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

@@ -196,8 +196,8 @@ theorem IndepFun.integrable_left_of_integrable_mul {β : Type _} [MeasurableSpac
     have M : Measurable fun x : β => (‖x‖₊ : ℝ≥0∞) := measurable_nnnorm.coe_nnreal_ennreal
     apply indep_fun.comp hXY M M
   have A : ∫⁻ ω, ‖X ω * Y ω‖₊ ∂μ < ∞ := h'XY.2
-  simp only [nnnorm_mul, ENNReal.coe_mul] at A 
-  rw [lintegral_mul_eq_lintegral_mul_lintegral_of_indep_fun'' hX.ennnorm hY.ennnorm J, H] at A 
+  simp only [nnnorm_mul, ENNReal.coe_mul] at A
+  rw [lintegral_mul_eq_lintegral_mul_lintegral_of_indep_fun'' hX.ennnorm hY.ennnorm J, H] at A
   simpa [ENNReal.top_mul', I] using A
 #align probability_theory.indep_fun.integrable_left_of_integrable_mul ProbabilityTheory.IndepFun.integrable_left_of_integrable_mul
 -/
@@ -222,8 +222,8 @@ theorem IndepFun.integrable_right_of_integrable_mul {β : Type _} [MeasurableSpa
     have M : Measurable fun x : β => (‖x‖₊ : ℝ≥0∞) := measurable_nnnorm.coe_nnreal_ennreal
     apply indep_fun.comp hXY M M
   have A : ∫⁻ ω, ‖X ω * Y ω‖₊ ∂μ < ∞ := h'XY.2
-  simp only [nnnorm_mul, ENNReal.coe_mul] at A 
-  rw [lintegral_mul_eq_lintegral_mul_lintegral_of_indep_fun'' hX.ennnorm hY.ennnorm J, H] at A 
+  simp only [nnnorm_mul, ENNReal.coe_mul] at A
+  rw [lintegral_mul_eq_lintegral_mul_lintegral_of_indep_fun'' hX.ennnorm hY.ennnorm J, H] at A
   simpa [ENNReal.top_mul', I] using A
 #align probability_theory.indep_fun.integrable_right_of_integrable_mul ProbabilityTheory.IndepFun.integrable_right_of_integrable_mul
 -/
@@ -328,7 +328,7 @@ theorem IndepFun.integral_mul (hXY : IndepFun X Y μ) (hX : AEStronglyMeasurable
       by
       rintro ⟨HX, HY⟩
       exact h (hXY.integrable_mul HX HY)
-    rw [not_and_or] at I 
+    rw [not_and_or] at I
     cases I <;> simp [integral_undef, I, h]
 #align probability_theory.indep_fun.integral_mul ProbabilityTheory.IndepFun.integral_mul
 -/

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

@@ -3,8 +3,8 @@ Copyright (c) 2021 Martin Zinkevich. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Martin Zinkevich, Vincent Beffara
 -/
-import Mathbin.MeasureTheory.Integral.SetIntegral
-import Mathbin.Probability.Independence.Basic
+import MeasureTheory.Integral.SetIntegral
+import Probability.Independence.Basic
 
 #align_import probability.integration from "leanprover-community/mathlib"@"7e5137f579de09a059a5ce98f364a04e221aabf0"
 

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

@@ -2,15 +2,12 @@
 Copyright (c) 2021 Martin Zinkevich. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Martin Zinkevich, Vincent Beffara
-
-! This file was ported from Lean 3 source module probability.integration
-! leanprover-community/mathlib commit 7e5137f579de09a059a5ce98f364a04e221aabf0
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.MeasureTheory.Integral.SetIntegral
 import Mathbin.Probability.Independence.Basic
 
+#align_import probability.integration from "leanprover-community/mathlib"@"7e5137f579de09a059a5ce98f364a04e221aabf0"
+
 /-!
 # Integration in Probability Theory
 

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

@@ -45,6 +45,7 @@ variable {Ω : Type _} {mΩ : MeasurableSpace Ω} {μ : Measure Ω} {f g : Ω 
 
 namespace ProbabilityTheory
 
+#print ProbabilityTheory.lintegral_mul_indicator_eq_lintegral_mul_lintegral_indicator /-
 /-- If a random variable `f` in `ℝ≥0∞` is independent of an event `T`, then if you restrict the
   random variable to `T`, then `E[f * indicator T c 0]=E[f] * E[indicator T c 0]`. It is useful for
   `lintegral_mul_eq_lintegral_mul_lintegral_of_independent_measurable_space`. -/
@@ -81,7 +82,9 @@ theorem lintegral_mul_indicator_eq_lintegral_mul_lintegral_indicator {Mf mΩ : M
     · exact fun n => h_mul_indicator _ (h_measM_f n)
     · exact fun m n h_le a => mul_le_mul_right' (h_mono_f h_le a) _
 #align probability_theory.lintegral_mul_indicator_eq_lintegral_mul_lintegral_indicator ProbabilityTheory.lintegral_mul_indicator_eq_lintegral_mul_lintegral_indicator
+-/
 
+#print ProbabilityTheory.lintegral_mul_eq_lintegral_mul_lintegral_of_independent_measurableSpace /-
 /-- If `f` and `g` are independent random variables with values in `ℝ≥0∞`,
    then `E[f * g] = E[f] * E[g]`. However, instead of directly using the independence
    of the random variables, it uses the independence of measurable spaces for the
@@ -114,7 +117,9 @@ theorem lintegral_mul_eq_lintegral_mul_lintegral_of_independent_measurableSpace
     · exact fun n => h_measM_f.mul (h_measM_f' n)
     · exact fun n m (h_le : n ≤ m) a => mul_le_mul_left' (h_mono_f' h_le a) _
 #align probability_theory.lintegral_mul_eq_lintegral_mul_lintegral_of_independent_measurable_space ProbabilityTheory.lintegral_mul_eq_lintegral_mul_lintegral_of_independent_measurableSpace
+-/
 
+#print ProbabilityTheory.lintegral_mul_eq_lintegral_mul_lintegral_of_indepFun /-
 /-- If `f` and `g` are independent random variables with values in `ℝ≥0∞`,
    then `E[f * g] = E[f] * E[g]`. -/
 theorem lintegral_mul_eq_lintegral_mul_lintegral_of_indepFun (h_meas_f : Measurable f)
@@ -124,7 +129,9 @@ theorem lintegral_mul_eq_lintegral_mul_lintegral_of_indepFun (h_meas_f : Measura
     (measurable_iff_comap_le.1 h_meas_f) (measurable_iff_comap_le.1 h_meas_g) h_indep_fun
     (Measurable.of_comap_le le_rfl) (Measurable.of_comap_le le_rfl)
 #align probability_theory.lintegral_mul_eq_lintegral_mul_lintegral_of_indep_fun ProbabilityTheory.lintegral_mul_eq_lintegral_mul_lintegral_of_indepFun
+-/
 
+#print ProbabilityTheory.lintegral_mul_eq_lintegral_mul_lintegral_of_indepFun' /-
 /-- If `f` and `g` with values in `ℝ≥0∞` are independent and almost everywhere measurable,
    then `E[f * g] = E[f] * E[g]` (slightly generalizing
    `lintegral_mul_eq_lintegral_mul_lintegral_of_indep_fun`). -/
@@ -140,13 +147,17 @@ theorem lintegral_mul_eq_lintegral_mul_lintegral_of_indepFun' (h_meas_f : AEMeas
       h_meas_g.measurable_mk
   exact h_indep_fun.ae_eq h_meas_f.ae_eq_mk h_meas_g.ae_eq_mk
 #align probability_theory.lintegral_mul_eq_lintegral_mul_lintegral_of_indep_fun' ProbabilityTheory.lintegral_mul_eq_lintegral_mul_lintegral_of_indepFun'
+-/
 
+#print ProbabilityTheory.lintegral_mul_eq_lintegral_mul_lintegral_of_indepFun'' /-
 theorem lintegral_mul_eq_lintegral_mul_lintegral_of_indepFun'' (h_meas_f : AEMeasurable f μ)
     (h_meas_g : AEMeasurable g μ) (h_indep_fun : IndepFun f g μ) :
     ∫⁻ ω, f ω * g ω ∂μ = (∫⁻ ω, f ω ∂μ) * ∫⁻ ω, g ω ∂μ :=
   lintegral_mul_eq_lintegral_mul_lintegral_of_indepFun' h_meas_f h_meas_g h_indep_fun
 #align probability_theory.lintegral_mul_eq_lintegral_mul_lintegral_of_indep_fun'' ProbabilityTheory.lintegral_mul_eq_lintegral_mul_lintegral_of_indepFun''
+-/
 
