae_strongly_measurable.prod_mk_left MeasureTheory.AeStronglyMeasurable.prod_mk_left
+#align measure_theory.ae_strongly_measurable.prod_mk_left MeasureTheory.AEStronglyMeasurable.prod_mk_left
 
 end
 
@@ -235,8 +235,8 @@ section
 
 theorem Integrable.swap [SigmaFinite μ] ⦃f : α × β → E⦄ (hf : Integrable f (μ.Prod ν)) :
     Integrable (f ∘ Prod.swap) (ν.Prod μ) :=
-  ⟨hf.AeStronglyMeasurable.prod_swap,
-    (lintegral_prod_swap _ hf.AeStronglyMeasurable.ennnorm : _).le.trans_lt hf.HasFiniteIntegral⟩
+  ⟨hf.AEStronglyMeasurable.prod_swap,
+    (lintegral_prod_swap _ hf.AEStronglyMeasurable.ennnorm : _).le.trans_lt hf.HasFiniteIntegral⟩
 #align measure_theory.integrable.swap MeasureTheory.Integrable.swap
 
 theorem integrable_swap_iff [SigmaFinite μ] ⦃f : α × β → E⦄ :
@@ -255,7 +255,7 @@ theorem hasFiniteIntegral_prod_iff ⦃f : α × β → E⦄ (h1f : StronglyMeasu
   simp only [has_finite_integral, lintegral_prod_of_measurable _ h1f.ennnorm]
   have : ∀ x, ∀ᵐ y ∂ν, 0 ≤ ‖f (x, y)‖ := fun x => eventually_of_forall fun y => norm_nonneg _
   simp_rw [integral_eq_lintegral_of_nonneg_ae (this _)
-      (h1f.norm.comp_measurable measurable_prod_mk_left).AeStronglyMeasurable,
+      (h1f.norm.comp_measurable measurable_prod_mk_left).AEStronglyMeasurable,
     ennnorm_eq_of_real to_real_nonneg, ofReal_norm_eq_coe_nnnorm]
   -- this fact is probably too specialized to be its own lemma
   have : ∀ {p q r : Prop} (h1 : r → p), (r ↔ p ∧ q) ↔ p → (r ↔ q) := fun p q r h1 => by
@@ -275,7 +275,7 @@ theorem hasFiniteIntegral_prod_iff ⦃f : α × β → E⦄ (h1f : StronglyMeasu
     exact h1f.ennnorm.lintegral_prod_right'
 #align measure_theory.has_finite_integral_prod_iff MeasureTheory.hasFiniteIntegral_prod_iff
 
-theorem hasFiniteIntegral_prod_iff' ⦃f : α × β → E⦄ (h1f : AeStronglyMeasurable f (μ.Prod ν)) :
+theorem hasFiniteIntegral_prod_iff' ⦃f : α × β → E⦄ (h1f : AEStronglyMeasurable f (μ.Prod ν)) :
     HasFiniteIntegral f (μ.Prod ν) ↔
       (∀ᵐ x ∂μ, HasFiniteIntegral (fun y => f (x, y)) ν) ∧
         HasFiniteIntegral (fun x => ∫ y, ‖f (x, y)‖ ∂ν) μ :=
@@ -295,7 +295,7 @@ theorem hasFiniteIntegral_prod_iff' ⦃f : α × β → E⦄ (h1f : AeStronglyMe
 
 /-- A binary function is integrable if the function `y ↦ f (x, y)` is integrable for almost every
   `x` and the function `x ↦ ∫ ‖f (x, y)‖ dy` is integrable. -/
-theorem integrable_prod_iff ⦃f : α × β → E⦄ (h1f : AeStronglyMeasurable f (μ.Prod ν)) :
+theorem integrable_prod_iff ⦃f : α × β → E⦄ (h1f : AEStronglyMeasurable f (μ.Prod ν)) :
     Integrable f (μ.Prod ν) ↔
       (∀ᵐ x ∂μ, Integrable (fun y => f (x, y)) ν) ∧ Integrable (fun x => ∫ y, ‖f (x, y)‖ ∂ν) μ :=
   by
@@ -306,7 +306,7 @@ theorem integrable_prod_iff ⦃f : α × β → E⦄ (h1f : AeStronglyMeasurable
 /-- A binary function is integrable if the function `x ↦ f (x, y)` is integrable for almost every
   `y` and the function `y ↦ ∫ ‖f (x, y)‖ dx` is integrable. -/
 theorem integrable_prod_iff' [SigmaFinite μ] ⦃f : α × β → E⦄
-    (h1f : AeStronglyMeasurable f (μ.Prod ν)) :
+    (h1f : AEStronglyMeasurable f (μ.Prod ν)) :
     Integrable f (μ.Prod ν) ↔
       (∀ᵐ y ∂ν, Integrable (fun x => f (x, y)) μ) ∧ Integrable (fun y => ∫ x, ‖f (x, y)‖ ∂μ) ν :=
   by
@@ -316,7 +316,7 @@ theorem integrable_prod_iff' [SigmaFinite μ] ⦃f : α × β → E⦄
 
 theorem Integrable.prod_left_ae [SigmaFinite μ] ⦃f : α × β → E⦄ (hf : Integrable f (μ.Prod ν)) :
     ∀ᵐ y ∂ν, Integrable (fun x => f (x, y)) μ :=
-  ((integrable_prod_iff' hf.AeStronglyMeasurable).mp hf).1
+  ((integrable_prod_iff' hf.AEStronglyMeasurable).mp hf).1
 #align measure_theory.integrable.prod_left_ae MeasureTheory.Integrable.prod_left_ae
 
 theorem Integrable.prod_right_ae [SigmaFinite μ] ⦃f : α × β → E⦄ (hf : Integrable f (μ.Prod ν)) :
@@ -326,7 +326,7 @@ theorem Integrable.prod_right_ae [SigmaFinite μ] ⦃f : α × β → E⦄ (hf :
 
 theorem Integrable.integral_norm_prod_left ⦃f : α × β → E⦄ (hf : Integrable f (μ.Prod ν)) :
     Integrable (fun x => ∫ y, ‖f (x, y)‖ ∂ν) μ :=
-  ((integrable_prod_iff hf.AeStronglyMeasurable).mp hf).2
+  ((integrable_prod_iff hf.AEStronglyMeasurable).mp hf).2
 #align measure_theory.integrable.integral_norm_prod_left MeasureTheory.Integrable.integral_norm_prod_left
 
 theorem Integrable.integral_norm_prod_right [SigmaFinite μ] ⦃f : α × β → E⦄
@@ -349,7 +349,7 @@ variable [NormedSpace ℝ E] [CompleteSpace E]
 
 theorem Integrable.integral_prod_left ⦃f : α × β → E⦄ (hf : Integrable f (μ.Prod ν)) :
     Integrable (fun x => ∫ y, f (x, y) ∂ν) μ :=
-  Integrable.mono hf.integral_norm_prod_left hf.AeStronglyMeasurable.integral_prod_right' <|
+  Integrable.mono hf.integral_norm_prod_left hf.AEStronglyMeasurable.integral_prod_right' <|
     eventually_of_forall fun x =>
       (norm_integral_le_integral_norm _).trans_eq <|
         (norm_of_nonneg <|
@@ -367,7 +367,7 @@ theorem Integrable.integral_prod_right [SigmaFinite μ] ⦃f : α × β → E⦄
 
 variable [SigmaFinite μ]
 
-theorem integral_prod_swap (f : α × β → E) (hf : AeStronglyMeasurable f (μ.Prod ν)) :
+theorem integral_prod_swap (f : α × β → E) (hf : AEStronglyMeasurable f (μ.Prod ν)) :
     (∫ z, f z.symm ∂ν.Prod μ) = ∫ z, f z ∂μ.Prod ν :=
   by
   rw [← prod_swap] at hf

