probability.kernel.integral_comp_prod ⟷ Mathlib.Probability.Kernel.IntegralCompProd

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

@@ -294,7 +294,7 @@ theorem integral_compProd :
   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), MeasureTheory.set_integral_const,
+      integral_indicator (measurable_prod_mk_left hs), MeasureTheory.setIntegral_const,
       integral_smul_const]
     congr 1
     rw [integral_to_real]
@@ -317,35 +317,35 @@ theorem integral_compProd :
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
-#print ProbabilityTheory.set_integral_compProd /-
-theorem set_integral_compProd {f : β × γ → E} {s : Set β} {t : Set γ} (hs : MeasurableSet s)
+#print ProbabilityTheory.setIntegral_compProd /-
+theorem setIntegral_compProd {f : β × γ → E} {s : Set β} {t : Set γ} (hs : MeasurableSet s)
     (ht : MeasurableSet t) (hf : IntegrableOn f (s ×ˢ t) ((κ ⊗ₖ η) a)) :
     ∫ z in s ×ˢ t, f z ∂(κ ⊗ₖ η) a = ∫ x in s, ∫ y in t, f (x, y) ∂η (a, x) ∂κ a :=
   by
   rw [← kernel.restrict_apply (κ ⊗ₖ η) (hs.prod ht), ← comp_prod_restrict, integral_comp_prod]
   · simp_rw [kernel.restrict_apply]
   · rw [comp_prod_restrict, kernel.restrict_apply]; exact hf
-#align probability_theory.set_integral_comp_prod ProbabilityTheory.set_integral_compProd
+#align probability_theory.set_integral_comp_prod ProbabilityTheory.setIntegral_compProd
 -/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
-#print ProbabilityTheory.set_integral_compProd_univ_right /-
-theorem set_integral_compProd_univ_right (f : β × γ → E) {s : Set β} (hs : MeasurableSet s)
+#print ProbabilityTheory.setIntegral_compProd_univ_right /-
+theorem setIntegral_compProd_univ_right (f : β × γ → E) {s : Set β} (hs : MeasurableSet s)
     (hf : IntegrableOn f (s ×ˢ univ) ((κ ⊗ₖ η) a)) :
     ∫ z in s ×ˢ univ, f z ∂(κ ⊗ₖ η) a = ∫ x in s, ∫ y, f (x, y) ∂η (a, x) ∂κ a := by
   simp_rw [set_integral_comp_prod hs MeasurableSet.univ hf, measure.restrict_univ]
-#align probability_theory.set_integral_comp_prod_univ_right ProbabilityTheory.set_integral_compProd_univ_right
+#align probability_theory.set_integral_comp_prod_univ_right ProbabilityTheory.setIntegral_compProd_univ_right
 -/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
-#print ProbabilityTheory.set_integral_compProd_univ_left /-
-theorem set_integral_compProd_univ_left (f : β × γ → E) {t : Set γ} (ht : MeasurableSet t)
+#print ProbabilityTheory.setIntegral_compProd_univ_left /-
+theorem setIntegral_compProd_univ_left (f : β × γ → E) {t : Set γ} (ht : MeasurableSet t)
     (hf : IntegrableOn f (univ ×ˢ t) ((κ ⊗ₖ η) a)) :
     ∫ z in univ ×ˢ t, f z ∂(κ ⊗ₖ η) a = ∫ x, ∫ y in t, f (x, y) ∂η (a, x) ∂κ a := by
   simp_rw [set_integral_comp_prod MeasurableSet.univ ht hf, measure.restrict_univ]
-#align probability_theory.set_integral_comp_prod_univ_left ProbabilityTheory.set_integral_compProd_univ_left
+#align probability_theory.set_integral_comp_prod_univ_left ProbabilityTheory.setIntegral_compProd_univ_left
 -/
 
 end ProbabilityTheory

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

@@ -3,8 +3,8 @@ Copyright (c) 2023 Rémy Degenne. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Rémy Degenne
 -/
-import Mathbin.Probability.Kernel.Composition
-import Mathbin.MeasureTheory.Integral.SetIntegral
+import Probability.Kernel.Composition
+import MeasureTheory.Integral.SetIntegral
 
 #align_import probability.kernel.integral_comp_prod from "leanprover-community/mathlib"@"f2ad3645af9effcdb587637dc28a6074edc813f9"
 

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

@@ -281,7 +281,7 @@ theorem kernel.continuous_integral_integral :
   simp_rw [← kernel.lintegral_comp_prod _ _ _ (this _), ← L1.of_real_norm_sub_eq_lintegral, ←
     of_real_zero]
   refine' (continuous_of_real.tendsto 0).comp _
-  rw [← tendsto_iff_norm_tendsto_zero]
+  rw [← tendsto_iff_norm_sub_tendsto_zero]
   exact tendsto_id
 #align probability_theory.kernel.continuous_integral_integral ProbabilityTheory.kernel.continuous_integral_integral
 -/

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

@@ -2,15 +2,12 @@
 Copyright (c) 2023 Rémy Degenne. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Rémy Degenne
-
-! This file was ported from Lean 3 source module probability.kernel.integral_comp_prod
-! leanprover-community/mathlib commit f2ad3645af9effcdb587637dc28a6074edc813f9
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Probability.Kernel.Composition
 import Mathbin.MeasureTheory.Integral.SetIntegral
 
+#align_import probability.kernel.integral_comp_prod from "leanprover-community/mathlib"@"f2ad3645af9effcdb587637dc28a6074edc813f9"
+
 /-!
 # Bochner integral of a function against the composition-product of two kernels
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/f2ad3645af9effcdb587637dc28a6074edc813f9

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Rémy Degenne
 
 ! This file was ported from Lean 3 source module probability.kernel.integral_comp_prod
-! leanprover-community/mathlib commit c0d694db494dd4f9aa57f2714b6e4c82b4ebc113
+! leanprover-community/mathlib commit f2ad3645af9effcdb587637dc28a6074edc813f9
 ! 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
 /-!
 # Bochner integral of a function against the composition-product of two kernels
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 We prove properties of the composition-product of two kernels. If `κ` is an s-finite kernel from
 `α` to `β` and `η` is an s-finite kernel from `α × β` to `γ`, we can form their composition-product
 `κ ⊗ₖ η : kernel α (β × γ)`. We proved in `probability.kernel.lintegral_comp_prod` that it verifies

mathlib commit https://github.com/leanprover-community/mathlib/commit/2a0ce625dbb0ffbc7d1316597de0b25c1ec75303

@@ -47,6 +47,7 @@ variable {α β γ E : Type _} {mα : MeasurableSpace α} {mβ : MeasurableSpace
 
 namespace ProbabilityTheory
 
+#print ProbabilityTheory.hasFiniteIntegral_prod_mk_left /-
 theorem hasFiniteIntegral_prod_mk_left (a : α) {s : Set (β × γ)} (h2s : (κ ⊗ₖ η) a s ≠ ∞) :
     HasFiniteIntegral (fun b => (η (a, b) (Prod.mk b ⁻¹' s)).toReal) (κ a) :=
   by
@@ -64,7 +65,9 @@ theorem hasFiniteIntegral_prod_mk_left (a : α) {s : Set (β × γ)} (h2s : (κ
     _ = (κ ⊗ₖ η) a s := (measure_to_measurable s)
     _ < ⊤ := h2s.lt_top
 #align probability_theory.has_finite_integral_prod_mk_left ProbabilityTheory.hasFiniteIntegral_prod_mk_left
+-/
 