+#print ProbabilityTheory.IndepFun.integrable_mul /-
 /-- The product of two independent, integrable, real_valued random variables is integrable. -/
 theorem IndepFun.integrable_mul {β : Type _} [MeasurableSpace β] {X Y : Ω → β}
     [NormedDivisionRing β] [BorelSpace β] (hXY : IndepFun X Y μ) (hX : Integrable X μ)
@@ -166,7 +177,9 @@ theorem IndepFun.integrable_mul {β : Type _} [MeasurableSpace β] {X Y : Ω →
   simp_rw [has_finite_integral, Pi.mul_apply, nnnorm_mul, ENNReal.coe_mul, hmul]
   exact ennreal.mul_lt_top_iff.mpr (Or.inl ⟨hX.2, hY.2⟩)
 #align probability_theory.indep_fun.integrable_mul ProbabilityTheory.IndepFun.integrable_mul
+-/
 
+#print ProbabilityTheory.IndepFun.integrable_left_of_integrable_mul /-
 /-- If the product of two independent real_valued random variables is integrable and
 the second one is not almost everywhere zero, then the first one is integrable. -/
 theorem IndepFun.integrable_left_of_integrable_mul {β : Type _} [MeasurableSpace β] {X Y : Ω → β}
@@ -190,7 +203,9 @@ theorem IndepFun.integrable_left_of_integrable_mul {β : Type _} [MeasurableSpac
   rw [lintegral_mul_eq_lintegral_mul_lintegral_of_indep_fun'' hX.ennnorm hY.ennnorm J, H] at A 
   simpa [ENNReal.top_mul', I] using A
 #align probability_theory.indep_fun.integrable_left_of_integrable_mul ProbabilityTheory.IndepFun.integrable_left_of_integrable_mul
+-/
 
+#print ProbabilityTheory.IndepFun.integrable_right_of_integrable_mul /-
 /-- If the product of two independent real_valued random variables is integrable and the
 first one is not almost everywhere zero, then the second one is integrable. -/
 theorem IndepFun.integrable_right_of_integrable_mul {β : Type _} [MeasurableSpace β] {X Y : Ω → β}
@@ -214,7 +229,9 @@ theorem IndepFun.integrable_right_of_integrable_mul {β : Type _} [MeasurableSpa
   rw [lintegral_mul_eq_lintegral_mul_lintegral_of_indep_fun'' hX.ennnorm hY.ennnorm J, H] at A 
   simpa [ENNReal.top_mul', I] using A
 #align probability_theory.indep_fun.integrable_right_of_integrable_mul ProbabilityTheory.IndepFun.integrable_right_of_integrable_mul
+-/
 
+#print ProbabilityTheory.IndepFun.integral_mul_of_nonneg /-
 /-- The (Bochner) integral of the product of two independent, nonnegative random
   variables is the product of their integrals. The proof is just plumbing around
   `lintegral_mul_eq_lintegral_mul_lintegral_of_indep_fun'`. -/
@@ -236,7 +253,9 @@ theorem IndepFun.integral_mul_of_nonneg (hXY : IndepFun X Y μ) (hXp : 0 ≤ X)
   apply lintegral_mul_eq_lintegral_mul_lintegral_of_indep_fun' h1 h2
   exact hXY.comp ENNReal.measurable_ofReal ENNReal.measurable_ofReal
 #align probability_theory.indep_fun.integral_mul_of_nonneg ProbabilityTheory.IndepFun.integral_mul_of_nonneg
+-/
 
+#print ProbabilityTheory.IndepFun.integral_mul_of_integrable /-
 /-- The (Bochner) integral of the product of two independent, integrable random
   variables is the product of their integrals. The proof is pedestrian decomposition
   into their positive and negative parts in order to apply `indep_fun.integral_mul_of_nonneg`
@@ -284,7 +303,9 @@ theorem IndepFun.integral_mul_of_integrable (hXY : IndepFun X Y μ) (hX : Integr
     hi4.integral_mul_of_nonneg hp2 hp4 hm2 hm4]
   ring
 #align probability_theory.indep_fun.integral_mul_of_integrable ProbabilityTheory.IndepFun.integral_mul_of_integrable
+-/
 
+#print ProbabilityTheory.IndepFun.integral_mul /-
 /-- The (Bochner) integral of the product of two independent random
   variables is the product of their integrals. -/
 theorem IndepFun.integral_mul (hXY : IndepFun X Y μ) (hX : AEStronglyMeasurable X μ)
@@ -313,13 +334,17 @@ theorem IndepFun.integral_mul (hXY : IndepFun X Y μ) (hX : AEStronglyMeasurable
     rw [not_and_or] at I 
     cases I <;> simp [integral_undef, I, h]
 #align probability_theory.indep_fun.integral_mul ProbabilityTheory.IndepFun.integral_mul
+-/
 
+#print ProbabilityTheory.IndepFun.integral_mul' /-
 theorem IndepFun.integral_mul' (hXY : IndepFun X Y μ) (hX : AEStronglyMeasurable X μ)
     (hY : AEStronglyMeasurable Y μ) :
     (integral μ fun ω => X ω * Y ω) = integral μ X * integral μ Y :=
   hXY.integral_mul hX hY
 #align probability_theory.indep_fun.integral_mul' ProbabilityTheory.IndepFun.integral_mul'
+-/
 
+#print ProbabilityTheory.indepFun_iff_integral_comp_mul /-
 /-- Independence of functions `f` and `g` into arbitrary types is characterized by the relation
   `E[(φ ∘ f) * (ψ ∘ g)] = E[φ ∘ f] * E[ψ ∘ g]` for all measurable `φ` and `ψ` with values in `ℝ`
   satisfying appropriate integrability conditions. -/
@@ -344,6 +369,7 @@ theorem indepFun_iff_integral_comp_mul [IsFiniteMeasure μ] {β β' : Type _} {m
     integral_indicator_one (hgm hB), Set.inter_indicator_one]
   exact ENNReal.mul_ne_top (measure_ne_top μ _) (measure_ne_top μ _)
 #align probability_theory.indep_fun_iff_integral_comp_mul ProbabilityTheory.indepFun_iff_integral_comp_mul
+-/
 
 end ProbabilityTheory
 

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

@@ -51,7 +51,7 @@ namespace ProbabilityTheory
 theorem lintegral_mul_indicator_eq_lintegral_mul_lintegral_indicator {Mf mΩ : MeasurableSpace Ω}
     {μ : Measure Ω} (hMf : Mf ≤ mΩ) (c : ℝ≥0∞) {T : Set Ω} (h_meas_T : MeasurableSet T)
     (h_ind : IndepSets {s | measurable_set[Mf] s} {T} μ) (h_meas_f : measurable[Mf] f) :
-    (∫⁻ ω, f ω * T.indicator (fun _ => c) ω ∂μ) =
+    ∫⁻ ω, f ω * T.indicator (fun _ => c) ω ∂μ =
       (∫⁻ ω, f ω ∂μ) * ∫⁻ ω, T.indicator (fun _ => c) ω ∂μ :=
   by
   revert f
@@ -91,7 +91,7 @@ theorem lintegral_mul_indicator_eq_lintegral_mul_lintegral_indicator {Mf mΩ : M
 theorem lintegral_mul_eq_lintegral_mul_lintegral_of_independent_measurableSpace
     {Mf Mg mΩ : MeasurableSpace Ω} {μ : Measure Ω} (hMf : Mf ≤ mΩ) (hMg : Mg ≤ mΩ)
     (h_ind : Indep Mf Mg μ) (h_meas_f : measurable[Mf] f) (h_meas_g : measurable[Mg] g) :
-    (∫⁻ ω, f ω * g ω ∂μ) = (∫⁻ ω, f ω ∂μ) * ∫⁻ ω, g ω ∂μ :=
+    ∫⁻ ω, f ω * g ω ∂μ = (∫⁻ ω, f ω ∂μ) * ∫⁻ ω, g ω ∂μ :=
   by
   revert g
   have h_measM_f : Measurable f := h_meas_f.mono hMf le_rfl
@@ -119,7 +119,7 @@ theorem lintegral_mul_eq_lintegral_mul_lintegral_of_independent_measurableSpace
    then `E[f * g] = E[f] * E[g]`. -/
 theorem lintegral_mul_eq_lintegral_mul_lintegral_of_indepFun (h_meas_f : Measurable f)
     (h_meas_g : Measurable g) (h_indep_fun : IndepFun f g μ) :
-    (∫⁻ ω, (f * g) ω ∂μ) = (∫⁻ ω, f ω ∂μ) * ∫⁻ ω, g ω ∂μ :=
+    ∫⁻ ω, (f * g) ω ∂μ = (∫⁻ ω, f ω ∂μ) * ∫⁻ ω, g ω ∂μ :=
   lintegral_mul_eq_lintegral_mul_lintegral_of_independent_measurableSpace
     (measurable_iff_comap_le.1 h_meas_f) (measurable_iff_comap_le.1 h_meas_g) h_indep_fun
     (Measurable.of_comap_le le_rfl) (Measurable.of_comap_le le_rfl)
@@ -130,7 +130,7 @@ theorem lintegral_mul_eq_lintegral_mul_lintegral_of_indepFun (h_meas_f : Measura
    `lintegral_mul_eq_lintegral_mul_lintegral_of_indep_fun`). -/
 theorem lintegral_mul_eq_lintegral_mul_lintegral_of_indepFun' (h_meas_f : AEMeasurable f μ)
     (h_meas_g : AEMeasurable g μ) (h_indep_fun : IndepFun f g μ) :
-    (∫⁻ ω, (f * g) ω ∂μ) = (∫⁻ ω, f ω ∂μ) * ∫⁻ ω, g ω ∂μ :=
+    ∫⁻ ω, (f * g) ω ∂μ = (∫⁻ ω, f ω ∂μ) * ∫⁻ ω, g ω ∂μ :=
   by
   have fg_ae : f * g =ᵐ[μ] h_meas_f.mk _ * h_meas_g.mk _ := h_meas_f.ae_eq_mk.mul h_meas_g.ae_eq_mk
   rw [lintegral_congr_ae h_meas_f.ae_eq_mk, lintegral_congr_ae h_meas_g.ae_eq_mk,
@@ -143,7 +143,7 @@ theorem lintegral_mul_eq_lintegral_mul_lintegral_of_indepFun' (h_meas_f : AEMeas
 