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

@@ -102,7 +102,7 @@ theorem MeasureTheory.StronglyMeasurable.integral_prod_right [SigmaFinite ν] 
       exact ⟨(x, z), rfl⟩
     simp only [simple_func.integral_eq_sum_of_subset (this _)]
     refine' Finset.stronglyMeasurable_sum _ fun x _ => _
-    refine' (Measurable.eNNReal_toReal _).StronglyMeasurable.smul_const _
+    refine' (Measurable.ennreal_toReal _).StronglyMeasurable.smul_const _
     simp (config := { singlePass := true }) only [simple_func.coe_comp, preimage_comp]
     apply measurable_measure_prod_mk_left
     exact (s n).measurableSet_fiber x
@@ -169,7 +169,7 @@ variable [SigmaFinite ν]
 theorem integrable_measure_prod_mk_left {s : Set (α × β)} (hs : MeasurableSet s)
     (h2s : (μ.Prod ν) s ≠ ∞) : Integrable (fun x => (ν (Prod.mk x ⁻¹' s)).toReal) μ :=
   by
-  refine' ⟨(measurable_measure_prod_mk_left hs).eNNReal_toReal.AEMeasurable.AeStronglyMeasurable, _⟩
+  refine' ⟨(measurable_measure_prod_mk_left hs).ennreal_toReal.AEMeasurable.AeStronglyMeasurable, _⟩
   simp_rw [has_finite_integral, ennnorm_eq_of_real to_real_nonneg]
   convert h2s.lt_top using 1; simp_rw [prod_apply hs]; apply lintegral_congr_ae
   refine' (ae_measure_lt_top hs h2s).mp _; apply eventually_of_forall; intro x hx

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

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

@@ -457,7 +457,7 @@ theorem integral_prod (f : α × β → E) (hf : Integrable f (μ.prod ν)) :
   apply Integrable.induction
   · intro c s hs h2s
     simp_rw [integral_indicator hs, ← indicator_comp_right, Function.comp,
-      integral_indicator (measurable_prod_mk_left hs), set_integral_const, integral_smul_const,
+      integral_indicator (measurable_prod_mk_left hs), setIntegral_const, integral_smul_const,
       integral_toReal (measurable_measure_prod_mk_left hs).aemeasurable
         (ae_measure_lt_top hs h2s.ne)]
     -- Porting note: was `simp_rw`
@@ -498,12 +498,16 @@ theorem integral_integral_swap ⦃f : α → β → E⦄ (hf : Integrable (uncur
 #align measure_theory.integral_integral_swap MeasureTheory.integral_integral_swap
 
 /-- **Fubini's Theorem** for set integrals. -/
-theorem set_integral_prod (f : α × β → E) {s : Set α} {t : Set β}
+theorem setIntegral_prod (f : α × β → E) {s : Set α} {t : Set β}
     (hf : IntegrableOn f (s ×ˢ t) (μ.prod ν)) :
     ∫ z in s ×ˢ t, f z ∂μ.prod ν = ∫ x in s, ∫ y in t, f (x, y) ∂ν ∂μ := by
   simp only [← Measure.prod_restrict s t, IntegrableOn] at hf ⊢
   exact integral_prod f hf
-#align measure_theory.set_integral_prod MeasureTheory.set_integral_prod
+#align measure_theory.set_integral_prod MeasureTheory.setIntegral_prod
+
+@[deprecated]
+alias set_integral_prod :=
+  setIntegral_prod -- deprecated on 2024-04-17
 
 theorem integral_prod_smul {𝕜 : Type*} [RCLike 𝕜] [NormedSpace 𝕜 E] (f : α → 𝕜) (g : β → E) :
     ∫ z, f z.1 • g z.2 ∂μ.prod ν = (∫ x, f x ∂μ) • ∫ y, g y ∂ν := by
@@ -521,13 +525,17 @@ theorem integral_prod_mul {L : Type*} [RCLike L] (f : α → L) (g : β → L) :
   integral_prod_smul f g
 #align measure_theory.integral_prod_mul MeasureTheory.integral_prod_mul
 
-theorem set_integral_prod_mul {L : Type*} [RCLike L] (f : α → L) (g : β → L) (s : Set α)
+theorem setIntegral_prod_mul {L : Type*} [RCLike L] (f : α → L) (g : β → L) (s : Set α)
     (t : Set β) :
     ∫ z in s ×ˢ t, f z.1 * g z.2 ∂μ.prod ν = (∫ x in s, f x ∂μ) * ∫ y in t, g y ∂ν := by
   -- Porting note: added
   rw [← Measure.prod_restrict s t]
   apply integral_prod_mul
-#align measure_theory.set_integral_prod_mul MeasureTheory.set_integral_prod_mul
+#align measure_theory.set_integral_prod_mul MeasureTheory.setIntegral_prod_mul
+
+@[deprecated]
+alias set_integral_prod_mul :=
+  setIntegral_prod_mul -- deprecated on 2024-04-17
 
 theorem integral_fun_snd (f : β → E) : ∫ z, f z.2 ∂μ.prod ν = (μ univ).toReal • ∫ y, f y ∂ν := by
   simpa using integral_prod_smul (1 : α → ℝ) f
@@ -556,12 +564,12 @@ lemma integral_integral_swap_of_hasCompactSupport
   calc
   ∫ x, (∫ y, f x y ∂ν) ∂μ = ∫ x, (∫ y in V, f x y ∂ν) ∂μ := by
     congr 1 with x
-    apply (set_integral_eq_integral_of_forall_compl_eq_zero (fun y hy ↦ ?_)).symm
+    apply (setIntegral_eq_integral_of_forall_compl_eq_zero (fun y hy ↦ ?_)).symm
     contrapose! hy
     have : (x, y) ∈ Function.support f.uncurry := hy
     exact mem_image_of_mem _ (subset_tsupport _ this)
   _ = ∫ x in U, (∫ y in V, f x y ∂ν) ∂μ := by
-    apply (set_integral_eq_integral_of_forall_compl_eq_zero (fun x hx ↦ ?_)).symm
+    apply (setIntegral_eq_integral_of_forall_compl_eq_zero (fun x hx ↦ ?_)).symm
     have : ∀ y, f x y = 0 := by
       intro y
       contrapose! hx
@@ -575,7 +583,7 @@ lemma integral_integral_swap_of_hasCompactSupport
     obtain ⟨C, hC⟩ : ∃ C, ∀ p, ‖f.uncurry p‖ ≤ C := hf.bounded_above_of_compact_support h'f
     exact hasFiniteIntegral_of_bounded (C := C) (eventually_of_forall hC)
   _ = ∫ y, (∫ x in U, f x y ∂μ) ∂ν := by
-    apply set_integral_eq_integral_of_forall_compl_eq_zero (fun y hy ↦ ?_)
+    apply setIntegral_eq_integral_of_forall_compl_eq_zero (fun y hy ↦ ?_)
     have : ∀ x, f x y = 0 := by
       intro x
       contrapose! hy
@@ -584,7 +592,7 @@ lemma integral_integral_swap_of_hasCompactSupport
     simp [this]
   _ = ∫ y, (∫ x, f x y ∂μ) ∂ν := by
     congr 1 with y
-    apply set_integral_eq_integral_of_forall_compl_eq_zero (fun x hx ↦ ?_)
+    apply setIntegral_eq_integral_of_forall_compl_eq_zero (fun x hx ↦ ?_)
     contrapose! hx
     have : (x, y) ∈ Function.support f.uncurry := hx
     exact mem_image_of_mem _ (subset_tsupport _ this)

In all cases, the original proof works now. I presume this is due to simp changes in Lean 4.7, but haven't verified.

@@ -234,9 +234,7 @@ theorem hasFiniteIntegral_prod_iff ⦃f : α × β → E⦄ (h1f : StronglyMeasu
     HasFiniteIntegral f (μ.prod ν) ↔
       (∀ᵐ x ∂μ, HasFiniteIntegral (fun y => f (x, y)) ν) ∧
         HasFiniteIntegral (fun x => ∫ y, ‖f (x, y)‖ ∂ν) μ := by
-  simp only [HasFiniteIntegral]
-  -- porting note (#10745): was `simp`
-  rw [lintegral_prod_of_measurable _ h1f.ennnorm]
+  simp only [HasFiniteIntegral, lintegral_prod_of_measurable _ h1f.ennnorm]
   have (x) : ∀ᵐ y ∂ν, 0 ≤ ‖f (x, y)‖ := by filter_upwards with y using norm_nonneg _
   simp_rw [integral_eq_lintegral_of_nonneg_ae (this _)
       (h1f.norm.comp_measurable measurable_prod_mk_left).aestronglyMeasurable,

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.