+#print ProbabilityTheory.integrable_kernel_prod_mk_left /-
 theorem integrable_kernel_prod_mk_left (a : α) {s : Set (β × γ)} (hs : MeasurableSet s)
     (h2s : (κ ⊗ₖ η) a s ≠ ∞) : Integrable (fun b => (η (a, b) (Prod.mk b ⁻¹' s)).toReal) (κ a) :=
   by
@@ -72,24 +75,30 @@ theorem integrable_kernel_prod_mk_left (a : α) {s : Set (β × γ)} (hs : Measu
   · exact (measurable_kernel_prod_mk_left' hs a).ennreal_toReal.AEStronglyMeasurable
   · exact has_finite_integral_prod_mk_left a h2s
 #align probability_theory.integrable_kernel_prod_mk_left ProbabilityTheory.integrable_kernel_prod_mk_left
+-/
 
+#print MeasureTheory.AEStronglyMeasurable.integral_kernel_compProd /-
 theorem MeasureTheory.AEStronglyMeasurable.integral_kernel_compProd [NormedSpace ℝ E]
     [CompleteSpace E] ⦃f : β × γ → E⦄ (hf : AEStronglyMeasurable f ((κ ⊗ₖ η) a)) :
     AEStronglyMeasurable (fun x => ∫ y, f (x, y) ∂η (a, x)) (κ a) :=
   ⟨fun x => ∫ y, hf.mk f (x, y) ∂η (a, x), hf.stronglyMeasurable_mk.integral_kernel_prod_right'', by
     filter_upwards [ae_ae_of_ae_comp_prod hf.ae_eq_mk] with _ hx using integral_congr_ae hx⟩
 #align measure_theory.ae_strongly_measurable.integral_kernel_comp_prod MeasureTheory.AEStronglyMeasurable.integral_kernel_compProd
+-/
 
+#print MeasureTheory.AEStronglyMeasurable.compProd_mk_left /-
 theorem MeasureTheory.AEStronglyMeasurable.compProd_mk_left {δ : Type _} [TopologicalSpace δ]
     {f : β × γ → δ} (hf : AEStronglyMeasurable f ((κ ⊗ₖ η) a)) :
     ∀ᵐ x ∂κ a, AEStronglyMeasurable (fun y => f (x, y)) (η (a, x)) := by
   filter_upwards [ae_ae_of_ae_comp_prod hf.ae_eq_mk] with x hx using
     ⟨fun y => hf.mk f (x, y), hf.strongly_measurable_mk.comp_measurable measurable_prod_mk_left, hx⟩
 #align measure_theory.ae_strongly_measurable.comp_prod_mk_left MeasureTheory.AEStronglyMeasurable.compProd_mk_left
+-/
 
 /-! ### Integrability -/
 
 
+#print ProbabilityTheory.hasFiniteIntegral_compProd_iff /-
 theorem hasFiniteIntegral_compProd_iff ⦃f : β × γ → E⦄ (h1f : StronglyMeasurable f) :
     HasFiniteIntegral f ((κ ⊗ₖ η) a) ↔
       (∀ᵐ x ∂κ a, HasFiniteIntegral (fun y => f (x, y)) (η (a, x))) ∧
@@ -109,7 +118,9 @@ theorem hasFiniteIntegral_compProd_iff ⦃f : β × γ → E⦄ (h1f : StronglyM
     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_kernel_prod_right''
 #align probability_theory.has_finite_integral_comp_prod_iff ProbabilityTheory.hasFiniteIntegral_compProd_iff
+-/
 
+#print ProbabilityTheory.hasFiniteIntegral_compProd_iff' /-
 theorem hasFiniteIntegral_compProd_iff' ⦃f : β × γ → E⦄
     (h1f : AEStronglyMeasurable f ((κ ⊗ₖ η) a)) :
     HasFiniteIntegral f ((κ ⊗ₖ η) a) ↔
@@ -127,7 +138,9 @@ theorem hasFiniteIntegral_compProd_iff' ⦃f : β × γ → E⦄
     filter_upwards [ae_ae_of_ae_comp_prod h1f.ae_eq_mk.symm] with _ hx using
       integral_congr_ae (eventually_eq.fun_comp hx _)
 #align probability_theory.has_finite_integral_comp_prod_iff' ProbabilityTheory.hasFiniteIntegral_compProd_iff'
+-/
 
+#print ProbabilityTheory.integrable_compProd_iff /-
 theorem integrable_compProd_iff ⦃f : β × γ → E⦄ (hf : AEStronglyMeasurable f ((κ ⊗ₖ η) a)) :
     Integrable f ((κ ⊗ₖ η) a) ↔
       (∀ᵐ x ∂κ a, Integrable (fun y => f (x, y)) (η (a, x))) ∧
@@ -136,17 +149,23 @@ theorem integrable_compProd_iff ⦃f : β × γ → E⦄ (hf : AEStronglyMeasura
   simp only [integrable, has_finite_integral_comp_prod_iff' hf, hf.norm.integral_kernel_comp_prod,
     hf, hf.comp_prod_mk_left, eventually_and, true_and_iff]
 #align probability_theory.integrable_comp_prod_iff ProbabilityTheory.integrable_compProd_iff
+-/
 
+#print MeasureTheory.Integrable.compProd_mk_left_ae /-
 theorem MeasureTheory.Integrable.compProd_mk_left_ae ⦃f : β × γ → E⦄
     (hf : Integrable f ((κ ⊗ₖ η) a)) : ∀ᵐ x ∂κ a, Integrable (fun y => f (x, y)) (η (a, x)) :=
   ((integrable_compProd_iff hf.AEStronglyMeasurable).mp hf).1
 #align measure_theory.integrable.comp_prod_mk_left_ae MeasureTheory.Integrable.compProd_mk_left_ae
+-/
 
+#print MeasureTheory.Integrable.integral_norm_compProd /-
 theorem MeasureTheory.Integrable.integral_norm_compProd ⦃f : β × γ → E⦄
     (hf : Integrable f ((κ ⊗ₖ η) a)) : Integrable (fun x => ∫ y, ‖f (x, y)‖ ∂η (a, x)) (κ a) :=
   ((integrable_compProd_iff hf.AEStronglyMeasurable).mp hf).2
 #align measure_theory.integrable.integral_norm_comp_prod MeasureTheory.Integrable.integral_norm_compProd
+-/
 
+#print MeasureTheory.Integrable.integral_compProd /-
 theorem MeasureTheory.Integrable.integral_compProd [NormedSpace ℝ E] [CompleteSpace E]
     ⦃f : β × γ → E⦄ (hf : Integrable f ((κ ⊗ₖ η) a)) :
     Integrable (fun x => ∫ y, f (x, y) ∂η (a, x)) (κ a) :=
@@ -157,6 +176,7 @@ theorem MeasureTheory.Integrable.integral_compProd [NormedSpace ℝ E] [Complete
             integral_nonneg_of_ae <|
               eventually_of_forall fun y => (norm_nonneg (f (x, y)) : _)).symm
 #align measure_theory.integrable.integral_comp_prod MeasureTheory.Integrable.integral_compProd
+-/
 
 /-! ### Bochner integral -/
 
@@ -164,6 +184,7 @@ theorem MeasureTheory.Integrable.integral_compProd [NormedSpace ℝ E] [Complete
 variable [NormedSpace ℝ E] [CompleteSpace E] {E' : Type _} [NormedAddCommGroup E']
   [CompleteSpace E'] [NormedSpace ℝ E']
 
+#print ProbabilityTheory.kernel.integral_fn_integral_add /-
 theorem kernel.integral_fn_integral_add ⦃f g : β × γ → E⦄ (F : E → E')
     (hf : Integrable f ((κ ⊗ₖ η) a)) (hg : Integrable g ((κ ⊗ₖ η) a)) :
     ∫ x, F (∫ y, f (x, y) + g (x, y) ∂η (a, x)) ∂κ a =
@@ -173,7 +194,9 @@ theorem kernel.integral_fn_integral_add ⦃f g : β × γ → E⦄ (F : E → E'
   filter_upwards [hf.comp_prod_mk_left_ae, hg.comp_prod_mk_left_ae] with _ h2f h2g
   simp [integral_add h2f h2g]
 #align probability_theory.kernel.integral_fn_integral_add ProbabilityTheory.kernel.integral_fn_integral_add
+-/
 