 theorem lintegral_mul_eq_lintegral_mul_lintegral_of_indepFun'' (h_meas_f : AEMeasurable f μ)
     (h_meas_g : AEMeasurable g μ) (h_indep_fun : IndepFun f g μ) :
-    (∫⁻ ω, f ω * g ω ∂μ) = (∫⁻ ω, f ω ∂μ) * ∫⁻ ω, g ω ∂μ :=
+    ∫⁻ ω, f ω * g ω ∂μ = (∫⁻ ω, f ω ∂μ) * ∫⁻ ω, g ω ∂μ :=
   lintegral_mul_eq_lintegral_mul_lintegral_of_indepFun' h_meas_f h_meas_g h_indep_fun
 #align probability_theory.lintegral_mul_eq_lintegral_mul_lintegral_of_indep_fun'' ProbabilityTheory.lintegral_mul_eq_lintegral_mul_lintegral_of_indepFun''
 
@@ -160,7 +160,7 @@ theorem IndepFun.integrable_mul {β : Type _} [MeasurableSpace β] {X Y : Ω →
     hXY'.comp measurable_coe_nnreal_ennreal measurable_coe_nnreal_ennreal
   have hnX : AEMeasurable nX μ := hX.1.AEMeasurable.nnnorm.coe_nnreal_ennreal
   have hnY : AEMeasurable nY μ := hY.1.AEMeasurable.nnnorm.coe_nnreal_ennreal
-  have hmul : (∫⁻ a, nX a * nY a ∂μ) = (∫⁻ a, nX a ∂μ) * ∫⁻ a, nY a ∂μ := by
+  have hmul : ∫⁻ a, nX a * nY a ∂μ = (∫⁻ a, nX a ∂μ) * ∫⁻ a, nY a ∂μ := by
     convert lintegral_mul_eq_lintegral_mul_lintegral_of_indep_fun' hnX hnY hXY''
   refine' ⟨hX.1.mul hY.1, _⟩
   simp_rw [has_finite_integral, Pi.mul_apply, nnnorm_mul, ENNReal.coe_mul, hmul]
@@ -174,7 +174,7 @@ theorem IndepFun.integrable_left_of_integrable_mul {β : Type _} [MeasurableSpac
     (hX : AEStronglyMeasurable X μ) (hY : AEStronglyMeasurable Y μ) (h'Y : ¬Y =ᵐ[μ] 0) :
     Integrable X μ := by
   refine' ⟨hX, _⟩
-  have I : (∫⁻ ω, ‖Y ω‖₊ ∂μ) ≠ 0 := by
+  have I : ∫⁻ ω, ‖Y ω‖₊ ∂μ ≠ 0 := by
     intro H
     have I : (fun ω => ↑‖Y ω‖₊) =ᵐ[μ] 0 := (lintegral_eq_zero_iff' hY.ennnorm).1 H
     apply h'Y
@@ -185,7 +185,7 @@ theorem IndepFun.integrable_left_of_integrable_mul {β : Type _} [MeasurableSpac
     by
     have M : Measurable fun x : β => (‖x‖₊ : ℝ≥0∞) := measurable_nnnorm.coe_nnreal_ennreal
     apply indep_fun.comp hXY M M
-  have A : (∫⁻ ω, ‖X ω * Y ω‖₊ ∂μ) < ∞ := h'XY.2
+  have A : ∫⁻ ω, ‖X ω * Y ω‖₊ ∂μ < ∞ := h'XY.2
   simp only [nnnorm_mul, ENNReal.coe_mul] at A 
   rw [lintegral_mul_eq_lintegral_mul_lintegral_of_indep_fun'' hX.ennnorm hY.ennnorm J, H] at A 
   simpa [ENNReal.top_mul', I] using A
@@ -198,7 +198,7 @@ theorem IndepFun.integrable_right_of_integrable_mul {β : Type _} [MeasurableSpa
     (hX : AEStronglyMeasurable X μ) (hY : AEStronglyMeasurable Y μ) (h'X : ¬X =ᵐ[μ] 0) :
     Integrable Y μ := by
   refine' ⟨hY, _⟩
-  have I : (∫⁻ ω, ‖X ω‖₊ ∂μ) ≠ 0 := by
+  have I : ∫⁻ ω, ‖X ω‖₊ ∂μ ≠ 0 := by
     intro H
     have I : (fun ω => ↑‖X ω‖₊) =ᵐ[μ] 0 := (lintegral_eq_zero_iff' hX.ennnorm).1 H
     apply h'X
@@ -209,7 +209,7 @@ theorem IndepFun.integrable_right_of_integrable_mul {β : Type _} [MeasurableSpa
     by
     have M : Measurable fun x : β => (‖x‖₊ : ℝ≥0∞) := measurable_nnnorm.coe_nnreal_ennreal
     apply indep_fun.comp hXY M M
-  have A : (∫⁻ ω, ‖X ω * Y ω‖₊ ∂μ) < ∞ := h'XY.2
+  have A : ∫⁻ ω, ‖X ω * Y ω‖₊ ∂μ < ∞ := h'XY.2
   simp only [nnnorm_mul, ENNReal.coe_mul] at A 
   rw [lintegral_mul_eq_lintegral_mul_lintegral_of_indep_fun'' hX.ennnorm hY.ennnorm J, H] at A 
   simpa [ENNReal.top_mul', I] using A

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

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Martin Zinkevich, Vincent Beffara
 
 ! This file was ported from Lean 3 source module probability.integration
-! leanprover-community/mathlib commit 2f8347015b12b0864dfaf366ec4909eb70c78740
+! leanprover-community/mathlib commit 7e5137f579de09a059a5ce98f364a04e221aabf0
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -14,6 +14,9 @@ import Mathbin.Probability.Independence.Basic
 /-!
 # Integration in Probability Theory
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 Integration results for independent random variables. Specifically, for two
 independent random variables X and Y over the extended non-negative
 reals, `E[X * Y] = E[X] * E[Y]`, and similar results.