@@ -314,7 +314,7 @@ theorem Integrable.prod_smul {𝕜 : Type*} [NontriviallyNormedField 𝕜] [Norm
   · exact eventually_of_forall fun x => hg.smul (f x)
   · simpa only [norm_smul, integral_mul_left] using hf.norm.mul_const _
 
-theorem Integrable.prod_mul {L : Type*} [IsROrC L] {f : α → L} {g : β → L} (hf : Integrable f μ)
+theorem Integrable.prod_mul {L : Type*} [RCLike L] {f : α → L} {g : β → L} (hf : Integrable f μ)
     (hg : Integrable g ν) : Integrable (fun z : α × β => f z.1 * g z.2) (μ.prod ν) :=
   hf.prod_smul hg
 #align measure_theory.integrable_prod_mul MeasureTheory.Integrable.prod_mul
@@ -507,7 +507,7 @@ theorem set_integral_prod (f : α × β → E) {s : Set α} {t : Set β}
   exact integral_prod f hf
 #align measure_theory.set_integral_prod MeasureTheory.set_integral_prod
 
-theorem integral_prod_smul {𝕜 : Type*} [IsROrC 𝕜] [NormedSpace 𝕜 E] (f : α → 𝕜) (g : β → E) :
+theorem integral_prod_smul {𝕜 : Type*} [RCLike 𝕜] [NormedSpace 𝕜 E] (f : α → 𝕜) (g : β → E) :
     ∫ z, f z.1 • g z.2 ∂μ.prod ν = (∫ x, f x ∂μ) • ∫ y, g y ∂ν := by
   by_cases hE : CompleteSpace E; swap; · simp [integral, hE]
   by_cases h : Integrable (fun z : α × β => f z.1 • g z.2) (μ.prod ν)
@@ -518,12 +518,12 @@ theorem integral_prod_smul {𝕜 : Type*} [IsROrC 𝕜] [NormedSpace 𝕜 E] (f
     exact h.1.prod_smul h.2
   cases' H with H H <;> simp [integral_undef h, integral_undef H]
 
-theorem integral_prod_mul {L : Type*} [IsROrC L] (f : α → L) (g : β → L) :
+theorem integral_prod_mul {L : Type*} [RCLike L] (f : α → L) (g : β → L) :
     ∫ z, f z.1 * g z.2 ∂μ.prod ν = (∫ x, f x ∂μ) * ∫ y, g y ∂ν :=
   integral_prod_smul f g
 #align measure_theory.integral_prod_mul MeasureTheory.integral_prod_mul
 
-theorem set_integral_prod_mul {L : Type*} [IsROrC L] (f : α → L) (g : β → L) (s : Set α)
+theorem set_integral_prod_mul {L : Type*} [RCLike L] (f : α → L) (g : β → L) (s : Set α)
     (t : Set β) :
     ∫ z in s ×ˢ t, f z.1 * g z.2 ∂μ.prod ν = (∫ x in s, f x ∂μ) * ∫ y in t, g y ∂ν := by
   -- Porting note: added

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.

@@ -98,9 +98,9 @@ theorem MeasureTheory.StronglyMeasurable.integral_prod_right [SigmaFinite ν] 
   have h2f' : Tendsto f' atTop (𝓝 fun x : α => ∫ y : β, f x y ∂ν) := by
     rw [tendsto_pi_nhds]; intro x
     by_cases hfx : Integrable (f x) ν
-    · have : ∀ n, Integrable (s' n x) ν := by
-        intro n; apply (hfx.norm.add hfx.norm).mono' (s' n x).aestronglyMeasurable
-        apply eventually_of_forall; intro y
+    · have (n) : Integrable (s' n x) ν := by
+        apply (hfx.norm.add hfx.norm).mono' (s' n x).aestronglyMeasurable
+        filter_upwards with y
         simp_rw [s', SimpleFunc.coe_comp]; exact SimpleFunc.norm_approxOn_zero_le _ _ (x, y) n
       simp only [f', hfx, SimpleFunc.integral_eq_integral _ (this _), indicator_of_mem,
         mem_setOf_eq]
@@ -162,7 +162,7 @@ theorem integrable_measure_prod_mk_left {s : Set (α × β)} (hs : MeasurableSet
   -- Porting note: was `simp_rw`
   rw [prod_apply hs]
   apply lintegral_congr_ae
-  refine' (ae_measure_lt_top hs h2s).mp _; apply eventually_of_forall; intro x hx
+  filter_upwards [ae_measure_lt_top hs h2s] with x hx
   rw [lt_top_iff_ne_top] at hx; simp [ofReal_toReal, hx]
 #align measure_theory.measure.integrable_measure_prod_mk_left MeasureTheory.Measure.integrable_measure_prod_mk_left
 
@@ -237,7 +237,7 @@ theorem hasFiniteIntegral_prod_iff ⦃f : α × β → E⦄ (h1f : StronglyMeasu
   simp only [HasFiniteIntegral]
   -- porting note (#10745): was `simp`
   rw [lintegral_prod_of_measurable _ h1f.ennnorm]
-  have : ∀ x, ∀ᵐ y ∂ν, 0 ≤ ‖f (x, y)‖ := fun x => eventually_of_forall fun y => norm_nonneg _
+  have (x) : ∀ᵐ y ∂ν, 0 ≤ ‖f (x, y)‖ := by filter_upwards with y using norm_nonneg _
   simp_rw [integral_eq_lintegral_of_nonneg_ae (this _)
       (h1f.norm.comp_measurable measurable_prod_mk_left).aestronglyMeasurable,
     ennnorm_eq_ofReal toReal_nonneg, ofReal_norm_eq_coe_nnnorm]
@@ -246,7 +246,7 @@ theorem hasFiniteIntegral_prod_iff ⦃f : α × β → E⦄ (h1f : StronglyMeasu
     rw [← and_congr_right_iff, and_iff_right_of_imp h1]
   rw [this]
   · intro h2f; rw [lintegral_congr_ae]
-    refine' h2f.mp _; apply eventually_of_forall; intro x hx; dsimp only
+    filter_upwards [h2f] with x hx
     rw [ofReal_toReal]; rw [← lt_top_iff_ne_top]; exact hx
   · intro h2f; refine' ae_lt_top _ h2f.ne; exact h1f.ennnorm.lintegral_prod_right'
 #align measure_theory.has_finite_integral_prod_iff MeasureTheory.hasFiniteIntegral_prod_iff
@@ -469,10 +469,8 @@ theorem integral_prod (f : α × β → E) (hf : Integrable f (μ.prod ν)) :
   · exact isClosed_eq continuous_integral continuous_integral_integral
   · rintro f g hfg - hf; convert hf using 1
     · exact integral_congr_ae hfg.symm
-    · refine' integral_congr_ae _
-      refine' (ae_ae_of_ae_prod hfg).mp _
-      apply eventually_of_forall; intro x hfgx
-      exact integral_congr_ae (ae_eq_symm hfgx)
+    · apply integral_congr_ae
+      filter_upwards [ae_ae_of_ae_prod hfg] with x hfgx using integral_congr_ae (ae_eq_symm hfgx)
 #align measure_theory.integral_prod MeasureTheory.integral_prod
 
 /-- Symmetric version of **Fubini's Theorem**: For integrable functions on `α × β`,

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)

@@ -48,13 +48,9 @@ open TopologicalSpace
 open Filter hiding prod_eq map
 
 variable {α α' β β' γ E : Type*}
-
 variable [MeasurableSpace α] [MeasurableSpace α'] [MeasurableSpace β] [MeasurableSpace β']
-
 variable [MeasurableSpace γ]
-
 variable {μ μ' : Measure α} {ν ν' : Measure β} {τ : Measure γ}
-
 variable [NormedAddCommGroup E]
 
 /-! ### Measurability

This is a very large PR, but it has been reviewed piecemeal already in PRs to the bump/v4.7.0 branch as we update to intermediate nightlies.

Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Kyle Miller <kmill31415@gmail.com> Co-authored-by: damiano <adomani@gmail.com>

@@ -96,7 +96,7 @@ theorem MeasureTheory.StronglyMeasurable.integral_prod_right [SigmaFinite ν] 
     simp only [SimpleFunc.integral_eq_sum_of_subset (this _)]
     refine' Finset.stronglyMeasurable_sum _ fun x _ => _
     refine' (Measurable.ennreal_toReal _).stronglyMeasurable.smul_const _
-    simp only [SimpleFunc.coe_comp, preimage_comp]
+    simp only [s', SimpleFunc.coe_comp, preimage_comp]
     apply measurable_measure_prod_mk_left
     exact (s n).measurableSet_fiber x
   have h2f' : Tendsto f' atTop (𝓝 fun x : α => ∫ y : β, f x y ∂ν) := by
@@ -105,8 +105,8 @@ theorem MeasureTheory.StronglyMeasurable.integral_prod_right [SigmaFinite ν] 
     · have : ∀ n, Integrable (s' n x) ν := by
         intro n; apply (hfx.norm.add hfx.norm).mono' (s' n x).aestronglyMeasurable
         apply eventually_of_forall; intro y
-        simp_rw [SimpleFunc.coe_comp]; exact SimpleFunc.norm_approxOn_zero_le _ _ (x, y) n
-      simp only [hfx, SimpleFunc.integral_eq_integral _ (this _), indicator_of_mem,
+        simp_rw [s', SimpleFunc.coe_comp]; exact SimpleFunc.norm_approxOn_zero_le _ _ (x, y) n
+      simp only [f', hfx, SimpleFunc.integral_eq_integral _ (this _), indicator_of_mem,
         mem_setOf_eq]
       refine'
         tendsto_integral_of_dominated_convergence (fun y => ‖f x y‖ + ‖f x y‖)
@@ -121,7 +121,7 @@ theorem MeasureTheory.StronglyMeasurable.integral_prod_right [SigmaFinite ν] 
         · simp
         apply subset_closure
         simp [-uncurry_apply_pair]
-    · simp [hfx, integral_undef]
+    · simp [f', hfx, integral_undef]
   exact stronglyMeasurable_of_tendsto _ hf' h2f'
 #align measure_theory.strongly_measurable.integral_prod_right MeasureTheory.StronglyMeasurable.integral_prod_right
 

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

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

@@ -4,6 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Floris van Doorn
 -/
 import Mathlib.MeasureTheory.Constructions.Prod.Basic
+import Mathlib.MeasureTheory.Integral.DominatedConvergence
 import Mathlib.MeasureTheory.Integral.SetIntegral
 
 #align_import measure_theory.constructions.prod.integral from "leanprover-community/mathlib"@"fd5edc43dc4f10b85abfe544b88f82cf13c5f844"

Classifies by adding issue number (#10745) to porting notes claiming was simp.

@@ -238,7 +238,7 @@ theorem hasFiniteIntegral_prod_iff ⦃f : α × β → E⦄ (h1f : StronglyMeasu
       (∀ᵐ x ∂μ, HasFiniteIntegral (fun y => f (x, y)) ν) ∧
         HasFiniteIntegral (fun x => ∫ y, ‖f (x, y)‖ ∂ν) μ := by
   simp only [HasFiniteIntegral]
-  -- Porting note: was `simp`
+  -- porting note (#10745): was `simp`
   rw [lintegral_prod_of_measurable _ h1f.ennnorm]
   have : ∀ x, ∀ᵐ y ∂ν, 0 ≤ ‖f (x, y)‖ := fun x => eventually_of_forall fun y => norm_nonneg _
   simp_rw [integral_eq_lintegral_of_nonneg_ae (this _)

Of the 18 uses of singlePass, in 3 cases we can just use rw, in 4 cases it isn't needed at all.

In the other 11 cases we are always use it as simp (config := {singlePass := true}) only [X] (i.e. with just a single simp lemma), and that simp call would loop forever (usually failing with a maxRecDepth error, sometimes with heartbeats). I've left these as is.

There's also one case where there was a missing only.

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

@@ -95,7 +95,7 @@ theorem MeasureTheory.StronglyMeasurable.integral_prod_right [SigmaFinite ν] 
     simp only [SimpleFunc.integral_eq_sum_of_subset (this _)]
     refine' Finset.stronglyMeasurable_sum _ fun x _ => _
     refine' (Measurable.ennreal_toReal _).stronglyMeasurable.smul_const _
-    simp (config := { singlePass := true }) only [SimpleFunc.coe_comp, preimage_comp]
+    simp only [SimpleFunc.coe_comp, preimage_comp]
     apply measurable_measure_prod_mk_left
     exact (s n).measurableSet_fiber x
   have h2f' : Tendsto f' atTop (𝓝 fun x : α => ∫ y : β, f x y ∂ν) := by

@@ -514,7 +514,7 @@ theorem set_integral_prod (f : α × β → E) {s : Set α} {t : Set β}
 
 theorem integral_prod_smul {𝕜 : Type*} [IsROrC 𝕜] [NormedSpace 𝕜 E] (f : α → 𝕜) (g : β → E) :
     ∫ z, f z.1 • g z.2 ∂μ.prod ν = (∫ x, f x ∂μ) • ∫ y, g y ∂ν := by
-  by_cases hE : CompleteSpace E; swap; simp [integral, hE]
+  by_cases hE : CompleteSpace E; swap; · simp [integral, hE]
   by_cases h : Integrable (fun z : α × β => f z.1 • g z.2) (μ.prod ν)
   · rw [integral_prod _ h]
     simp_rw [integral_smul, integral_smul_const]

@@ -24,6 +24,9 @@ In this file we prove Fubini's theorem.
   Tonelli's theorem (see `MeasureTheory.lintegral_prod`). The lemma
   `MeasureTheory.Integrable.integral_prod_right` states that the inner integral of the right-hand
   side is integrable.
+* `MeasureTheory.integral_integral_swap_of_hasCompactSupport`: a version of Fubini theorem for
+  continuous functions with compact support, which does not assume that the measures are σ-finite
+  contrary to all the usual versions of Fubini.
 
 ## Tags
 
@@ -540,4 +543,59 @@ theorem integral_fun_fst (f : α → E) : ∫ z, f z.1 ∂μ.prod ν = (ν univ)
   rw [← integral_prod_swap]
   apply integral_fun_snd
 
+section
+
+variable {X Y : Type*}
+    [TopologicalSpace X] [TopologicalSpace Y] [MeasurableSpace X] [MeasurableSpace Y]
+    [OpensMeasurableSpace X] [OpensMeasurableSpace Y]
+
+/-- A version of *Fubini theorem* for continuous functions with compact support: one may swap
+the order of integration with respect to locally finite measures. One does not assume that the
+measures are σ-finite, contrary to the usual Fubini theorem. -/
+lemma integral_integral_swap_of_hasCompactSupport
+    {f : X → Y → E} (hf : Continuous f.uncurry) (h'f : HasCompactSupport f.uncurry)
+    {μ : Measure X} {ν : Measure Y} [IsFiniteMeasureOnCompacts μ] [IsFiniteMeasureOnCompacts ν] :
+    ∫ x, (∫ y, f x y ∂ν) ∂μ = ∫ y, (∫ x, f x y ∂μ) ∂ν := by
+  let U := Prod.fst '' (tsupport f.uncurry)
+  have : Fact (μ U < ∞) := ⟨(IsCompact.image h'f continuous_fst).measure_lt_top⟩
+  let V := Prod.snd '' (tsupport f.uncurry)
+  have : Fact (ν V < ∞) := ⟨(IsCompact.image h'f continuous_snd).measure_lt_top⟩
+  calc
+  ∫ x, (∫ y, f x y ∂ν) ∂μ = ∫ x, (∫ y in V, f x y ∂ν) ∂μ := by
+    congr 1 with x
+    apply (set_integral_eq_integral_of_forall_compl_eq_zero (fun y hy ↦ ?_)).symm
+    contrapose! hy
+    have : (x, y) ∈ Function.support f.uncurry := hy
+    exact mem_image_of_mem _ (subset_tsupport _ this)
+  _ = ∫ x in U, (∫ y in V, f x y ∂ν) ∂μ := by
+    apply (set_integral_eq_integral_of_forall_compl_eq_zero (fun x hx ↦ ?_)).symm
+    have : ∀ y, f x y = 0 := by
+      intro y
+      contrapose! hx
+      have : (x, y) ∈ Function.support f.uncurry := hx
+      exact mem_image_of_mem _ (subset_tsupport _ this)
+    simp [this]
+  _ = ∫ y in V, (∫ x in U, f x y ∂μ) ∂ν := by
+    apply integral_integral_swap
+    apply (integrableOn_iff_integrable_of_support_subset (subset_tsupport f.uncurry)).mp
+    refine ⟨(h'f.stronglyMeasurable_of_prod hf).aestronglyMeasurable, ?_⟩
+    obtain ⟨C, hC⟩ : ∃ C, ∀ p, ‖f.uncurry p‖ ≤ C := hf.bounded_above_of_compact_support h'f
+    exact hasFiniteIntegral_of_bounded (C := C) (eventually_of_forall hC)
+  _ = ∫ y, (∫ x in U, f x y ∂μ) ∂ν := by
+    apply set_integral_eq_integral_of_forall_compl_eq_zero (fun y hy ↦ ?_)
+    have : ∀ x, f x y = 0 := by
+      intro x
+      contrapose! hy
+      have : (x, y) ∈ Function.support f.uncurry := hy
+      exact mem_image_of_mem _ (subset_tsupport _ this)
+    simp [this]
+  _ = ∫ y, (∫ x, f x y ∂μ) ∂ν := by
+    congr 1 with y
+    apply set_integral_eq_integral_of_forall_compl_eq_zero (fun x hx ↦ ?_)
+    contrapose! hx
+    have : (x, y) ∈ Function.support f.uncurry := hx
+    exact mem_image_of_mem _ (subset_tsupport _ this)
+
+end
+
 end MeasureTheory