+#print ProbabilityTheory.kernel.integral_fn_integral_sub /-
 theorem kernel.integral_fn_integral_sub ⦃f g : β × γ → E⦄ (F : E → E')
     (hf : Integrable f ((κ ⊗ₖ η) a)) (hg : Integrable g ((κ ⊗ₖ η) a)) :
     ∫ x, F (∫ y, f (x, y) - g (x, y) ∂η (a, x)) ∂κ a =
@@ -183,7 +206,9 @@ theorem kernel.integral_fn_integral_sub ⦃f g : β × γ → E⦄ (F : E → E'
   filter_upwards [hf.comp_prod_mk_left_ae, hg.comp_prod_mk_left_ae] with _ h2f h2g
   simp [integral_sub h2f h2g]
 #align probability_theory.kernel.integral_fn_integral_sub ProbabilityTheory.kernel.integral_fn_integral_sub
+-/
 
+#print ProbabilityTheory.kernel.lintegral_fn_integral_sub /-
 theorem kernel.lintegral_fn_integral_sub ⦃f g : β × γ → E⦄ (F : E → ℝ≥0∞)
     (hf : Integrable f ((κ ⊗ₖ η) a)) (hg : Integrable g ((κ ⊗ₖ η) a)) :
     ∫⁻ x, F (∫ y, f (x, y) - g (x, y) ∂η (a, x)) ∂κ a =
@@ -193,7 +218,9 @@ theorem kernel.lintegral_fn_integral_sub ⦃f g : β × γ → E⦄ (F : E → 
   filter_upwards [hf.comp_prod_mk_left_ae, hg.comp_prod_mk_left_ae] with _ h2f h2g
   simp [integral_sub h2f h2g]
 #align probability_theory.kernel.lintegral_fn_integral_sub ProbabilityTheory.kernel.lintegral_fn_integral_sub
+-/
 
+#print ProbabilityTheory.kernel.integral_integral_add /-
 theorem kernel.integral_integral_add ⦃f g : β × γ → E⦄ (hf : Integrable f ((κ ⊗ₖ η) a))
     (hg : Integrable g ((κ ⊗ₖ η) a)) :
     ∫ x, ∫ y, f (x, y) + g (x, y) ∂η (a, x) ∂κ a =
@@ -201,14 +228,18 @@ theorem kernel.integral_integral_add ⦃f g : β × γ → E⦄ (hf : Integrable
   (kernel.integral_fn_integral_add id hf hg).trans <|
     integral_add hf.integral_compProd hg.integral_compProd
 #align probability_theory.kernel.integral_integral_add ProbabilityTheory.kernel.integral_integral_add
+-/
 
+#print ProbabilityTheory.kernel.integral_integral_add' /-
 theorem kernel.integral_integral_add' ⦃f g : β × γ → E⦄ (hf : Integrable f ((κ ⊗ₖ η) a))
     (hg : Integrable g ((κ ⊗ₖ η) a)) :
     ∫ x, ∫ y, (f + g) (x, y) ∂η (a, x) ∂κ a =
       ∫ x, ∫ y, f (x, y) ∂η (a, x) ∂κ a + ∫ x, ∫ y, g (x, y) ∂η (a, x) ∂κ a :=
   kernel.integral_integral_add hf hg
 #align probability_theory.kernel.integral_integral_add' ProbabilityTheory.kernel.integral_integral_add'
+-/
 
+#print ProbabilityTheory.kernel.integral_integral_sub /-
 theorem kernel.integral_integral_sub ⦃f g : β × γ → E⦄ (hf : Integrable f ((κ ⊗ₖ η) a))
     (hg : Integrable g ((κ ⊗ₖ η) a)) :
     ∫ x, ∫ y, f (x, y) - g (x, y) ∂η (a, x) ∂κ a =
@@ -216,14 +247,18 @@ theorem kernel.integral_integral_sub ⦃f g : β × γ → E⦄ (hf : Integrable
   (kernel.integral_fn_integral_sub id hf hg).trans <|
     integral_sub hf.integral_compProd hg.integral_compProd
 #align probability_theory.kernel.integral_integral_sub ProbabilityTheory.kernel.integral_integral_sub
+-/
 
+#print ProbabilityTheory.kernel.integral_integral_sub' /-
 theorem kernel.integral_integral_sub' ⦃f g : β × γ → E⦄ (hf : Integrable f ((κ ⊗ₖ η) a))
     (hg : Integrable g ((κ ⊗ₖ η) a)) :
     ∫ x, ∫ y, (f - g) (x, y) ∂η (a, x) ∂κ a =
       ∫ x, ∫ y, f (x, y) ∂η (a, x) ∂κ a - ∫ x, ∫ y, g (x, y) ∂η (a, x) ∂κ a :=
   kernel.integral_integral_sub hf hg
 #align probability_theory.kernel.integral_integral_sub' ProbabilityTheory.kernel.integral_integral_sub'
+-/
 
+#print ProbabilityTheory.kernel.continuous_integral_integral /-
 theorem kernel.continuous_integral_integral :
     Continuous fun f : α × β →₁[(κ ⊗ₖ η) a] E => ∫ x, ∫ y, f (x, y) ∂η (a, x) ∂κ a :=
   by
@@ -249,7 +284,9 @@ theorem kernel.continuous_integral_integral :
   rw [← tendsto_iff_norm_tendsto_zero]
   exact tendsto_id
 #align probability_theory.kernel.continuous_integral_integral ProbabilityTheory.kernel.continuous_integral_integral
+-/
 
+#print ProbabilityTheory.integral_compProd /-
 theorem integral_compProd :
     ∀ {f : β × γ → E} (hf : Integrable f ((κ ⊗ₖ η) a)),
       ∫ z, f z ∂(κ ⊗ₖ η) a = ∫ x, ∫ y, f (x, y) ∂η (a, x) ∂κ a :=
@@ -276,9 +313,11 @@ theorem integral_compProd :
       refine' (ae_ae_of_ae_comp_prod hfg).mp (eventually_of_forall _)
       exact fun x hfgx => integral_congr_ae (ae_eq_symm hfgx)
 #align probability_theory.integral_comp_prod ProbabilityTheory.integral_compProd
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print ProbabilityTheory.set_integral_compProd /-
 theorem set_integral_compProd {f : β × γ → E} {s : Set β} {t : Set γ} (hs : MeasurableSet s)
     (ht : MeasurableSet t) (hf : IntegrableOn f (s ×ˢ t) ((κ ⊗ₖ η) a)) :
     ∫ z in s ×ˢ t, f z ∂(κ ⊗ₖ η) a = ∫ x in s, ∫ y in t, f (x, y) ∂η (a, x) ∂κ a :=
@@ -287,22 +326,27 @@ theorem set_integral_compProd {f : β × γ → E} {s : Set β} {t : Set γ} (hs
   · simp_rw [kernel.restrict_apply]
   · rw [comp_prod_restrict, kernel.restrict_apply]; exact hf
 #align probability_theory.set_integral_comp_prod ProbabilityTheory.set_integral_compProd
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print ProbabilityTheory.set_integral_compProd_univ_right /-
 theorem set_integral_compProd_univ_right (f : β × γ → E) {s : Set β} (hs : MeasurableSet s)
     (hf : IntegrableOn f (s ×ˢ univ) ((κ ⊗ₖ η) a)) :
     ∫ z in s ×ˢ univ, f z ∂(κ ⊗ₖ η) a = ∫ x in s, ∫ y, f (x, y) ∂η (a, x) ∂κ a := by
   simp_rw [set_integral_comp_prod hs MeasurableSet.univ hf, measure.restrict_univ]
 #align probability_theory.set_integral_comp_prod_univ_right ProbabilityTheory.set_integral_compProd_univ_right
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print ProbabilityTheory.set_integral_compProd_univ_left /-
 theorem set_integral_compProd_univ_left (f : β × γ → E) {t : Set γ} (ht : MeasurableSet t)
     (hf : IntegrableOn f (univ ×ˢ t) ((κ ⊗ₖ η) a)) :
     ∫ z in univ ×ˢ t, f z ∂(κ ⊗ₖ η) a = ∫ x, ∫ y in t, f (x, y) ∂η (a, x) ∂κ a := by
   simp_rw [set_integral_comp_prod MeasurableSet.univ ht hf, measure.restrict_univ]
 #align probability_theory.set_integral_comp_prod_univ_left ProbabilityTheory.set_integral_compProd_univ_left
+-/
 