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

@@ -125,7 +125,7 @@ theorem lintegral_mul_eq_lintegral_mul_lintegral_of_indepFun (h_meas_f : Measura
 /-- If `f` and `g` with values in `ℝ≥0∞` are independent and almost everywhere measurable,
    then `E[f * g] = E[f] * E[g]` (slightly generalizing
    `lintegral_mul_eq_lintegral_mul_lintegral_of_indep_fun`). -/
-theorem lintegral_mul_eq_lintegral_mul_lintegral_of_indep_fun' (h_meas_f : AEMeasurable f μ)
+theorem lintegral_mul_eq_lintegral_mul_lintegral_of_indepFun' (h_meas_f : AEMeasurable f μ)
     (h_meas_g : AEMeasurable g μ) (h_indep_fun : IndepFun f g μ) :
     (∫⁻ ω, (f * g) ω ∂μ) = (∫⁻ ω, f ω ∂μ) * ∫⁻ ω, g ω ∂μ :=
   by
@@ -136,13 +136,13 @@ theorem lintegral_mul_eq_lintegral_mul_lintegral_of_indep_fun' (h_meas_f : AEMea
     lintegral_mul_eq_lintegral_mul_lintegral_of_indep_fun h_meas_f.measurable_mk
       h_meas_g.measurable_mk
   exact h_indep_fun.ae_eq h_meas_f.ae_eq_mk h_meas_g.ae_eq_mk
-#align probability_theory.lintegral_mul_eq_lintegral_mul_lintegral_of_indep_fun' ProbabilityTheory.lintegral_mul_eq_lintegral_mul_lintegral_of_indep_fun'
+#align probability_theory.lintegral_mul_eq_lintegral_mul_lintegral_of_indep_fun' ProbabilityTheory.lintegral_mul_eq_lintegral_mul_lintegral_of_indepFun'
 
-theorem lintegral_mul_eq_lintegral_mul_lintegral_of_indep_fun'' (h_meas_f : AEMeasurable f μ)
+theorem lintegral_mul_eq_lintegral_mul_lintegral_of_indepFun'' (h_meas_f : AEMeasurable f μ)
     (h_meas_g : AEMeasurable g μ) (h_indep_fun : IndepFun f g μ) :
     (∫⁻ ω, f ω * g ω ∂μ) = (∫⁻ ω, f ω ∂μ) * ∫⁻ ω, g ω ∂μ :=
-  lintegral_mul_eq_lintegral_mul_lintegral_of_indep_fun' h_meas_f h_meas_g h_indep_fun
-#align probability_theory.lintegral_mul_eq_lintegral_mul_lintegral_of_indep_fun'' ProbabilityTheory.lintegral_mul_eq_lintegral_mul_lintegral_of_indep_fun''
+  lintegral_mul_eq_lintegral_mul_lintegral_of_indepFun' h_meas_f h_meas_g h_indep_fun
+#align probability_theory.lintegral_mul_eq_lintegral_mul_lintegral_of_indep_fun'' ProbabilityTheory.lintegral_mul_eq_lintegral_mul_lintegral_of_indepFun''
 
 /-- The product of two independent, integrable, real_valued random variables is integrable. -/
 theorem IndepFun.integrable_mul {β : Type _} [MeasurableSpace β] {X Y : Ω → β}

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

@@ -47,7 +47,7 @@ namespace ProbabilityTheory
   `lintegral_mul_eq_lintegral_mul_lintegral_of_independent_measurable_space`. -/
 theorem lintegral_mul_indicator_eq_lintegral_mul_lintegral_indicator {Mf mΩ : MeasurableSpace Ω}
     {μ : Measure Ω} (hMf : Mf ≤ mΩ) (c : ℝ≥0∞) {T : Set Ω} (h_meas_T : MeasurableSet T)
-    (h_ind : IndepSetsCat { s | measurable_set[Mf] s } {T} μ) (h_meas_f : measurable[Mf] f) :
+    (h_ind : IndepSets {s | measurable_set[Mf] s} {T} μ) (h_meas_f : measurable[Mf] f) :
     (∫⁻ ω, f ω * T.indicator (fun _ => c) ω ∂μ) =
       (∫⁻ ω, f ω ∂μ) * ∫⁻ ω, T.indicator (fun _ => c) ω ∂μ :=
   by
@@ -87,7 +87,7 @@ theorem lintegral_mul_indicator_eq_lintegral_mul_lintegral_indicator {Mf mΩ : M
    a more common variant of the product of independent variables. -/
 theorem lintegral_mul_eq_lintegral_mul_lintegral_of_independent_measurableSpace
     {Mf Mg mΩ : MeasurableSpace Ω} {μ : Measure Ω} (hMf : Mf ≤ mΩ) (hMg : Mg ≤ mΩ)
-    (h_ind : IndepCat Mf Mg μ) (h_meas_f : measurable[Mf] f) (h_meas_g : measurable[Mg] g) :
+    (h_ind : Indep Mf Mg μ) (h_meas_f : measurable[Mf] f) (h_meas_g : measurable[Mg] g) :
     (∫⁻ ω, f ω * g ω ∂μ) = (∫⁻ ω, f ω ∂μ) * ∫⁻ ω, g ω ∂μ :=
   by
   revert g
@@ -114,19 +114,19 @@ theorem lintegral_mul_eq_lintegral_mul_lintegral_of_independent_measurableSpace
 
 /-- If `f` and `g` are independent random variables with values in `ℝ≥0∞`,
    then `E[f * g] = E[f] * E[g]`. -/
-theorem lintegral_mul_eq_lintegral_mul_lintegral_of_indepFunCat (h_meas_f : Measurable f)
-    (h_meas_g : Measurable g) (h_indep_fun : IndepFunCat f g μ) :
+theorem lintegral_mul_eq_lintegral_mul_lintegral_of_indepFun (h_meas_f : Measurable f)
+    (h_meas_g : Measurable g) (h_indep_fun : IndepFun f g μ) :
     (∫⁻ ω, (f * g) ω ∂μ) = (∫⁻ ω, f ω ∂μ) * ∫⁻ ω, g ω ∂μ :=
   lintegral_mul_eq_lintegral_mul_lintegral_of_independent_measurableSpace
     (measurable_iff_comap_le.1 h_meas_f) (measurable_iff_comap_le.1 h_meas_g) h_indep_fun
     (Measurable.of_comap_le le_rfl) (Measurable.of_comap_le le_rfl)
-#align probability_theory.lintegral_mul_eq_lintegral_mul_lintegral_of_indep_fun ProbabilityTheory.lintegral_mul_eq_lintegral_mul_lintegral_of_indepFunCat
+#align probability_theory.lintegral_mul_eq_lintegral_mul_lintegral_of_indep_fun ProbabilityTheory.lintegral_mul_eq_lintegral_mul_lintegral_of_indepFun
 
 /-- If `f` and `g` with values in `ℝ≥0∞` are independent and almost everywhere measurable,
    then `E[f * g] = E[f] * E[g]` (slightly generalizing
    `lintegral_mul_eq_lintegral_mul_lintegral_of_indep_fun`). -/
 theorem lintegral_mul_eq_lintegral_mul_lintegral_of_indep_fun' (h_meas_f : AEMeasurable f μ)
-    (h_meas_g : AEMeasurable g μ) (h_indep_fun : IndepFunCat f g μ) :
+    (h_meas_g : AEMeasurable g μ) (h_indep_fun : IndepFun f g μ) :
     (∫⁻ ω, (f * g) ω ∂μ) = (∫⁻ ω, f ω ∂μ) * ∫⁻ ω, g ω ∂μ :=
   by
   have fg_ae : f * g =ᵐ[μ] h_meas_f.mk _ * h_meas_g.mk _ := h_meas_f.ae_eq_mk.mul h_meas_g.ae_eq_mk
@@ -139,14 +139,14 @@ theorem lintegral_mul_eq_lintegral_mul_lintegral_of_indep_fun' (h_meas_f : AEMea
 #align probability_theory.lintegral_mul_eq_lintegral_mul_lintegral_of_indep_fun' ProbabilityTheory.lintegral_mul_eq_lintegral_mul_lintegral_of_indep_fun'
 
 theorem lintegral_mul_eq_lintegral_mul_lintegral_of_indep_fun'' (h_meas_f : AEMeasurable f μ)
-    (h_meas_g : AEMeasurable g μ) (h_indep_fun : IndepFunCat f g μ) :
+    (h_meas_g : AEMeasurable g μ) (h_indep_fun : IndepFun f g μ) :
     (∫⁻ ω, f ω * g ω ∂μ) = (∫⁻ ω, f ω ∂μ) * ∫⁻ ω, g ω ∂μ :=
   lintegral_mul_eq_lintegral_mul_lintegral_of_indep_fun' h_meas_f h_meas_g h_indep_fun
 #align probability_theory.lintegral_mul_eq_lintegral_mul_lintegral_of_indep_fun'' ProbabilityTheory.lintegral_mul_eq_lintegral_mul_lintegral_of_indep_fun''
 
 /-- The product of two independent, integrable, real_valued random variables is integrable. -/
-theorem IndepFunCat.integrable_mul {β : Type _} [MeasurableSpace β] {X Y : Ω → β}
-    [NormedDivisionRing β] [BorelSpace β] (hXY : IndepFunCat X Y μ) (hX : Integrable X μ)
+theorem IndepFun.integrable_mul {β : Type _} [MeasurableSpace β] {X Y : Ω → β}
+    [NormedDivisionRing β] [BorelSpace β] (hXY : IndepFun X Y μ) (hX : Integrable X μ)
     (hY : Integrable Y μ) : Integrable (X * Y) μ :=
   by
   let nX : Ω → ENNReal := fun a => ‖X a‖₊
@@ -162,12 +162,12 @@ theorem IndepFunCat.integrable_mul {β : Type _} [MeasurableSpace β] {X Y : Ω
   refine' ⟨hX.1.mul hY.1, _⟩
   simp_rw [has_finite_integral, Pi.mul_apply, nnnorm_mul, ENNReal.coe_mul, hmul]
   exact ennreal.mul_lt_top_iff.mpr (Or.inl ⟨hX.2, hY.2⟩)
-#align probability_theory.indep_fun.integrable_mul ProbabilityTheory.IndepFunCat.integrable_mul
+#align probability_theory.indep_fun.integrable_mul ProbabilityTheory.IndepFun.integrable_mul
 