• Generalize integral_prod_mul to integral_prod_smul, add Integrable.prod_smul.
• Rename integrable_prod_mul to Integrable.prod_mul.
• Add integral_fun_fst and integral_fun_snd.

@@ -306,13 +306,18 @@ theorem Integrable.integral_norm_prod_right [SigmaFinite μ] ⦃f : α × β →
   hf.swap.integral_norm_prod_left
 #align measure_theory.integrable.integral_norm_prod_right MeasureTheory.Integrable.integral_norm_prod_right
 
-theorem integrable_prod_mul {L : Type*} [IsROrC L] {f : α → L} {g : β → L} (hf : Integrable f μ)
-    (hg : Integrable g ν) : Integrable (fun z : α × β => f z.1 * g z.2) (μ.prod ν) := by
+theorem Integrable.prod_smul {𝕜 : Type*} [NontriviallyNormedField 𝕜] [NormedSpace 𝕜 E]
+    {f : α → 𝕜} {g : β → E} (hf : Integrable f μ) (hg : Integrable g ν) :
+    Integrable (fun z : α × β => f z.1 • g z.2) (μ.prod ν) := by
   refine' (integrable_prod_iff _).2 ⟨_, _⟩
-  · exact hf.1.fst.mul hg.1.snd
-  · exact eventually_of_forall fun x => hg.const_mul (f x)
-  · simpa only [norm_mul, integral_mul_left] using hf.norm.mul_const _
-#align measure_theory.integrable_prod_mul MeasureTheory.integrable_prod_mul
+  · exact hf.1.fst.smul hg.1.snd
+  · exact eventually_of_forall fun x => hg.smul (f x)
+  · simpa only [norm_smul, integral_mul_left] using hf.norm.mul_const _
+
+theorem Integrable.prod_mul {L : Type*} [IsROrC L] {f : α → L} {g : β → L} (hf : Integrable f μ)
+    (hg : Integrable g ν) : Integrable (fun z : α × β => f z.1 * g z.2) (μ.prod ν) :=
+  hf.prod_smul hg
+#align measure_theory.integrable_prod_mul MeasureTheory.Integrable.prod_mul
 
 end
 
@@ -504,15 +509,20 @@ theorem set_integral_prod (f : α × β → E) {s : Set α} {t : Set β}
   exact integral_prod f hf
 #align measure_theory.set_integral_prod MeasureTheory.set_integral_prod
 
-theorem integral_prod_mul {L : Type*} [IsROrC L] (f : α → L) (g : β → L) :
-    ∫ z, f z.1 * g z.2 ∂μ.prod ν = (∫ x, f x ∂μ) * ∫ y, g y ∂ν := by
-  by_cases h : Integrable (fun z : α × β => f z.1 * g z.2) (μ.prod ν)
+theorem integral_prod_smul {𝕜 : Type*} [IsROrC 𝕜] [NormedSpace 𝕜 E] (f : α → 𝕜) (g : β → E) :
+    ∫ z, f z.1 • g z.2 ∂μ.prod ν = (∫ x, f x ∂μ) • ∫ y, g y ∂ν := by
+  by_cases hE : CompleteSpace E; swap; simp [integral, hE]
+  by_cases h : Integrable (fun z : α × β => f z.1 • g z.2) (μ.prod ν)
   · rw [integral_prod _ h]
-    simp_rw [integral_mul_left, integral_mul_right]
+    simp_rw [integral_smul, integral_smul_const]
   have H : ¬Integrable f μ ∨ ¬Integrable g ν := by
     contrapose! h
-    exact integrable_prod_mul h.1 h.2
+    exact h.1.prod_smul h.2
   cases' H with H H <;> simp [integral_undef h, integral_undef H]
+
+theorem integral_prod_mul {L : Type*} [IsROrC L] (f : α → L) (g : β → L) :
+    ∫ z, f z.1 * g z.2 ∂μ.prod ν = (∫ x, f x ∂μ) * ∫ y, g y ∂ν :=
+  integral_prod_smul f g
 #align measure_theory.integral_prod_mul MeasureTheory.integral_prod_mul
 
 theorem set_integral_prod_mul {L : Type*} [IsROrC L] (f : α → L) (g : β → L) (s : Set α)
@@ -523,4 +533,11 @@ theorem set_integral_prod_mul {L : Type*} [IsROrC L] (f : α → L) (g : β →
   apply integral_prod_mul
 #align measure_theory.set_integral_prod_mul MeasureTheory.set_integral_prod_mul
 
+theorem integral_fun_snd (f : β → E) : ∫ z, f z.2 ∂μ.prod ν = (μ univ).toReal • ∫ y, f y ∂ν := by
+  simpa using integral_prod_smul (1 : α → ℝ) f
+
+theorem integral_fun_fst (f : α → E) : ∫ z, f z.1 ∂μ.prod ν = (ν univ).toReal • ∫ x, f x ∂μ := by
+  rw [← integral_prod_swap]
+  apply integral_fun_snd
+
 end MeasureTheory

• Drop CompleteSpace assumption in all theorems about Bochner integral on α × β.
• Drop measurability assumption in lintegral_prod_swap.

@@ -69,13 +69,14 @@ theorem measurableSet_integrable [SigmaFinite ν] ⦃f : α → β → E⦄
 
 section
 
-variable [NormedSpace ℝ E] [CompleteSpace E]
+variable [NormedSpace ℝ E]
 
 /-- The Bochner integral is measurable. This shows that the integrand of (the right-hand-side of)
   Fubini's theorem is measurable.
   This version has `f` in curried form. -/
 theorem MeasureTheory.StronglyMeasurable.integral_prod_right [SigmaFinite ν] ⦃f : α → β → E⦄
     (hf : StronglyMeasurable (uncurry f)) : StronglyMeasurable fun x => ∫ y, f x y ∂ν := by
+  by_cases hE : CompleteSpace E; swap; · simp [integral, hE, stronglyMeasurable_const]
   borelize E
   haveI : SeparableSpace (range (uncurry f) ∪ {0} : Set E) :=
     hf.separableSpace_range_union_singleton
@@ -195,7 +196,7 @@ theorem MeasureTheory.AEStronglyMeasurable.snd {γ} [TopologicalSpace γ] [Sigma
 /-- The Bochner integral is a.e.-measurable.
   This shows that the integrand of (the right-hand-side of) Fubini's theorem is a.e.-measurable. -/
 theorem MeasureTheory.AEStronglyMeasurable.integral_prod_right' [SigmaFinite ν] [NormedSpace ℝ E]
-    [CompleteSpace E] ⦃f : α × β → E⦄ (hf : AEStronglyMeasurable f (μ.prod ν)) :
+    ⦃f : α × β → E⦄ (hf : AEStronglyMeasurable f (μ.prod ν)) :
     AEStronglyMeasurable (fun x => ∫ y, f (x, y) ∂ν) μ :=
   ⟨fun x => ∫ y, hf.mk f (x, y) ∂ν, hf.stronglyMeasurable_mk.integral_prod_right', by
     filter_upwards [ae_ae_of_ae_prod hf.ae_eq_mk] with _ hx using integral_congr_ae hx⟩
@@ -217,7 +218,6 @@ variable [SigmaFinite ν]
 