 end ProbabilityTheory
 

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

@@ -53,7 +53,7 @@ theorem hasFiniteIntegral_prod_mk_left (a : α) {s : Set (β × γ)} (h2s : (κ
   let t := to_measurable ((κ ⊗ₖ η) a) s
   simp_rw [has_finite_integral, ennnorm_eq_of_real to_real_nonneg]
   calc
-    (∫⁻ b, ENNReal.ofReal (η (a, b) (Prod.mk b ⁻¹' s)).toReal ∂κ a) ≤
+    ∫⁻ b, ENNReal.ofReal (η (a, b) (Prod.mk b ⁻¹' s)).toReal ∂κ a ≤
         ∫⁻ b, η (a, b) (Prod.mk b ⁻¹' t) ∂κ a :=
       by
       refine' lintegral_mono_ae _
@@ -166,8 +166,8 @@ variable [NormedSpace ℝ E] [CompleteSpace E] {E' : Type _} [NormedAddCommGroup
 
 theorem kernel.integral_fn_integral_add ⦃f g : β × γ → E⦄ (F : E → E')
     (hf : Integrable f ((κ ⊗ₖ η) a)) (hg : Integrable g ((κ ⊗ₖ η) a)) :
-    (∫ x, F (∫ y, f (x, y) + g (x, y) ∂η (a, x)) ∂κ a) =
-      ∫ x, F ((∫ y, f (x, y) ∂η (a, x)) + ∫ y, g (x, y) ∂η (a, x)) ∂κ a :=
+    ∫ x, F (∫ y, f (x, y) + g (x, y) ∂η (a, x)) ∂κ a =
+      ∫ x, F (∫ y, f (x, y) ∂η (a, x) + ∫ y, g (x, y) ∂η (a, x)) ∂κ a :=
   by
   refine' integral_congr_ae _
   filter_upwards [hf.comp_prod_mk_left_ae, hg.comp_prod_mk_left_ae] with _ h2f h2g
@@ -176,8 +176,8 @@ theorem kernel.integral_fn_integral_add ⦃f g : β × γ → E⦄ (F : E → E'
 
 theorem kernel.integral_fn_integral_sub ⦃f g : β × γ → E⦄ (F : E → E')
     (hf : Integrable f ((κ ⊗ₖ η) a)) (hg : Integrable g ((κ ⊗ₖ η) a)) :
-    (∫ x, F (∫ y, f (x, y) - g (x, y) ∂η (a, x)) ∂κ a) =
-      ∫ x, F ((∫ y, f (x, y) ∂η (a, x)) - ∫ y, g (x, y) ∂η (a, x)) ∂κ a :=
+    ∫ x, F (∫ y, f (x, y) - g (x, y) ∂η (a, x)) ∂κ a =
+      ∫ x, F (∫ y, f (x, y) ∂η (a, x) - ∫ y, g (x, y) ∂η (a, x)) ∂κ a :=
   by
   refine' integral_congr_ae _
   filter_upwards [hf.comp_prod_mk_left_ae, hg.comp_prod_mk_left_ae] with _ h2f h2g
@@ -186,8 +186,8 @@ theorem kernel.integral_fn_integral_sub ⦃f g : β × γ → E⦄ (F : E → E'
 
 theorem kernel.lintegral_fn_integral_sub ⦃f g : β × γ → E⦄ (F : E → ℝ≥0∞)
     (hf : Integrable f ((κ ⊗ₖ η) a)) (hg : Integrable g ((κ ⊗ₖ η) a)) :
-    (∫⁻ x, F (∫ y, f (x, y) - g (x, y) ∂η (a, x)) ∂κ a) =
-      ∫⁻ x, F ((∫ y, f (x, y) ∂η (a, x)) - ∫ y, g (x, y) ∂η (a, x)) ∂κ a :=
+    ∫⁻ x, F (∫ y, f (x, y) - g (x, y) ∂η (a, x)) ∂κ a =
+      ∫⁻ x, F (∫ y, f (x, y) ∂η (a, x) - ∫ y, g (x, y) ∂η (a, x)) ∂κ a :=
   by
   refine' lintegral_congr_ae _
   filter_upwards [hf.comp_prod_mk_left_ae, hg.comp_prod_mk_left_ae] with _ h2f h2g
@@ -196,31 +196,31 @@ theorem kernel.lintegral_fn_integral_sub ⦃f g : β × γ → E⦄ (F : E → 
 
 theorem kernel.integral_integral_add ⦃f g : β × γ → E⦄ (hf : Integrable f ((κ ⊗ₖ η) a))
     (hg : Integrable g ((κ ⊗ₖ η) a)) :
-    (∫ x, ∫ y, f (x, y) + g (x, y) ∂η (a, x) ∂κ a) =
-      (∫ x, ∫ y, f (x, y) ∂η (a, x) ∂κ a) + ∫ x, ∫ y, g (x, y) ∂η (a, x) ∂κ a :=
+    ∫ x, ∫ y, f (x, y) + g (x, y) ∂η (a, x) ∂κ a =
+      ∫ x, ∫ y, f (x, y) ∂η (a, x) ∂κ a + ∫ x, ∫ y, g (x, y) ∂η (a, x) ∂κ a :=
   (kernel.integral_fn_integral_add id hf hg).trans <|
     integral_add hf.integral_compProd hg.integral_compProd
 #align probability_theory.kernel.integral_integral_add ProbabilityTheory.kernel.integral_integral_add
 
 theorem kernel.integral_integral_add' ⦃f g : β × γ → E⦄ (hf : Integrable f ((κ ⊗ₖ η) a))
     (hg : Integrable g ((κ ⊗ₖ η) a)) :
-    (∫ x, ∫ y, (f + g) (x, y) ∂η (a, x) ∂κ a) =
-      (∫ x, ∫ y, f (x, y) ∂η (a, x) ∂κ a) + ∫ x, ∫ y, g (x, y) ∂η (a, x) ∂κ a :=
+    ∫ x, ∫ y, (f + g) (x, y) ∂η (a, x) ∂κ a =
+      ∫ x, ∫ y, f (x, y) ∂η (a, x) ∂κ a + ∫ x, ∫ y, g (x, y) ∂η (a, x) ∂κ a :=
   kernel.integral_integral_add hf hg
 #align probability_theory.kernel.integral_integral_add' ProbabilityTheory.kernel.integral_integral_add'
 