 /-- If the product of two independent real_valued random variables is integrable and
 the second one is not almost everywhere zero, then the first one is integrable. -/
-theorem IndepFunCat.integrable_left_of_integrable_mul {β : Type _} [MeasurableSpace β] {X Y : Ω → β}
-    [NormedDivisionRing β] [BorelSpace β] (hXY : IndepFunCat X Y μ) (h'XY : Integrable (X * Y) μ)
+theorem IndepFun.integrable_left_of_integrable_mul {β : Type _} [MeasurableSpace β] {X Y : Ω → β}
+    [NormedDivisionRing β] [BorelSpace β] (hXY : IndepFun X Y μ) (h'XY : Integrable (X * Y) μ)
     (hX : AEStronglyMeasurable X μ) (hY : AEStronglyMeasurable Y μ) (h'Y : ¬Y =ᵐ[μ] 0) :
     Integrable X μ := by
   refine' ⟨hX, _⟩
@@ -175,7 +175,7 @@ theorem IndepFunCat.integrable_left_of_integrable_mul {β : Type _} [MeasurableS
     intro H
     have I : (fun ω => ↑‖Y ω‖₊) =ᵐ[μ] 0 := (lintegral_eq_zero_iff' hY.ennnorm).1 H
     apply h'Y
-    filter_upwards [I]with ω hω
+    filter_upwards [I] with ω hω
     simpa using hω
   apply lt_top_iff_ne_top.2 fun H => _
   have J : indep_fun (fun ω => ↑‖X ω‖₊) (fun ω => ↑‖Y ω‖₊) μ :=
@@ -186,21 +186,20 @@ theorem IndepFunCat.integrable_left_of_integrable_mul {β : Type _} [MeasurableS
   simp only [nnnorm_mul, ENNReal.coe_mul] at A 
   rw [lintegral_mul_eq_lintegral_mul_lintegral_of_indep_fun'' hX.ennnorm hY.ennnorm J, H] at A 
   simpa [ENNReal.top_mul', I] using A
-#align probability_theory.indep_fun.integrable_left_of_integrable_mul ProbabilityTheory.IndepFunCat.integrable_left_of_integrable_mul
+#align probability_theory.indep_fun.integrable_left_of_integrable_mul ProbabilityTheory.IndepFun.integrable_left_of_integrable_mul
 
 /-- If the product of two independent real_valued random variables is integrable and the
 first one is not almost everywhere zero, then the second one is integrable. -/
-theorem IndepFunCat.integrable_right_of_integrable_mul {β : Type _} [MeasurableSpace β]
-    {X Y : Ω → β} [NormedDivisionRing β] [BorelSpace β] (hXY : IndepFunCat X Y μ)
-    (h'XY : Integrable (X * Y) μ) (hX : AEStronglyMeasurable X μ) (hY : AEStronglyMeasurable Y μ)
-    (h'X : ¬X =ᵐ[μ] 0) : Integrable Y μ :=
-  by
+theorem IndepFun.integrable_right_of_integrable_mul {β : Type _} [MeasurableSpace β] {X Y : Ω → β}
+    [NormedDivisionRing β] [BorelSpace β] (hXY : IndepFun X Y μ) (h'XY : Integrable (X * Y) μ)
+    (hX : AEStronglyMeasurable X μ) (hY : AEStronglyMeasurable Y μ) (h'X : ¬X =ᵐ[μ] 0) :
+    Integrable Y μ := by
   refine' ⟨hY, _⟩
   have I : (∫⁻ ω, ‖X ω‖₊ ∂μ) ≠ 0 := by
     intro H
     have I : (fun ω => ↑‖X ω‖₊) =ᵐ[μ] 0 := (lintegral_eq_zero_iff' hX.ennnorm).1 H
     apply h'X
-    filter_upwards [I]with ω hω
+    filter_upwards [I] with ω hω
     simpa using hω
   apply lt_top_iff_ne_top.2 fun H => _
   have J : indep_fun (fun ω => ↑‖X ω‖₊) (fun ω => ↑‖Y ω‖₊) μ :=
@@ -211,12 +210,12 @@ theorem IndepFunCat.integrable_right_of_integrable_mul {β : Type _} [Measurable
   simp only [nnnorm_mul, ENNReal.coe_mul] at A 
   rw [lintegral_mul_eq_lintegral_mul_lintegral_of_indep_fun'' hX.ennnorm hY.ennnorm J, H] at A 
   simpa [ENNReal.top_mul', I] using A
-#align probability_theory.indep_fun.integrable_right_of_integrable_mul ProbabilityTheory.IndepFunCat.integrable_right_of_integrable_mul
+#align probability_theory.indep_fun.integrable_right_of_integrable_mul ProbabilityTheory.IndepFun.integrable_right_of_integrable_mul
 
 /-- The (Bochner) integral of the product of two independent, nonnegative random
   variables is the product of their integrals. The proof is just plumbing around
   `lintegral_mul_eq_lintegral_mul_lintegral_of_indep_fun'`. -/
-theorem IndepFunCat.integral_mul_of_nonneg (hXY : IndepFunCat X Y μ) (hXp : 0 ≤ X) (hYp : 0 ≤ Y)
+theorem IndepFun.integral_mul_of_nonneg (hXY : IndepFun X Y μ) (hXp : 0 ≤ X) (hYp : 0 ≤ Y)
     (hXm : AEMeasurable X μ) (hYm : AEMeasurable Y μ) :
     integral μ (X * Y) = integral μ X * integral μ Y :=
   by
@@ -233,13 +232,13 @@ theorem IndepFunCat.integral_mul_of_nonneg (hXY : IndepFunCat X Y μ) (hXp : 0 
   congr
   apply lintegral_mul_eq_lintegral_mul_lintegral_of_indep_fun' h1 h2
   exact hXY.comp ENNReal.measurable_ofReal ENNReal.measurable_ofReal
-#align probability_theory.indep_fun.integral_mul_of_nonneg ProbabilityTheory.IndepFunCat.integral_mul_of_nonneg
+#align probability_theory.indep_fun.integral_mul_of_nonneg ProbabilityTheory.IndepFun.integral_mul_of_nonneg
 
 /-- The (Bochner) integral of the product of two independent, integrable random
   variables is the product of their integrals. The proof is pedestrian decomposition
   into their positive and negative parts in order to apply `indep_fun.integral_mul_of_nonneg`
   four times. -/
-theorem IndepFunCat.integral_mul_of_integrable (hXY : IndepFunCat X Y μ) (hX : Integrable X μ)
+theorem IndepFun.integral_mul_of_integrable (hXY : IndepFun X Y μ) (hX : Integrable X μ)
     (hY : Integrable Y μ) : integral μ (X * Y) = integral μ X * integral μ Y :=
   by
   let pos : ℝ → ℝ := fun x => max x 0
@@ -281,22 +280,22 @@ theorem IndepFunCat.integral_mul_of_integrable (hXY : IndepFunCat X Y μ) (hX :
     hi2.integral_mul_of_nonneg hp2 hp3 hm2 hm3, hi3.integral_mul_of_nonneg hp1 hp4 hm1 hm4,
     hi4.integral_mul_of_nonneg hp2 hp4 hm2 hm4]
   ring
-#align probability_theory.indep_fun.integral_mul_of_integrable ProbabilityTheory.IndepFunCat.integral_mul_of_integrable
+#align probability_theory.indep_fun.integral_mul_of_integrable ProbabilityTheory.IndepFun.integral_mul_of_integrable
 