 /-! ### Integrability on a product -/
 
-
 section
 
 theorem integrable_swap_iff [SigmaFinite μ] {f : α × β → E} :
@@ -316,7 +316,7 @@ theorem integrable_prod_mul {L : Type*} [IsROrC L] {f : α → L} {g : β → L}
 
 end
 
-variable [NormedSpace ℝ E] [CompleteSpace E]
+variable [NormedSpace ℝ E]
 
 theorem Integrable.integral_prod_left ⦃f : α × β → E⦄ (hf : Integrable f (μ.prod ν)) :
     Integrable (fun x => ∫ y, f (x, y) ∂ν) μ :=
@@ -342,7 +342,7 @@ theorem integral_prod_swap (f : α × β → E) :
   measurePreserving_swap.integral_comp MeasurableEquiv.prodComm.measurableEmbedding _
 #align measure_theory.integral_prod_swap MeasureTheory.integral_prod_swap
 
-variable {E' : Type*} [NormedAddCommGroup E'] [CompleteSpace E'] [NormedSpace ℝ E']
+variable {E' : Type*} [NormedAddCommGroup E'] [NormedSpace ℝ E']
 
 /-! Some rules about the sum/difference of double integrals. They follow from `integral_add`, but
   we separate them out as separate lemmas, because they involve quite some steps. -/
@@ -447,9 +447,10 @@ theorem continuous_integral_integral :
   `integrable_prod_iff` can be useful to show that the function in question in integrable.
   `MeasureTheory.Integrable.integral_prod_right` is useful to show that the inner integral
   of the right-hand side is integrable. -/
-theorem integral_prod :
-    ∀ (f : α × β → E) (_ : Integrable f (μ.prod ν)),
-      ∫ z, f z ∂μ.prod ν = ∫ x, ∫ y, f (x, y) ∂ν ∂μ := by
+theorem integral_prod (f : α × β → E) (hf : Integrable f (μ.prod ν)) :
+    ∫ z, f z ∂μ.prod ν = ∫ x, ∫ y, f (x, y) ∂ν ∂μ := by
+  by_cases hE : CompleteSpace E; swap; · simp only [integral, dif_neg hE]
+  revert f
   apply Integrable.induction
   · intro c s hs h2s
     simp_rw [integral_indicator hs, ← indicator_comp_right, Function.comp,
@@ -519,7 +520,7 @@ theorem set_integral_prod_mul {L : Type*} [IsROrC L] (f : α → L) (g : β →
     ∫ z in s ×ˢ t, f z.1 * g z.2 ∂μ.prod ν = (∫ x in s, f x ∂μ) * ∫ y in t, g y ∂ν := by
   -- Porting note: added
   rw [← Measure.prod_restrict s t]
-  simp only [← Measure.prod_restrict s t, IntegrableOn, integral_prod_mul]
+  apply integral_prod_mul
 #align measure_theory.set_integral_prod_mul MeasureTheory.set_integral_prod_mul
 
 end MeasureTheory

Drop some measurability assumptions by using the fact that Prod.swap is a measurable equivalence.

@@ -220,17 +220,16 @@ variable [SigmaFinite ν]
 
 section
 
+theorem integrable_swap_iff [SigmaFinite μ] {f : α × β → E} :
+    Integrable (f ∘ Prod.swap) (ν.prod μ) ↔ Integrable f (μ.prod ν) :=
+  measurePreserving_swap.integrable_comp_emb MeasurableEquiv.prodComm.measurableEmbedding
+#align measure_theory.integrable_swap_iff MeasureTheory.integrable_swap_iff
+
 theorem Integrable.swap [SigmaFinite μ] ⦃f : α × β → E⦄ (hf : Integrable f (μ.prod ν)) :
     Integrable (f ∘ Prod.swap) (ν.prod μ) :=
-  ⟨hf.aestronglyMeasurable.prod_swap,
-    (lintegral_prod_swap _ hf.aestronglyMeasurable.ennnorm : _).le.trans_lt hf.hasFiniteIntegral⟩
+  integrable_swap_iff.2 hf
 #align measure_theory.integrable.swap MeasureTheory.Integrable.swap
 
-theorem integrable_swap_iff [SigmaFinite μ] ⦃f : α × β → E⦄ :
-    Integrable (f ∘ Prod.swap) (ν.prod μ) ↔ Integrable f (μ.prod ν) :=
-  ⟨fun hf => hf.swap, fun hf => hf.swap⟩
-#align measure_theory.integrable_swap_iff MeasureTheory.integrable_swap_iff
-
 theorem hasFiniteIntegral_prod_iff ⦃f : α × β → E⦄ (h1f : StronglyMeasurable f) :
     HasFiniteIntegral f (μ.prod ν) ↔
       (∀ᵐ x ∂μ, HasFiniteIntegral (fun y => f (x, y)) ν) ∧
@@ -336,13 +335,11 @@ theorem Integrable.integral_prod_right [SigmaFinite μ] ⦃f : α × β → E⦄
 
 /-! ### The Bochner integral on a product -/
 
-
 variable [SigmaFinite μ]
 
-theorem integral_prod_swap (f : α × β → E) (hf : AEStronglyMeasurable f (μ.prod ν)) :
-    ∫ z, f z.swap ∂ν.prod μ = ∫ z, f z ∂μ.prod ν := by
-  rw [← prod_swap] at hf
-  rw [← integral_map measurable_swap.aemeasurable hf, prod_swap]
+theorem integral_prod_swap (f : α × β → E) :
+    ∫ z, f z.swap ∂ν.prod μ = ∫ z, f z ∂μ.prod ν :=
+  measurePreserving_swap.integral_comp MeasurableEquiv.prodComm.measurableEmbedding _
 #align measure_theory.integral_prod_swap MeasureTheory.integral_prod_swap
 
 variable {E' : Type*} [NormedAddCommGroup E'] [CompleteSpace E'] [NormedSpace ℝ E']
@@ -477,7 +474,7 @@ theorem integral_prod :
   This version has the integrals on the right-hand side in the other order. -/
 theorem integral_prod_symm (f : α × β → E) (hf : Integrable f (μ.prod ν)) :
     ∫ z, f z ∂μ.prod ν = ∫ y, ∫ x, f (x, y) ∂μ ∂ν := by
-  simp_rw [← integral_prod_swap f hf.aestronglyMeasurable]; exact integral_prod _ hf.swap
+  rw [← integral_prod_swap f]; exact integral_prod _ hf.swap
 #align measure_theory.integral_prod_symm MeasureTheory.integral_prod_symm
 
 /-- Reversed version of **Fubini's Theorem**. -/

Rename:

• tendsto_iff_norm_tendsto_one → tendsto_iff_norm_div_tendsto_zero;
• tendsto_iff_norm_tendsto_zero → tendsto_iff_norm_sub_tendsto_zero;
• tendsto_one_iff_norm_tendsto_one → tendsto_one_iff_norm_tendsto_zero;
• Filter.Tendsto.continuous_of_equicontinuous_at → Filter.Tendsto.continuous_of_equicontinuousAt.

@@ -442,7 +442,7 @@ theorem continuous_integral_integral :
     rw [← lintegral_prod_of_measurable _ (this _), ← L1.ofReal_norm_sub_eq_lintegral]
   rw [← ofReal_zero]
   refine' (continuous_ofReal.tendsto 0).comp _
-  rw [← tendsto_iff_norm_tendsto_zero]; exact tendsto_id
+  rw [← tendsto_iff_norm_sub_tendsto_zero]; exact tendsto_id
 #align measure_theory.continuous_integral_integral MeasureTheory.continuous_integral_integral
 
 /-- **Fubini's Theorem**: For integrable functions on `α × β`,

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

This has nice performance benefits.