 theorem kernel.integral_integral_sub ⦃f g : β × γ → E⦄ (hf : Integrable f ((κ ⊗ₖ η) a))
     (hg : Integrable g ((κ ⊗ₖ η) a)) :
-    (∫ x, ∫ y, f (x, y) - g (x, y) ∂η (a, x) ∂κ a) =
-      (∫ x, ∫ y, f (x, y) ∂η (a, x) ∂κ a) - ∫ x, ∫ y, g (x, y) ∂η (a, x) ∂κ a :=
+    ∫ x, ∫ y, f (x, y) - g (x, y) ∂η (a, x) ∂κ a =
+      ∫ x, ∫ y, f (x, y) ∂η (a, x) ∂κ a - ∫ x, ∫ y, g (x, y) ∂η (a, x) ∂κ a :=
   (kernel.integral_fn_integral_sub id hf hg).trans <|
     integral_sub hf.integral_compProd hg.integral_compProd
 #align probability_theory.kernel.integral_integral_sub ProbabilityTheory.kernel.integral_integral_sub
 
 theorem kernel.integral_integral_sub' ⦃f g : β × γ → E⦄ (hf : Integrable f ((κ ⊗ₖ η) a))
     (hg : Integrable g ((κ ⊗ₖ η) a)) :
-    (∫ x, ∫ y, (f - g) (x, y) ∂η (a, x) ∂κ a) =
-      (∫ x, ∫ y, f (x, y) ∂η (a, x) ∂κ a) - ∫ x, ∫ y, g (x, y) ∂η (a, x) ∂κ a :=
+    ∫ x, ∫ y, (f - g) (x, y) ∂η (a, x) ∂κ a =
+      ∫ x, ∫ y, f (x, y) ∂η (a, x) ∂κ a - ∫ x, ∫ y, g (x, y) ∂η (a, x) ∂κ a :=
   kernel.integral_integral_sub hf hg
 #align probability_theory.kernel.integral_integral_sub' ProbabilityTheory.kernel.integral_integral_sub'
 
@@ -252,7 +252,7 @@ theorem kernel.continuous_integral_integral :
 
 theorem integral_compProd :
     ∀ {f : β × γ → E} (hf : Integrable f ((κ ⊗ₖ η) a)),
-      (∫ z, f z ∂(κ ⊗ₖ η) a) = ∫ x, ∫ y, f (x, y) ∂η (a, x) ∂κ a :=
+      ∫ z, f z ∂(κ ⊗ₖ η) a = ∫ x, ∫ y, f (x, y) ∂η (a, x) ∂κ a :=
   by
   apply integrable.induction
   · intro c s hs h2s
@@ -281,7 +281,7 @@ theorem integral_compProd :
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 theorem set_integral_compProd {f : β × γ → E} {s : Set β} {t : Set γ} (hs : MeasurableSet s)
     (ht : MeasurableSet t) (hf : IntegrableOn f (s ×ˢ t) ((κ ⊗ₖ η) a)) :
-    (∫ z in s ×ˢ t, f z ∂(κ ⊗ₖ η) a) = ∫ x in s, ∫ y in t, f (x, y) ∂η (a, x) ∂κ a :=
+    ∫ z in s ×ˢ t, f z ∂(κ ⊗ₖ η) a = ∫ x in s, ∫ y in t, f (x, y) ∂η (a, x) ∂κ a :=
   by
   rw [← kernel.restrict_apply (κ ⊗ₖ η) (hs.prod ht), ← comp_prod_restrict, integral_comp_prod]
   · simp_rw [kernel.restrict_apply]
@@ -292,7 +292,7 @@ theorem set_integral_compProd {f : β × γ → E} {s : Set β} {t : Set γ} (hs
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 theorem set_integral_compProd_univ_right (f : β × γ → E) {s : Set β} (hs : MeasurableSet s)
     (hf : IntegrableOn f (s ×ˢ univ) ((κ ⊗ₖ η) a)) :
-    (∫ z in s ×ˢ univ, f z ∂(κ ⊗ₖ η) a) = ∫ x in s, ∫ y, f (x, y) ∂η (a, x) ∂κ a := by
+    ∫ z in s ×ˢ univ, f z ∂(κ ⊗ₖ η) a = ∫ x in s, ∫ y, f (x, y) ∂η (a, x) ∂κ a := by
   simp_rw [set_integral_comp_prod hs MeasurableSet.univ hf, measure.restrict_univ]
 #align probability_theory.set_integral_comp_prod_univ_right ProbabilityTheory.set_integral_compProd_univ_right
 
@@ -300,7 +300,7 @@ theorem set_integral_compProd_univ_right (f : β × γ → E) {s : Set β} (hs :
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 theorem set_integral_compProd_univ_left (f : β × γ → E) {t : Set γ} (ht : MeasurableSet t)
     (hf : IntegrableOn f (univ ×ˢ t) ((κ ⊗ₖ η) a)) :
-    (∫ z in univ ×ˢ t, f z ∂(κ ⊗ₖ η) a) = ∫ x, ∫ y in t, f (x, y) ∂η (a, x) ∂κ a := by
+    ∫ z in univ ×ˢ t, f z ∂(κ ⊗ₖ η) a = ∫ x, ∫ y in t, f (x, y) ∂η (a, x) ∂κ a := by
   simp_rw [set_integral_comp_prod MeasurableSet.univ ht hf, measure.restrict_univ]
 #align probability_theory.set_integral_comp_prod_univ_left ProbabilityTheory.set_integral_compProd_univ_left
 

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

@@ -63,7 +63,6 @@ theorem hasFiniteIntegral_prod_mk_left (a : α) {s : Set (β × γ)} (h2s : (κ
     _ ≤ (κ ⊗ₖ η) a t := (le_comp_prod_apply _ _ _ _)
     _ = (κ ⊗ₖ η) a s := (measure_to_measurable s)
     _ < ⊤ := h2s.lt_top
-    
 #align probability_theory.has_finite_integral_prod_mk_left ProbabilityTheory.hasFiniteIntegral_prod_mk_left
 
 theorem integrable_kernel_prod_mk_left (a : α) {s : Set (β × γ)} (hs : MeasurableSet s)

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

@@ -57,7 +57,7 @@ theorem hasFiniteIntegral_prod_mk_left (a : α) {s : Set (β × γ)} (h2s : (κ
         ∫⁻ b, η (a, b) (Prod.mk b ⁻¹' t) ∂κ a :=
       by
       refine' lintegral_mono_ae _
-      filter_upwards [ae_kernel_lt_top a h2s]with b hb
+      filter_upwards [ae_kernel_lt_top a h2s] with b hb
       rw [of_real_to_real hb.ne]
       exact measure_mono (preimage_mono (subset_to_measurable _ _))
     _ ≤ (κ ⊗ₖ η) a t := (le_comp_prod_apply _ _ _ _)
@@ -78,15 +78,14 @@ theorem MeasureTheory.AEStronglyMeasurable.integral_kernel_compProd [NormedSpace
     [CompleteSpace E] ⦃f : β × γ → E⦄ (hf : AEStronglyMeasurable f ((κ ⊗ₖ η) a)) :
     AEStronglyMeasurable (fun x => ∫ y, f (x, y) ∂η (a, x)) (κ a) :=
   ⟨fun x => ∫ y, hf.mk f (x, y) ∂η (a, x), hf.stronglyMeasurable_mk.integral_kernel_prod_right'', by
-    filter_upwards [ae_ae_of_ae_comp_prod hf.ae_eq_mk]with _ hx using integral_congr_ae hx⟩
+    filter_upwards [ae_ae_of_ae_comp_prod hf.ae_eq_mk] with _ hx using integral_congr_ae hx⟩
 #align measure_theory.ae_strongly_measurable.integral_kernel_comp_prod MeasureTheory.AEStronglyMeasurable.integral_kernel_compProd
 
 theorem MeasureTheory.AEStronglyMeasurable.compProd_mk_left {δ : Type _} [TopologicalSpace δ]
     {f : β × γ → δ} (hf : AEStronglyMeasurable f ((κ ⊗ₖ η) a)) :
     ∀ᵐ x ∂κ a, AEStronglyMeasurable (fun y => f (x, y)) (η (a, x)) := by
-  filter_upwards [ae_ae_of_ae_comp_prod
-      hf.ae_eq_mk]with x hx using⟨fun y => hf.mk f (x, y),
-      hf.strongly_measurable_mk.comp_measurable measurable_prod_mk_left, hx⟩
+  filter_upwards [ae_ae_of_ae_comp_prod hf.ae_eq_mk] with x hx using
+    ⟨fun y => hf.mk f (x, y), hf.strongly_measurable_mk.comp_measurable measurable_prod_mk_left, hx⟩
 #align measure_theory.ae_strongly_measurable.comp_prod_mk_left MeasureTheory.AEStronglyMeasurable.compProd_mk_left
 