 /-- The (Bochner) integral of the product of two independent random
   variables is the product of their integrals. -/
-theorem IndepFunCat.integral_mul (hXY : IndepFunCat X Y μ) (hX : AEStronglyMeasurable X μ)
+theorem IndepFun.integral_mul (hXY : IndepFun X Y μ) (hX : AEStronglyMeasurable X μ)
     (hY : AEStronglyMeasurable Y μ) : integral μ (X * Y) = integral μ X * integral μ Y :=
   by
   by_cases h'X : X =ᵐ[μ] 0
   · have h' : X * Y =ᵐ[μ] 0 := by
-      filter_upwards [h'X]with ω hω
+      filter_upwards [h'X] with ω hω
       simp [hω]
     simp only [integral_congr_ae h'X, integral_congr_ae h', Pi.zero_apply, integral_const,
       Algebra.id.smul_eq_mul, MulZeroClass.mul_zero, MulZeroClass.zero_mul]
   by_cases h'Y : Y =ᵐ[μ] 0
   · have h' : X * Y =ᵐ[μ] 0 := by
-      filter_upwards [h'Y]with ω hω
+      filter_upwards [h'Y] with ω hω
       simp [hω]
     simp only [integral_congr_ae h'Y, integral_congr_ae h', Pi.zero_apply, integral_const,
       Algebra.id.smul_eq_mul, MulZeroClass.mul_zero, MulZeroClass.zero_mul]
@@ -310,20 +309,20 @@ theorem IndepFunCat.integral_mul (hXY : IndepFunCat X Y μ) (hX : AEStronglyMeas
       exact h (hXY.integrable_mul HX HY)
     rw [not_and_or] at I 
     cases I <;> simp [integral_undef, I, h]
-#align probability_theory.indep_fun.integral_mul ProbabilityTheory.IndepFunCat.integral_mul
+#align probability_theory.indep_fun.integral_mul ProbabilityTheory.IndepFun.integral_mul
 
-theorem IndepFunCat.integral_mul' (hXY : IndepFunCat X Y μ) (hX : AEStronglyMeasurable X μ)
+theorem IndepFun.integral_mul' (hXY : IndepFun X Y μ) (hX : AEStronglyMeasurable X μ)
     (hY : AEStronglyMeasurable Y μ) :
     (integral μ fun ω => X ω * Y ω) = integral μ X * integral μ Y :=
   hXY.integral_mul hX hY
-#align probability_theory.indep_fun.integral_mul' ProbabilityTheory.IndepFunCat.integral_mul'
+#align probability_theory.indep_fun.integral_mul' ProbabilityTheory.IndepFun.integral_mul'
 
 /-- Independence of functions `f` and `g` into arbitrary types is characterized by the relation
   `E[(φ ∘ f) * (ψ ∘ g)] = E[φ ∘ f] * E[ψ ∘ g]` for all measurable `φ` and `ψ` with values in `ℝ`
   satisfying appropriate integrability conditions. -/
-theorem indepFunCat_iff_integral_comp_mul [FiniteMeasure μ] {β β' : Type _} {mβ : MeasurableSpace β}
+theorem indepFun_iff_integral_comp_mul [IsFiniteMeasure μ] {β β' : Type _} {mβ : MeasurableSpace β}
     {mβ' : MeasurableSpace β'} {f : Ω → β} {g : Ω → β'} {hfm : Measurable f} {hgm : Measurable g} :
-    IndepFunCat f g μ ↔
+    IndepFun f g μ ↔
       ∀ {φ : β → ℝ} {ψ : β' → ℝ},
         Measurable φ →
           Measurable ψ →
@@ -341,7 +340,7 @@ theorem indepFunCat_iff_integral_comp_mul [FiniteMeasure μ] {β β' : Type _} {
     integral_indicator_one ((hfm hA).inter (hgm hB)), ← integral_indicator_one (hfm hA), ←
     integral_indicator_one (hgm hB), Set.inter_indicator_one]
   exact ENNReal.mul_ne_top (measure_ne_top μ _) (measure_ne_top μ _)
-#align probability_theory.indep_fun_iff_integral_comp_mul ProbabilityTheory.indepFunCat_iff_integral_comp_mul
+#align probability_theory.indep_fun_iff_integral_comp_mul ProbabilityTheory.indepFun_iff_integral_comp_mul
 
 end ProbabilityTheory
 

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

@@ -183,8 +183,8 @@ theorem IndepFunCat.integrable_left_of_integrable_mul {β : Type _} [MeasurableS
     have M : Measurable fun x : β => (‖x‖₊ : ℝ≥0∞) := measurable_nnnorm.coe_nnreal_ennreal
     apply indep_fun.comp hXY M M
   have A : (∫⁻ ω, ‖X ω * Y ω‖₊ ∂μ) < ∞ := h'XY.2
-  simp only [nnnorm_mul, ENNReal.coe_mul] at A
-  rw [lintegral_mul_eq_lintegral_mul_lintegral_of_indep_fun'' hX.ennnorm hY.ennnorm J, H] at A
+  simp only [nnnorm_mul, ENNReal.coe_mul] at A 
+  rw [lintegral_mul_eq_lintegral_mul_lintegral_of_indep_fun'' hX.ennnorm hY.ennnorm J, H] at A 
   simpa [ENNReal.top_mul', I] using A
 #align probability_theory.indep_fun.integrable_left_of_integrable_mul ProbabilityTheory.IndepFunCat.integrable_left_of_integrable_mul
 
@@ -208,8 +208,8 @@ theorem IndepFunCat.integrable_right_of_integrable_mul {β : Type _} [Measurable
     have M : Measurable fun x : β => (‖x‖₊ : ℝ≥0∞) := measurable_nnnorm.coe_nnreal_ennreal
     apply indep_fun.comp hXY M M
   have A : (∫⁻ ω, ‖X ω * Y ω‖₊ ∂μ) < ∞ := h'XY.2
-  simp only [nnnorm_mul, ENNReal.coe_mul] at A
-  rw [lintegral_mul_eq_lintegral_mul_lintegral_of_indep_fun'' hX.ennnorm hY.ennnorm J, H] at A
+  simp only [nnnorm_mul, ENNReal.coe_mul] at A 
+  rw [lintegral_mul_eq_lintegral_mul_lintegral_of_indep_fun'' hX.ennnorm hY.ennnorm J, H] at A 
   simpa [ENNReal.top_mul', I] using A
 #align probability_theory.indep_fun.integrable_right_of_integrable_mul ProbabilityTheory.IndepFunCat.integrable_right_of_integrable_mul
 
@@ -308,7 +308,7 @@ theorem IndepFunCat.integral_mul (hXY : IndepFunCat X Y μ) (hX : AEStronglyMeas
       by
       rintro ⟨HX, HY⟩
       exact h (hXY.integrable_mul HX HY)
-    rw [not_and_or] at I
+    rw [not_and_or] at I 
     cases I <;> simp [integral_undef, I, h]
 #align probability_theory.indep_fun.integral_mul ProbabilityTheory.IndepFunCat.integral_mul
 

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

@@ -36,7 +36,7 @@ noncomputable section
 
 open Set MeasureTheory
 
-open ENNReal MeasureTheory
+open scoped ENNReal MeasureTheory
 
 variable {Ω : Type _} {mΩ : MeasurableSpace Ω} {μ : Measure Ω} {f g : Ω → ℝ≥0∞} {X Y : Ω → ℝ}
 

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

@@ -168,7 +168,7 @@ theorem IndepFunCat.integrable_mul {β : Type _} [MeasurableSpace β] {X Y : Ω
 the second one is not almost everywhere zero, then the first one is integrable. -/
 theorem IndepFunCat.integrable_left_of_integrable_mul {β : Type _} [MeasurableSpace β] {X Y : Ω → β}
     [NormedDivisionRing β] [BorelSpace β] (hXY : IndepFunCat X Y μ) (h'XY : Integrable (X * Y) μ)
-    (hX : AeStronglyMeasurable X μ) (hY : AeStronglyMeasurable Y μ) (h'Y : ¬Y =ᵐ[μ] 0) :
+    (hX : AEStronglyMeasurable X μ) (hY : AEStronglyMeasurable Y μ) (h'Y : ¬Y =ᵐ[μ] 0) :
     Integrable X μ := by
   refine' ⟨hX, _⟩
   have I : (∫⁻ ω, ‖Y ω‖₊ ∂μ) ≠ 0 := by
@@ -192,7 +192,7 @@ theorem IndepFunCat.integrable_left_of_integrable_mul {β : Type _} [MeasurableS
 first one is not almost everywhere zero, then the second one is integrable. -/
 theorem IndepFunCat.integrable_right_of_integrable_mul {β : Type _} [MeasurableSpace β]
     {X Y : Ω → β} [NormedDivisionRing β] [BorelSpace β] (hXY : IndepFunCat X Y μ)
-    (h'XY : Integrable (X * Y) μ) (hX : AeStronglyMeasurable X μ) (hY : AeStronglyMeasurable Y μ)
+    (h'XY : Integrable (X * Y) μ) (hX : AEStronglyMeasurable X μ) (hY : AEStronglyMeasurable Y μ)
     (h'X : ¬X =ᵐ[μ] 0) : Integrable Y μ :=
   by
   refine' ⟨hY, _⟩
@@ -285,8 +285,8 @@ theorem IndepFunCat.integral_mul_of_integrable (hXY : IndepFunCat X Y μ) (hX :
 