@@ -43,7 +43,7 @@ open TopologicalSpace
 
 open Filter hiding prod_eq map
 
-variable {α α' β β' γ E : Type _}
+variable {α α' β β' γ E : Type*}
 
 variable [MeasurableSpace α] [MeasurableSpace α'] [MeasurableSpace β] [MeasurableSpace β']
 
@@ -175,7 +175,7 @@ open MeasureTheory.Measure
 
 section
 
-nonrec theorem MeasureTheory.AEStronglyMeasurable.prod_swap {γ : Type _} [TopologicalSpace γ]
+nonrec theorem MeasureTheory.AEStronglyMeasurable.prod_swap {γ : Type*} [TopologicalSpace γ]
     [SigmaFinite μ] [SigmaFinite ν] {f : β × α → γ} (hf : AEStronglyMeasurable f (ν.prod μ)) :
     AEStronglyMeasurable (fun z : α × β => f z.swap) (μ.prod ν) := by
   rw [← prod_swap] at hf
@@ -201,7 +201,7 @@ theorem MeasureTheory.AEStronglyMeasurable.integral_prod_right' [SigmaFinite ν]
     filter_upwards [ae_ae_of_ae_prod hf.ae_eq_mk] with _ hx using integral_congr_ae hx⟩
 #align measure_theory.ae_strongly_measurable.integral_prod_right' MeasureTheory.AEStronglyMeasurable.integral_prod_right'
 
-theorem MeasureTheory.AEStronglyMeasurable.prod_mk_left {γ : Type _} [SigmaFinite ν]
+theorem MeasureTheory.AEStronglyMeasurable.prod_mk_left {γ : Type*} [SigmaFinite ν]
     [TopologicalSpace γ] {f : α × β → γ} (hf : AEStronglyMeasurable f (μ.prod ν)) :
     ∀ᵐ x ∂μ, AEStronglyMeasurable (fun y => f (x, y)) ν := by
   filter_upwards [ae_ae_of_ae_prod hf.ae_eq_mk] with x hx
@@ -307,7 +307,7 @@ theorem Integrable.integral_norm_prod_right [SigmaFinite μ] ⦃f : α × β →
   hf.swap.integral_norm_prod_left
 #align measure_theory.integrable.integral_norm_prod_right MeasureTheory.Integrable.integral_norm_prod_right
 
-theorem integrable_prod_mul {L : Type _} [IsROrC L] {f : α → L} {g : β → L} (hf : Integrable f μ)
+theorem integrable_prod_mul {L : Type*} [IsROrC L] {f : α → L} {g : β → L} (hf : Integrable f μ)
     (hg : Integrable g ν) : Integrable (fun z : α × β => f z.1 * g z.2) (μ.prod ν) := by
   refine' (integrable_prod_iff _).2 ⟨_, _⟩
   · exact hf.1.fst.mul hg.1.snd
@@ -345,7 +345,7 @@ theorem integral_prod_swap (f : α × β → E) (hf : AEStronglyMeasurable f (μ
   rw [← integral_map measurable_swap.aemeasurable hf, prod_swap]
 #align measure_theory.integral_prod_swap MeasureTheory.integral_prod_swap
 
-variable {E' : Type _} [NormedAddCommGroup E'] [CompleteSpace E'] [NormedSpace ℝ E']
+variable {E' : Type*} [NormedAddCommGroup E'] [CompleteSpace E'] [NormedSpace ℝ E']
 
 /-! Some rules about the sum/difference of double integrals. They follow from `integral_add`, but
   we separate them out as separate lemmas, because they involve quite some steps. -/
@@ -506,7 +506,7 @@ theorem set_integral_prod (f : α × β → E) {s : Set α} {t : Set β}
   exact integral_prod f hf
 #align measure_theory.set_integral_prod MeasureTheory.set_integral_prod
 
-theorem integral_prod_mul {L : Type _} [IsROrC L] (f : α → L) (g : β → L) :
+theorem integral_prod_mul {L : Type*} [IsROrC L] (f : α → L) (g : β → L) :
     ∫ z, f z.1 * g z.2 ∂μ.prod ν = (∫ x, f x ∂μ) * ∫ y, g y ∂ν := by
   by_cases h : Integrable (fun z : α × β => f z.1 * g z.2) (μ.prod ν)
   · rw [integral_prod _ h]
@@ -517,7 +517,7 @@ theorem integral_prod_mul {L : Type _} [IsROrC L] (f : α → L) (g : β → L)
   cases' H with H H <;> simp [integral_undef h, integral_undef H]
 #align measure_theory.integral_prod_mul MeasureTheory.integral_prod_mul
 
-theorem set_integral_prod_mul {L : Type _} [IsROrC L] (f : α → L) (g : β → L) (s : Set α)
+theorem set_integral_prod_mul {L : Type*} [IsROrC L] (f : α → L) (g : β → L) (s : Set α)
     (t : Set β) :
     ∫ z in s ×ˢ t, f z.1 * g z.2 ∂μ.prod ν = (∫ x in s, f x ∂μ) * ∫ y in t, g y ∂ν := by
   -- Porting note: added

• depends on: #5966

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

@@ -2,15 +2,12 @@
 Copyright (c) 2020 Floris van Doorn. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Floris van Doorn
-
-! This file was ported from Lean 3 source module measure_theory.constructions.prod.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.MeasureTheory.Constructions.Prod.Basic
 import Mathlib.MeasureTheory.Integral.SetIntegral
 
+#align_import measure_theory.constructions.prod.integral from "leanprover-community/mathlib"@"fd5edc43dc4f10b85abfe544b88f82cf13c5f844"
+
 /-!
 # Integration with respect to the product measure
 

This is the second half of the changes originally in #5699, removing all occurrences of ; after a space and implementing a linter rule to enforce it.

In most cases this 2-character substring has a space after it, so the following command was run first:

find . -type f -name "*.lean" -exec sed -i -E 's/ ; /; /g' {} \;

The remaining cases were few enough in number that they were done manually.

@@ -127,7 +127,7 @@ theorem MeasureTheory.StronglyMeasurable.integral_prod_right [SigmaFinite ν] 
   Fubini's theorem is measurable. -/
 theorem MeasureTheory.StronglyMeasurable.integral_prod_right' [SigmaFinite ν] ⦃f : α × β → E⦄
     (hf : StronglyMeasurable f) : StronglyMeasurable fun x => ∫ y, f (x, y) ∂ν := by
-  rw [← uncurry_curry f] at hf ; exact hf.integral_prod_right
+  rw [← uncurry_curry f] at hf; exact hf.integral_prod_right
 #align measure_theory.strongly_measurable.integral_prod_right' MeasureTheory.StronglyMeasurable.integral_prod_right'
 
 /-- The Bochner integral is measurable. This shows that the integrand of (the right-hand-side of)
@@ -165,7 +165,7 @@ theorem integrable_measure_prod_mk_left {s : Set (α × β)} (hs : MeasurableSet
   rw [prod_apply hs]
   apply lintegral_congr_ae
   refine' (ae_measure_lt_top hs h2s).mp _; apply eventually_of_forall; intro x hx
-  rw [lt_top_iff_ne_top] at hx ; simp [ofReal_toReal, hx]
+  rw [lt_top_iff_ne_top] at hx; simp [ofReal_toReal, hx]
 #align measure_theory.measure.integrable_measure_prod_mk_left MeasureTheory.Measure.integrable_measure_prod_mk_left
 
 end Measure

@@ -21,7 +21,7 @@ In this file we prove Fubini's theorem.
 * `MeasureTheory.integrable_prod_iff` states that a binary function is integrable iff both
   * `y ↦ f (x, y)` is integrable for almost every `x`, and
   * the function `x ↦ ∫ ‖f (x, y)‖ dy` is integrable.
-* `MeasureTheory.integral_prod`: Fubini's theorem. It states that for a integrable function
+* `MeasureTheory.integral_prod`: Fubini's theorem. It states that for an integrable function
   `α × β → E` (where `E` is a second countable Banach space) we have
   `∫ z, f z ∂(μ.prod ν) = ∫ x, ∫ y, f (x, y) ∂ν ∂μ`. This theorem has the same variants as
   Tonelli's theorem (see `MeasureTheory.lintegral_prod`). The lemma