 /-! ### Integrability -/
@@ -126,8 +125,8 @@ theorem hasFiniteIntegral_compProd_iff' ⦃f : β × γ → E⦄
     intro x hx
     exact has_finite_integral_congr hx
   · apply has_finite_integral_congr
-    filter_upwards [ae_ae_of_ae_comp_prod
-        h1f.ae_eq_mk.symm]with _ hx using integral_congr_ae (eventually_eq.fun_comp hx _)
+    filter_upwards [ae_ae_of_ae_comp_prod h1f.ae_eq_mk.symm] with _ hx using
+      integral_congr_ae (eventually_eq.fun_comp hx _)
 #align probability_theory.has_finite_integral_comp_prod_iff' ProbabilityTheory.hasFiniteIntegral_compProd_iff'
 
 theorem integrable_compProd_iff ⦃f : β × γ → E⦄ (hf : AEStronglyMeasurable f ((κ ⊗ₖ η) a)) :
@@ -172,7 +171,7 @@ theorem kernel.integral_fn_integral_add ⦃f g : β × γ → E⦄ (F : E → E'
       ∫ x, F ((∫ y, f (x, y) ∂η (a, x)) + ∫ y, g (x, y) ∂η (a, x)) ∂κ a :=
   by
   refine' integral_congr_ae _
-  filter_upwards [hf.comp_prod_mk_left_ae, hg.comp_prod_mk_left_ae]with _ h2f h2g
+  filter_upwards [hf.comp_prod_mk_left_ae, hg.comp_prod_mk_left_ae] with _ h2f h2g
   simp [integral_add h2f h2g]
 #align probability_theory.kernel.integral_fn_integral_add ProbabilityTheory.kernel.integral_fn_integral_add
 
@@ -182,7 +181,7 @@ theorem kernel.integral_fn_integral_sub ⦃f g : β × γ → E⦄ (F : E → E'
       ∫ x, F ((∫ y, f (x, y) ∂η (a, x)) - ∫ y, g (x, y) ∂η (a, x)) ∂κ a :=
   by
   refine' integral_congr_ae _
-  filter_upwards [hf.comp_prod_mk_left_ae, hg.comp_prod_mk_left_ae]with _ h2f h2g
+  filter_upwards [hf.comp_prod_mk_left_ae, hg.comp_prod_mk_left_ae] with _ h2f h2g
   simp [integral_sub h2f h2g]
 #align probability_theory.kernel.integral_fn_integral_sub ProbabilityTheory.kernel.integral_fn_integral_sub
 
@@ -192,7 +191,7 @@ theorem kernel.lintegral_fn_integral_sub ⦃f g : β × γ → E⦄ (F : E → 
       ∫⁻ x, F ((∫ y, f (x, y) ∂η (a, x)) - ∫ y, g (x, y) ∂η (a, x)) ∂κ a :=
   by
   refine' lintegral_congr_ae _
-  filter_upwards [hf.comp_prod_mk_left_ae, hg.comp_prod_mk_left_ae]with _ h2f h2g
+  filter_upwards [hf.comp_prod_mk_left_ae, hg.comp_prod_mk_left_ae] with _ h2f h2g
   simp [integral_sub h2f h2g]
 #align probability_theory.kernel.lintegral_fn_integral_sub ProbabilityTheory.kernel.lintegral_fn_integral_sub
 

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

@@ -37,7 +37,7 @@ kernels.
 
 noncomputable section
 
-open Topology ENNReal MeasureTheory ProbabilityTheory
+open scoped Topology ENNReal MeasureTheory ProbabilityTheory
 
 open Set Function Real ENNReal MeasureTheory Filter ProbabilityTheory ProbabilityTheory.kernel
 

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

@@ -106,18 +106,10 @@ theorem hasFiniteIntegral_compProd_iff ⦃f : β × γ → E⦄ (h1f : StronglyM
   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_kernel_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_kernel_prod_right''
 #align probability_theory.has_finite_integral_comp_prod_iff ProbabilityTheory.hasFiniteIntegral_compProd_iff
 
 theorem hasFiniteIntegral_compProd_iff' ⦃f : β × γ → E⦄
@@ -295,8 +287,7 @@ theorem set_integral_compProd {f : β × γ → E} {s : Set β} {t : Set γ} (hs
   by
   rw [← kernel.restrict_apply (κ ⊗ₖ η) (hs.prod ht), ← comp_prod_restrict, integral_comp_prod]
   · simp_rw [kernel.restrict_apply]
-  · rw [comp_prod_restrict, kernel.restrict_apply]
-    exact hf
+  · rw [comp_prod_restrict, kernel.restrict_apply]; exact hf
 #align probability_theory.set_integral_comp_prod ProbabilityTheory.set_integral_compProd
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/

mathlib commit https://github.com/leanprover-community/mathlib/commit/8d33f09cd7089ecf074b4791907588245aec5d1b

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

@@ -249,7 +249,7 @@ theorem integral_compProd :
   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), MeasureTheory.set_integral_const,
+      integral_indicator (measurable_prod_mk_left hs), MeasureTheory.setIntegral_const,
       integral_smul_const]
     congr 1
     rw [integral_toReal]
@@ -269,25 +269,37 @@ theorem integral_compProd :
         integral_congr_ae (ae_eq_symm hfgx)
 #align probability_theory.integral_comp_prod ProbabilityTheory.integral_compProd
 
-theorem set_integral_compProd {f : β × γ → E} {s : Set β} {t : Set γ} (hs : MeasurableSet s)
+theorem setIntegral_compProd {f : β × γ → E} {s : Set β} {t : Set γ} (hs : MeasurableSet s)
     (ht : MeasurableSet t) (hf : IntegrableOn f (s ×ˢ t) ((κ ⊗ₖ η) a)) :
     ∫ z in s ×ˢ t, f z ∂(κ ⊗ₖ η) a = ∫ x in s, ∫ y in t, f (x, y) ∂η (a, x) ∂κ a := by
   -- Porting note: `compProd_restrict` needed some explicit argumnts
   rw [← kernel.restrict_apply (κ ⊗ₖ η) (hs.prod ht), ← compProd_restrict hs ht, integral_compProd]
   · simp_rw [kernel.restrict_apply]
   · rw [compProd_restrict, kernel.restrict_apply]; exact hf
-#align probability_theory.set_integral_comp_prod ProbabilityTheory.set_integral_compProd
+#align probability_theory.set_integral_comp_prod ProbabilityTheory.setIntegral_compProd
 