 /-- The (Bochner) integral of the product of two independent random
   variables is the product of their integrals. -/
-theorem IndepFunCat.integral_mul (hXY : IndepFunCat X Y μ) (hX : AeStronglyMeasurable X μ)
-    (hY : AeStronglyMeasurable Y μ) : integral μ (X * Y) = integral μ X * integral μ Y :=
+theorem IndepFunCat.integral_mul (hXY : IndepFunCat X Y μ) (hX : AEStronglyMeasurable X μ)
+    (hY : AEStronglyMeasurable Y μ) : integral μ (X * Y) = integral μ X * integral μ Y :=
   by
   by_cases h'X : X =ᵐ[μ] 0
   · have h' : X * Y =ᵐ[μ] 0 := by
@@ -312,8 +312,8 @@ theorem IndepFunCat.integral_mul (hXY : IndepFunCat X Y μ) (hX : AeStronglyMeas
     cases I <;> simp [integral_undef, I, h]
 #align probability_theory.indep_fun.integral_mul ProbabilityTheory.IndepFunCat.integral_mul
 
-theorem IndepFunCat.integral_mul' (hXY : IndepFunCat X Y μ) (hX : AeStronglyMeasurable X μ)
-    (hY : AeStronglyMeasurable Y μ) :
+theorem IndepFunCat.integral_mul' (hXY : IndepFunCat X Y μ) (hX : AEStronglyMeasurable X μ)
+    (hY : AEStronglyMeasurable Y μ) :
     (integral μ fun ω => X ω * Y ω) = integral μ X * integral μ Y :=
   hXY.integral_mul hX hY
 #align probability_theory.indep_fun.integral_mul' ProbabilityTheory.IndepFunCat.integral_mul'

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

@@ -54,7 +54,7 @@ theorem lintegral_mul_indicator_eq_lintegral_mul_lintegral_indicator {Mf mΩ : M
   revert f
   have h_mul_indicator : ∀ g, Measurable g → Measurable fun a => g a * T.indicator (fun x => c) a :=
     fun g h_mg => h_mg.mul (measurable_const.indicator h_meas_T)
-  apply Measurable.eNNReal_induction
+  apply Measurable.ennreal_induction
   · intro c' s' h_meas_s'
     simp_rw [← inter_indicator_mul]
     rw [lintegral_indicator _ (MeasurableSet.inter (hMf _ h_meas_s') h_meas_T),
@@ -92,7 +92,7 @@ theorem lintegral_mul_eq_lintegral_mul_lintegral_of_independent_measurableSpace
   by
   revert g
   have h_measM_f : Measurable f := h_meas_f.mono hMf le_rfl
-  apply Measurable.eNNReal_induction
+  apply Measurable.ennreal_induction
   · intro c s h_s
     apply lintegral_mul_indicator_eq_lintegral_mul_lintegral_indicator hMf _ (hMg _ h_s) _ h_meas_f
     apply indep_sets_of_indep_sets_of_le_right h_ind

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

@@ -154,9 +154,9 @@ theorem IndepFunCat.integrable_mul {β : Type _} [MeasurableSpace β] {X Y : Ω
   have hXY' : indep_fun (fun a => ‖X a‖₊) (fun a => ‖Y a‖₊) μ :=
     hXY.comp measurable_nnnorm measurable_nnnorm
   have hXY'' : indep_fun nX nY μ :=
-    hXY'.comp measurable_coe_nNReal_eNNReal measurable_coe_nNReal_eNNReal
-  have hnX : AEMeasurable nX μ := hX.1.AEMeasurable.nnnorm.coe_nNReal_eNNReal
-  have hnY : AEMeasurable nY μ := hY.1.AEMeasurable.nnnorm.coe_nNReal_eNNReal
+    hXY'.comp measurable_coe_nnreal_ennreal measurable_coe_nnreal_ennreal
+  have hnX : AEMeasurable nX μ := hX.1.AEMeasurable.nnnorm.coe_nnreal_ennreal
+  have hnY : AEMeasurable nY μ := hY.1.AEMeasurable.nnnorm.coe_nnreal_ennreal
   have hmul : (∫⁻ a, nX a * nY a ∂μ) = (∫⁻ a, nX a ∂μ) * ∫⁻ a, nY a ∂μ := by
     convert lintegral_mul_eq_lintegral_mul_lintegral_of_indep_fun' hnX hnY hXY''
   refine' ⟨hX.1.mul hY.1, _⟩

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

@@ -72,8 +72,8 @@ theorem lintegral_mul_indicator_eq_lintegral_mul_lintegral_indicator {Mf mΩ : M
       right_distrib, h_ind_f', h_ind_g]
   · intro f h_meas_f h_mono_f h_ind_f
     have h_measM_f : ∀ n, Measurable (f n) := fun n => (h_meas_f n).mono hMf le_rfl
-    simp_rw [ENNReal.supᵢ_mul]
-    rw [lintegral_supr h_measM_f h_mono_f, lintegral_supr, ENNReal.supᵢ_mul]
+    simp_rw [ENNReal.iSup_mul]
+    rw [lintegral_supr h_measM_f h_mono_f, lintegral_supr, ENNReal.iSup_mul]
     · simp_rw [← h_ind_f]
     · exact fun n => h_mul_indicator _ (h_measM_f n)
     · exact fun m n h_le a => mul_le_mul_right' (h_mono_f h_le a) _
@@ -105,8 +105,8 @@ theorem lintegral_mul_eq_lintegral_mul_lintegral_of_independent_measurableSpace
       h_ind_f', h_ind_g']
   · intro f' h_meas_f' h_mono_f' h_ind_f'
     have h_measM_f' : ∀ n, Measurable (f' n) := fun n => (h_meas_f' n).mono hMg le_rfl
-    simp_rw [ENNReal.mul_supᵢ]
-    rw [lintegral_supr, lintegral_supr h_measM_f' h_mono_f', ENNReal.mul_supᵢ]
+    simp_rw [ENNReal.mul_iSup]
+    rw [lintegral_supr, lintegral_supr h_measM_f' h_mono_f', ENNReal.mul_iSup]
     · simp_rw [← h_ind_f']
     · exact fun n => h_measM_f.mul (h_measM_f' n)
     · exact fun n m (h_le : n ≤ m) a => mul_le_mul_left' (h_mono_f' h_le a) _

mathlib commit https://github.com/leanprover-community/mathlib/commit/2f8347015b12b0864dfaf366ec4909eb70c78740

@@ -4,12 +4,12 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Martin Zinkevich, Vincent Beffara
 
 ! This file was ported from Lean 3 source module probability.integration
-! leanprover-community/mathlib commit 57ac39bd365c2f80589a700f9fbb664d3a1a30c2
+! leanprover-community/mathlib commit 2f8347015b12b0864dfaf366ec4909eb70c78740
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
 import Mathbin.MeasureTheory.Integral.SetIntegral
-import Mathbin.Probability.Independence
+import Mathbin.Probability.Independence.Basic
 
 /-!
 # Integration in Probability Theory

mathlib commit https://github.com/leanprover-community/mathlib/commit/28b2a92f2996d28e580450863c130955de0ed398

@@ -4,12 +4,12 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Martin Zinkevich, Vincent Beffara
 
 ! This file was ported from Lean 3 source module probability.integration
-! leanprover-community/mathlib commit 2f8347015b12b0864dfaf366ec4909eb70c78740
+! leanprover-community/mathlib commit 57ac39bd365c2f80589a700f9fbb664d3a1a30c2
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
 import Mathbin.MeasureTheory.Integral.SetIntegral
-import Mathbin.Probability.Independence.Basic
+import Mathbin.Probability.Independence
 
 /-!
 # Integration in Probability Theory

mathlib commit https://github.com/leanprover-community/mathlib/commit/2f8347015b12b0864dfaf366ec4909eb70c78740

@@ -4,12 +4,12 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Martin Zinkevich, Vincent Beffara
 
 ! This file was ported from Lean 3 source module probability.integration
-! leanprover-community/mathlib commit 57ac39bd365c2f80589a700f9fbb664d3a1a30c2
+! leanprover-community/mathlib commit 2f8347015b12b0864dfaf366ec4909eb70c78740
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
 import Mathbin.MeasureTheory.Integral.SetIntegral
-import Mathbin.Probability.Independence
+import Mathbin.Probability.Independence.Basic
 