@@ -343,7 +343,7 @@ theorem Integrable.integral_prod_right [SigmaFinite μ] ⦃f : α × β → E⦄
 variable [SigmaFinite μ]
 
 theorem integral_prod_swap (f : α × β → E) (hf : AEStronglyMeasurable f (μ.prod ν)) :
-    (∫ z, f z.swap ∂ν.prod μ) = ∫ z, f z ∂μ.prod ν := by
+    ∫ z, f z.swap ∂ν.prod μ = ∫ z, f z ∂μ.prod ν := by
   rw [← prod_swap] at hf
   rw [← integral_map measurable_swap.aemeasurable hf, prod_swap]
 #align measure_theory.integral_prod_swap MeasureTheory.integral_prod_swap
@@ -455,7 +455,7 @@ theorem continuous_integral_integral :
   of the right-hand side is integrable. -/
 theorem integral_prod :
     ∀ (f : α × β → E) (_ : Integrable f (μ.prod ν)),
-      (∫ z, f z ∂μ.prod ν) = ∫ x, ∫ y, f (x, y) ∂ν ∂μ := by
+      ∫ z, f z ∂μ.prod ν = ∫ x, ∫ y, f (x, y) ∂ν ∂μ := by
   apply Integrable.induction
   · intro c s hs h2s
     simp_rw [integral_indicator hs, ← indicator_comp_right, Function.comp,
@@ -479,38 +479,38 @@ theorem integral_prod :
   the Bochner integral of `f` is equal to the iterated Bochner integral.
   This version has the integrals on the right-hand side in the other order. -/
 theorem integral_prod_symm (f : α × β → E) (hf : Integrable f (μ.prod ν)) :
-    (∫ z, f z ∂μ.prod ν) = ∫ y, ∫ x, f (x, y) ∂μ ∂ν := by
+    ∫ z, f z ∂μ.prod ν = ∫ y, ∫ x, f (x, y) ∂μ ∂ν := by
   simp_rw [← integral_prod_swap f hf.aestronglyMeasurable]; exact integral_prod _ hf.swap
 #align measure_theory.integral_prod_symm MeasureTheory.integral_prod_symm
 
 /-- Reversed version of **Fubini's Theorem**. -/
 theorem integral_integral {f : α → β → E} (hf : Integrable (uncurry f) (μ.prod ν)) :
-    (∫ x, ∫ y, f x y ∂ν ∂μ) = ∫ z, f z.1 z.2 ∂μ.prod ν :=
+    ∫ x, ∫ y, f x y ∂ν ∂μ = ∫ z, f z.1 z.2 ∂μ.prod ν :=
   (integral_prod _ hf).symm
 #align measure_theory.integral_integral MeasureTheory.integral_integral
 
 /-- Reversed version of **Fubini's Theorem** (symmetric version). -/
 theorem integral_integral_symm {f : α → β → E} (hf : Integrable (uncurry f) (μ.prod ν)) :
-    (∫ x, ∫ y, f x y ∂ν ∂μ) = ∫ z, f z.2 z.1 ∂ν.prod μ :=
+    ∫ x, ∫ y, f x y ∂ν ∂μ = ∫ z, f z.2 z.1 ∂ν.prod μ :=
   (integral_prod_symm _ hf.swap).symm
 #align measure_theory.integral_integral_symm MeasureTheory.integral_integral_symm
 
 /-- Change the order of Bochner integration. -/
 theorem integral_integral_swap ⦃f : α → β → E⦄ (hf : Integrable (uncurry f) (μ.prod ν)) :
-    (∫ x, ∫ y, f x y ∂ν ∂μ) = ∫ y, ∫ x, f x y ∂μ ∂ν :=
+    ∫ x, ∫ y, f x y ∂ν ∂μ = ∫ y, ∫ x, f x y ∂μ ∂ν :=
   (integral_integral hf).trans (integral_prod_symm _ hf)
 #align measure_theory.integral_integral_swap MeasureTheory.integral_integral_swap
 
 /-- **Fubini's Theorem** for set integrals. -/
 theorem set_integral_prod (f : α × β → E) {s : Set α} {t : Set β}
     (hf : IntegrableOn f (s ×ˢ t) (μ.prod ν)) :
-    (∫ z in s ×ˢ t, f z ∂μ.prod ν) = ∫ x in s, ∫ y in t, f (x, y) ∂ν ∂μ := by
+    ∫ z in s ×ˢ t, f z ∂μ.prod ν = ∫ x in s, ∫ y in t, f (x, y) ∂ν ∂μ := by
   simp only [← Measure.prod_restrict s t, IntegrableOn] at hf ⊢
   exact integral_prod f hf
 #align measure_theory.set_integral_prod MeasureTheory.set_integral_prod
 
 theorem integral_prod_mul {L : Type _} [IsROrC L] (f : α → L) (g : β → L) :
-    (∫ z, f z.1 * g z.2 ∂μ.prod ν) = (∫ x, f x ∂μ) * ∫ y, g y ∂ν := by
+    ∫ z, f z.1 * g z.2 ∂μ.prod ν = (∫ x, f x ∂μ) * ∫ y, g y ∂ν := by
   by_cases h : Integrable (fun z : α × β => f z.1 * g z.2) (μ.prod ν)
   · rw [integral_prod _ h]
     simp_rw [integral_mul_left, integral_mul_right]
@@ -522,7 +522,7 @@ theorem integral_prod_mul {L : Type _} [IsROrC L] (f : α → L) (g : β → L)
 
 theorem set_integral_prod_mul {L : Type _} [IsROrC L] (f : α → L) (g : β → L) (s : Set α)
     (t : Set β) :
-    (∫ z in s ×ˢ t, f z.1 * g z.2 ∂μ.prod ν) = (∫ x in s, f x ∂μ) * ∫ y in t, g y ∂ν := by
+    ∫ z in s ×ˢ t, f z.1 * g z.2 ∂μ.prod ν = (∫ x in s, f x ∂μ) * ∫ y in t, g y ∂ν := by
   -- Porting note: added
   rw [← Measure.prod_restrict s t]
   simp only [← Measure.prod_restrict s t, IntegrableOn, integral_prod_mul]

The bumps to nightly-2023-06-10, which includes @gebner's https://github.com/leanprover/lean4/pull/2266.

After this is merged I encourage everyone to look around at simp regressions!

• depends on: #4954 (I've moved changes that work without lean4#2266 to this PR)

Co-authored-by: Scott Morrison <scott.morrison@anu.edu.au>

@@ -506,8 +506,6 @@ theorem set_integral_prod (f : α × β → E) {s : Set α} {t : Set β}
     (hf : IntegrableOn f (s ×ˢ t) (μ.prod ν)) :
     (∫ z in s ×ˢ t, f z ∂μ.prod ν) = ∫ x in s, ∫ y in t, f (x, y) ∂ν ∂μ := by
   simp only [← Measure.prod_restrict s t, IntegrableOn] at hf ⊢
-  -- Porting note: added
-  rw [← Measure.prod_restrict s t] at hf ⊢
   exact integral_prod f hf
 #align measure_theory.set_integral_prod MeasureTheory.set_integral_prod
 

@@ -18,14 +18,14 @@ In this file we prove Fubini's theorem.
 
 ## Main results
 
-* `measure_theory.integrable_prod_iff` states that a binary function is integrable iff both
+* `MeasureTheory.integrable_prod_iff` states that a binary function is integrable iff both
   * `y ↦ f (x, y)` is integrable for almost every `x`, and
   * the function `x ↦ ∫ ‖f (x, y)‖ dy` is integrable.
-* `measure_theory.integral_prod`: Fubini's theorem. It states that for a integrable function
+* `MeasureTheory.integral_prod`: Fubini's theorem. It states that for a integrable function
   `α × β → E` (where `E` is a second countable Banach space) we have
   `∫ z, f z ∂(μ.prod ν) = ∫ x, ∫ y, f (x, y) ∂ν ∂μ`. This theorem has the same variants as
-  Tonelli's theorem (see `measure_theory.lintegral_prod`). The lemma
-  `measure_theory.integrable.integral_prod_right` states that the inner integral of the right-hand
+  Tonelli's theorem (see `MeasureTheory.lintegral_prod`). The lemma
+  `MeasureTheory.Integrable.integral_prod_right` states that the inner integral of the right-hand
   side is integrable.
 
 ## Tags
@@ -451,7 +451,7 @@ theorem continuous_integral_integral :
 /-- **Fubini's Theorem**: For integrable functions on `α × β`,
   the Bochner integral of `f` is equal to the iterated Bochner integral.
   `integrable_prod_iff` can be useful to show that the function in question in integrable.
-  `measure_theory.integrable.integral_prod_right` is useful to show that the inner integral
+  `MeasureTheory.Integrable.integral_prod_right` is useful to show that the inner integral
   of the right-hand side is integrable. -/
 theorem integral_prod :
     ∀ (f : α × β → E) (_ : Integrable f (μ.prod ν)),