-theorem set_integral_compProd_univ_right (f : β × γ → E) {s : Set β} (hs : MeasurableSet s)
+@[deprecated]
+alias set_integral_compProd :=
+  setIntegral_compProd -- deprecated on 2024-04-17
+
+theorem setIntegral_compProd_univ_right (f : β × γ → E) {s : Set β} (hs : MeasurableSet s)
     (hf : IntegrableOn f (s ×ˢ univ) ((κ ⊗ₖ η) a)) :
     ∫ z in s ×ˢ univ, f z ∂(κ ⊗ₖ η) a = ∫ x in s, ∫ y, f (x, y) ∂η (a, x) ∂κ a := by
-  simp_rw [set_integral_compProd hs MeasurableSet.univ hf, Measure.restrict_univ]
-#align probability_theory.set_integral_comp_prod_univ_right ProbabilityTheory.set_integral_compProd_univ_right
+  simp_rw [setIntegral_compProd hs MeasurableSet.univ hf, Measure.restrict_univ]
+#align probability_theory.set_integral_comp_prod_univ_right ProbabilityTheory.setIntegral_compProd_univ_right
+
+@[deprecated]
+alias set_integral_compProd_univ_right :=
+  setIntegral_compProd_univ_right -- deprecated on 2024-04-17
 
-theorem set_integral_compProd_univ_left (f : β × γ → E) {t : Set γ} (ht : MeasurableSet t)
+theorem setIntegral_compProd_univ_left (f : β × γ → E) {t : Set γ} (ht : MeasurableSet t)
     (hf : IntegrableOn f (univ ×ˢ t) ((κ ⊗ₖ η) a)) :
     ∫ z in univ ×ˢ t, f z ∂(κ ⊗ₖ η) a = ∫ x, ∫ y in t, f (x, y) ∂η (a, x) ∂κ a := by
-  simp_rw [set_integral_compProd MeasurableSet.univ ht hf, Measure.restrict_univ]
-#align probability_theory.set_integral_comp_prod_univ_left ProbabilityTheory.set_integral_compProd_univ_left
+  simp_rw [setIntegral_compProd MeasurableSet.univ ht hf, Measure.restrict_univ]
+#align probability_theory.set_integral_comp_prod_univ_left ProbabilityTheory.setIntegral_compProd_univ_left
+
+@[deprecated]
+alias set_integral_compProd_univ_left :=
+  setIntegral_compProd_univ_left -- deprecated on 2024-04-17
 
 end ProbabilityTheory

Let κ : kernel α (β × Ω) be a finite kernel, where Ω is a standard Borel space. Then if α is countable or β has a countably generated σ-algebra (for example if it is standard Borel), then there exists a kernel (α × β) Ω called conditional kernel and denoted by condKernel κ such that κ = fst κ ⊗ₖ condKernel κ.

Properties of integrals involving condKernel are collated in the file Integral.lean. The conditional kernel is unique (almost everywhere w.r.t. fst κ): this is proved in the file Unique.lean.

Co-authored-by: sgouezel <sebastien.gouezel@univ-rennes1.fr> Co-authored-by: Rémy Degenne <remydegenne@gmail.com>

@@ -69,7 +69,7 @@ theorem integrable_kernel_prod_mk_left (a : α) {s : Set (β × γ)} (hs : Measu
 #align probability_theory.integrable_kernel_prod_mk_left ProbabilityTheory.integrable_kernel_prod_mk_left
 
 theorem _root_.MeasureTheory.AEStronglyMeasurable.integral_kernel_compProd [NormedSpace ℝ E]
-    [CompleteSpace E] ⦃f : β × γ → E⦄ (hf : AEStronglyMeasurable f ((κ ⊗ₖ η) a)) :
+    ⦃f : β × γ → E⦄ (hf : AEStronglyMeasurable f ((κ ⊗ₖ η) a)) :
     AEStronglyMeasurable (fun x => ∫ y, f (x, y) ∂η (a, x)) (κ a) :=
   ⟨fun x => ∫ y, hf.mk f (x, y) ∂η (a, x), hf.stronglyMeasurable_mk.integral_kernel_prod_right'', by
     filter_upwards [ae_ae_of_ae_compProd hf.ae_eq_mk] with _ hx using integral_congr_ae hx⟩
@@ -138,7 +138,7 @@ theorem _root_.MeasureTheory.Integrable.integral_norm_compProd ⦃f : β × γ 
   ((integrable_compProd_iff hf.aestronglyMeasurable).mp hf).2
 #align measure_theory.integrable.integral_norm_comp_prod MeasureTheory.Integrable.integral_norm_compProd
 
-theorem _root_.MeasureTheory.Integrable.integral_compProd [NormedSpace ℝ E] [CompleteSpace E]
+theorem _root_.MeasureTheory.Integrable.integral_compProd [NormedSpace ℝ E]
     ⦃f : β × γ → E⦄ (hf : Integrable f ((κ ⊗ₖ η) a)) :
     Integrable (fun x => ∫ y, f (x, y) ∂η (a, x)) (κ a) :=
   Integrable.mono hf.integral_norm_compProd hf.aestronglyMeasurable.integral_kernel_compProd <|
@@ -152,7 +152,7 @@ theorem _root_.MeasureTheory.Integrable.integral_compProd [NormedSpace ℝ E] [C
 /-! ### Bochner integral -/
 
 
-variable [NormedSpace ℝ E] [CompleteSpace E] {E' : Type*} [NormedAddCommGroup E']
+variable [NormedSpace ℝ E] {E' : Type*} [NormedAddCommGroup E']
   [CompleteSpace E'] [NormedSpace ℝ E']
 
 theorem kernel.integral_fn_integral_add ⦃f g : β × γ → E⦄ (F : E → E')
@@ -244,6 +244,8 @@ theorem kernel.continuous_integral_integral :
 theorem integral_compProd :
     ∀ {f : β × γ → E} (_ : Integrable f ((κ ⊗ₖ η) a)),
       ∫ z, f z ∂(κ ⊗ₖ η) a = ∫ x, ∫ y, f (x, y) ∂η (a, x) ∂κ a := by
+  by_cases hE : CompleteSpace E; swap
+  · simp [integral, hE]
   apply Integrable.induction
   · intro c s hs h2s
     simp_rw [integral_indicator hs, ← indicator_comp_right, Function.comp,

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

@@ -56,8 +56,8 @@ theorem hasFiniteIntegral_prod_mk_left (a : α) {s : Set (β × γ)} (h2s : (κ
       filter_upwards [ae_kernel_lt_top a h2s] with b hb
       rw [ofReal_toReal hb.ne]
       exact measure_mono (preimage_mono (subset_toMeasurable _ _))
-    _ ≤ (κ ⊗ₖ η) a t := (le_compProd_apply _ _ _ _)
-    _ = (κ ⊗ₖ η) a s := (measure_toMeasurable s)
+    _ ≤ (κ ⊗ₖ η) a t := le_compProd_apply _ _ _ _
+    _ = (κ ⊗ₖ η) a s := measure_toMeasurable s
     _ < ⊤ := h2s.lt_top
 #align probability_theory.has_finite_integral_prod_mk_left ProbabilityTheory.hasFiniteIntegral_prod_mk_left
 

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.

@@ -99,9 +99,9 @@ theorem hasFiniteIntegral_compProd_iff ⦃f : β × γ → E⦄ (h1f : StronglyM
     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_kernel_prod_right''
+  · intro h2f; refine ae_lt_top ?_ h2f.ne; exact h1f.ennnorm.lintegral_kernel_prod_right''
 #align probability_theory.has_finite_integral_comp_prod_iff ProbabilityTheory.hasFiniteIntegral_compProd_iff
 
 theorem hasFiniteIntegral_compProd_iff' ⦃f : β × γ → E⦄
@@ -113,9 +113,8 @@ theorem hasFiniteIntegral_compProd_iff' ⦃f : β × γ → E⦄
     hasFiniteIntegral_compProd_iff h1f.stronglyMeasurable_mk]
   apply and_congr
   · apply eventually_congr
-    filter_upwards [ae_ae_of_ae_compProd h1f.ae_eq_mk.symm]
-    intro x hx
-    exact hasFiniteIntegral_congr hx
+    filter_upwards [ae_ae_of_ae_compProd h1f.ae_eq_mk.symm] with x hx using
+      hasFiniteIntegral_congr hx
   · apply hasFiniteIntegral_congr
     filter_upwards [ae_ae_of_ae_compProd h1f.ae_eq_mk.symm] with _ hx using
       integral_congr_ae (EventuallyEq.fun_comp hx _)
@@ -263,9 +262,9 @@ theorem integral_compProd :
   · intro f g hfg _ hf
     convert hf using 1
     · exact integral_congr_ae hfg.symm
-    · refine' integral_congr_ae _
-      refine' (ae_ae_of_ae_compProd hfg).mp (eventually_of_forall _)
-      exact fun x hfgx => integral_congr_ae (ae_eq_symm hfgx)
+    · apply integral_congr_ae
+      filter_upwards [ae_ae_of_ae_compProd hfg] with x hfgx using
+        integral_congr_ae (ae_eq_symm hfgx)
 #align probability_theory.integral_comp_prod ProbabilityTheory.integral_compProd
 
 theorem set_integral_compProd {f : β × γ → E} {s : Set β} {t : Set γ} (hs : MeasurableSet s)

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.

@@ -238,7 +238,7 @@ theorem kernel.continuous_integral_integral :
   simp_rw [← kernel.lintegral_compProd _ _ _ (this _), ← L1.ofReal_norm_sub_eq_lintegral, ←
     ofReal_zero]
   refine' (continuous_ofReal.tendsto 0).comp _
-  rw [← tendsto_iff_norm_tendsto_zero]
+  rw [← tendsto_iff_norm_sub_tendsto_zero]
   exact tendsto_id
 #align probability_theory.kernel.continuous_integral_integral ProbabilityTheory.kernel.continuous_integral_integral
 

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

This has nice performance benefits.

@@ -39,7 +39,7 @@ open scoped Topology ENNReal MeasureTheory ProbabilityTheory
 
 open Set Function Real ENNReal MeasureTheory Filter ProbabilityTheory ProbabilityTheory.kernel
 
-variable {α β γ E : Type _} {mα : MeasurableSpace α} {mβ : MeasurableSpace β}
+variable {α β γ E : Type*} {mα : MeasurableSpace α} {mβ : MeasurableSpace β}
   {mγ : MeasurableSpace γ} [NormedAddCommGroup E] {κ : kernel α β} [IsSFiniteKernel κ]
   {η : kernel (α × β) γ} [IsSFiniteKernel η] {a : α}
 
@@ -75,7 +75,7 @@ theorem _root_.MeasureTheory.AEStronglyMeasurable.integral_kernel_compProd [Norm
     filter_upwards [ae_ae_of_ae_compProd hf.ae_eq_mk] with _ hx using integral_congr_ae hx⟩
 #align measure_theory.ae_strongly_measurable.integral_kernel_comp_prod MeasureTheory.AEStronglyMeasurable.integral_kernel_compProd
 
-theorem _root_.MeasureTheory.AEStronglyMeasurable.compProd_mk_left {δ : Type _} [TopologicalSpace δ]
+theorem _root_.MeasureTheory.AEStronglyMeasurable.compProd_mk_left {δ : Type*} [TopologicalSpace δ]
     {f : β × γ → δ} (hf : AEStronglyMeasurable f ((κ ⊗ₖ η) a)) :
     ∀ᵐ x ∂κ a, AEStronglyMeasurable (fun y => f (x, y)) (η (a, x)) := by
   filter_upwards [ae_ae_of_ae_compProd hf.ae_eq_mk] with x hx using
@@ -153,7 +153,7 @@ theorem _root_.MeasureTheory.Integrable.integral_compProd [NormedSpace ℝ E] [C
 /-! ### Bochner integral -/
 
 
-variable [NormedSpace ℝ E] [CompleteSpace E] {E' : Type _} [NormedAddCommGroup E']
+variable [NormedSpace ℝ E] [CompleteSpace E] {E' : Type*} [NormedAddCommGroup E']
   [CompleteSpace E'] [NormedSpace ℝ E']
 
 theorem kernel.integral_fn_integral_add ⦃f g : β × γ → E⦄ (F : E → E')

• 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) 2023 Rémy Degenne. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Rémy Degenne
-
-! This file was ported from Lean 3 source module probability.kernel.integral_comp_prod
-! leanprover-community/mathlib commit c0d694db494dd4f9aa57f2714b6e4c82b4ebc113
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Probability.Kernel.Composition
 import Mathlib.MeasureTheory.Integral.SetIntegral
 
+#align_import probability.kernel.integral_comp_prod from "leanprover-community/mathlib"@"c0d694db494dd4f9aa57f2714b6e4c82b4ebc113"
+
 /-!
 # Bochner integral of a function against the composition-product of two kernels
 

@@ -16,9 +16,9 @@ import Mathlib.MeasureTheory.Integral.SetIntegral
 
 We prove properties of the composition-product of two kernels. If `κ` is an s-finite kernel from
 `α` to `β` and `η` is an s-finite kernel from `α × β` to `γ`, we can form their composition-product
-`κ ⊗ₖ η : kernel α (β × γ)`. We proved in `probability.kernel.lintegral_comp_prod` that it verifies
-`∫⁻ bc, f bc ∂((κ ⊗ₖ η) a) = ∫⁻ b, ∫⁻ c, f (b, c) ∂(η (a, b)) ∂(κ a)`. In this file, we prove the
-same equality for the Bochner integral.
+`κ ⊗ₖ η : kernel α (β × γ)`. We proved in `ProbabilityTheory.kernel.lintegral_compProd` that it
+verifies `∫⁻ bc, f bc ∂((κ ⊗ₖ η) a) = ∫⁻ b, ∫⁻ c, f (b, c) ∂(η (a, b)) ∂(κ a)`. In this file, we
+prove the same equality for the Bochner integral.
 
 ## Main statements
 
@@ -27,7 +27,8 @@ same equality for the Bochner integral.
 
 ## Implementation details
 
-This file is to a large extent a copy of part of `measure_theory.constructions.prod`. The product of
+This file is to a large extent a copy of part of
+`Mathlib/MeasureTheory/Constructions/Prod/Basic.lean`. The product of
 two measures is a particular case of composition-product of kernels and it turns out that once the
 measurablity of the Lebesgue integral of a kernel is proved, almost all proofs about integrals
 against products of measures extend with minimal modifications to the composition-product of two
@@ -52,8 +53,8 @@ theorem hasFiniteIntegral_prod_mk_left (a : α) {s : Set (β × γ)} (h2s : (κ
   let t := toMeasurable ((κ ⊗ₖ η) a) s
   simp_rw [HasFiniteIntegral, ennnorm_eq_ofReal toReal_nonneg]
   calc
-    ∫⁻ b, ENNReal.ofReal (η (a, b) (Prod.mk b ⁻¹' s)).toReal ∂κ a ≤
-        ∫⁻ b, η (a, b) (Prod.mk b ⁻¹' t) ∂κ a := by
+    ∫⁻ b, ENNReal.ofReal (η (a, b) (Prod.mk b ⁻¹' s)).toReal ∂κ a
+    _ ≤ ∫⁻ b, η (a, b) (Prod.mk b ⁻¹' t) ∂κ a := by
       refine' lintegral_mono_ae _
       filter_upwards [ae_kernel_lt_top a h2s] with b hb
       rw [ofReal_toReal hb.ne]

Co-authored-by: Johan Commelin <johan@commelin.net> Co-authored-by: Moritz Firsching <firsching@google.com>