 /-!
 # Integration in Probability Theory

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

@@ -321,9 +321,8 @@ theorem IndepFunCat.integral_mul' (hXY : IndepFunCat X Y μ) (hX : AeStronglyMea
 /-- Independence of functions `f` and `g` into arbitrary types is characterized by the relation
   `E[(φ ∘ f) * (ψ ∘ g)] = E[φ ∘ f] * E[ψ ∘ g]` for all measurable `φ` and `ψ` with values in `ℝ`
   satisfying appropriate integrability conditions. -/
-theorem indepFunCat_iff_integral_comp_mul [IsFiniteMeasure μ] {β β' : Type _}
-    {mβ : MeasurableSpace β} {mβ' : MeasurableSpace β'} {f : Ω → β} {g : Ω → β'}
-    {hfm : Measurable f} {hgm : Measurable g} :
+theorem indepFunCat_iff_integral_comp_mul [FiniteMeasure μ] {β β' : Type _} {mβ : MeasurableSpace β}
+    {mβ' : MeasurableSpace β'} {f : Ω → β} {g : Ω → β'} {hfm : Measurable f} {hgm : Measurable g} :
     IndepFunCat f g μ ↔
       ∀ {φ : β → ℝ} {ψ : β' → ℝ},
         Measurable φ →

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

@@ -125,8 +125,8 @@ theorem lintegral_mul_eq_lintegral_mul_lintegral_of_indepFunCat (h_meas_f : Meas
 /-- If `f` and `g` with values in `ℝ≥0∞` are independent and almost everywhere measurable,
    then `E[f * g] = E[f] * E[g]` (slightly generalizing
    `lintegral_mul_eq_lintegral_mul_lintegral_of_indep_fun`). -/
-theorem lintegral_mul_eq_lintegral_mul_lintegral_of_indep_fun' (h_meas_f : AeMeasurable f μ)
-    (h_meas_g : AeMeasurable g μ) (h_indep_fun : IndepFunCat f g μ) :
+theorem lintegral_mul_eq_lintegral_mul_lintegral_of_indep_fun' (h_meas_f : AEMeasurable f μ)
+    (h_meas_g : AEMeasurable g μ) (h_indep_fun : IndepFunCat f g μ) :
     (∫⁻ ω, (f * g) ω ∂μ) = (∫⁻ ω, f ω ∂μ) * ∫⁻ ω, g ω ∂μ :=
   by
   have fg_ae : f * g =ᵐ[μ] h_meas_f.mk _ * h_meas_g.mk _ := h_meas_f.ae_eq_mk.mul h_meas_g.ae_eq_mk
@@ -138,14 +138,14 @@ theorem lintegral_mul_eq_lintegral_mul_lintegral_of_indep_fun' (h_meas_f : AeMea
   exact h_indep_fun.ae_eq h_meas_f.ae_eq_mk h_meas_g.ae_eq_mk
 #align probability_theory.lintegral_mul_eq_lintegral_mul_lintegral_of_indep_fun' ProbabilityTheory.lintegral_mul_eq_lintegral_mul_lintegral_of_indep_fun'
 
-theorem lintegral_mul_eq_lintegral_mul_lintegral_of_indep_fun'' (h_meas_f : AeMeasurable f μ)
-    (h_meas_g : AeMeasurable g μ) (h_indep_fun : IndepFunCat f g μ) :
+theorem lintegral_mul_eq_lintegral_mul_lintegral_of_indep_fun'' (h_meas_f : AEMeasurable f μ)
+    (h_meas_g : AEMeasurable g μ) (h_indep_fun : IndepFunCat f g μ) :
     (∫⁻ ω, f ω * g ω ∂μ) = (∫⁻ ω, f ω ∂μ) * ∫⁻ ω, g ω ∂μ :=
   lintegral_mul_eq_lintegral_mul_lintegral_of_indep_fun' h_meas_f h_meas_g h_indep_fun
 #align probability_theory.lintegral_mul_eq_lintegral_mul_lintegral_of_indep_fun'' ProbabilityTheory.lintegral_mul_eq_lintegral_mul_lintegral_of_indep_fun''
 
 /-- The product of two independent, integrable, real_valued random variables is integrable. -/
-theorem IndepFunCat.integrableMul {β : Type _} [MeasurableSpace β] {X Y : Ω → β}
+theorem IndepFunCat.integrable_mul {β : Type _} [MeasurableSpace β] {X Y : Ω → β}
     [NormedDivisionRing β] [BorelSpace β] (hXY : IndepFunCat X Y μ) (hX : Integrable X μ)
     (hY : Integrable Y μ) : Integrable (X * Y) μ :=
   by
@@ -155,18 +155,18 @@ theorem IndepFunCat.integrableMul {β : Type _} [MeasurableSpace β] {X Y : Ω 
     hXY.comp measurable_nnnorm measurable_nnnorm
   have hXY'' : indep_fun nX nY μ :=
     hXY'.comp measurable_coe_nNReal_eNNReal measurable_coe_nNReal_eNNReal
-  have hnX : AeMeasurable nX μ := hX.1.AeMeasurable.nnnorm.coe_nNReal_eNNReal
-  have hnY : AeMeasurable nY μ := hY.1.AeMeasurable.nnnorm.coe_nNReal_eNNReal
+  have hnX : AEMeasurable nX μ := hX.1.AEMeasurable.nnnorm.coe_nNReal_eNNReal
+  have hnY : AEMeasurable nY μ := hY.1.AEMeasurable.nnnorm.coe_nNReal_eNNReal
   have hmul : (∫⁻ a, nX a * nY a ∂μ) = (∫⁻ a, nX a ∂μ) * ∫⁻ a, nY a ∂μ := by
     convert lintegral_mul_eq_lintegral_mul_lintegral_of_indep_fun' hnX hnY hXY''
   refine' ⟨hX.1.mul hY.1, _⟩
   simp_rw [has_finite_integral, Pi.mul_apply, nnnorm_mul, ENNReal.coe_mul, hmul]
   exact ennreal.mul_lt_top_iff.mpr (Or.inl ⟨hX.2, hY.2⟩)
-#align probability_theory.indep_fun.integrable_mul ProbabilityTheory.IndepFunCat.integrableMul
+#align probability_theory.indep_fun.integrable_mul ProbabilityTheory.IndepFunCat.integrable_mul
 
 /-- If the product of two independent real_valued random variables is integrable and
 the second one is not almost everywhere zero, then the first one is integrable. -/
-theorem IndepFunCat.integrableLeftOfIntegrableMul {β : Type _} [MeasurableSpace β] {X Y : Ω → β}
+theorem IndepFunCat.integrable_left_of_integrable_mul {β : Type _} [MeasurableSpace β] {X Y : Ω → β}
     [NormedDivisionRing β] [BorelSpace β] (hXY : IndepFunCat X Y μ) (h'XY : Integrable (X * Y) μ)
     (hX : AeStronglyMeasurable X μ) (hY : AeStronglyMeasurable Y μ) (h'Y : ¬Y =ᵐ[μ] 0) :
     Integrable X μ := by
@@ -186,14 +186,15 @@ theorem IndepFunCat.integrableLeftOfIntegrableMul {β : Type _} [MeasurableSpace
   simp only [nnnorm_mul, ENNReal.coe_mul] at A
   rw [lintegral_mul_eq_lintegral_mul_lintegral_of_indep_fun'' hX.ennnorm hY.ennnorm J, H] at A
   simpa [ENNReal.top_mul', I] using A
-#align probability_theory.indep_fun.integrable_left_of_integrable_mul ProbabilityTheory.IndepFunCat.integrableLeftOfIntegrableMul
+#align probability_theory.indep_fun.integrable_left_of_integrable_mul ProbabilityTheory.IndepFunCat.integrable_left_of_integrable_mul
 
 /-- If the product of two independent real_valued random variables is integrable and the
 first one is not almost everywhere zero, then the second one is integrable. -/
-theorem IndepFunCat.integrableRightOfIntegrableMul {β : Type _} [MeasurableSpace β] {X Y : Ω → β}
-    [NormedDivisionRing β] [BorelSpace β] (hXY : IndepFunCat X Y μ) (h'XY : Integrable (X * Y) μ)
-    (hX : AeStronglyMeasurable X μ) (hY : AeStronglyMeasurable Y μ) (h'X : ¬X =ᵐ[μ] 0) :
-    Integrable Y μ := by
+theorem IndepFunCat.integrable_right_of_integrable_mul {β : Type _} [MeasurableSpace β]
+    {X Y : Ω → β} [NormedDivisionRing β] [BorelSpace β] (hXY : IndepFunCat X Y μ)
+    (h'XY : Integrable (X * Y) μ) (hX : AeStronglyMeasurable X μ) (hY : AeStronglyMeasurable Y μ)
+    (h'X : ¬X =ᵐ[μ] 0) : Integrable Y μ :=
+  by
   refine' ⟨hY, _⟩
   have I : (∫⁻ ω, ‖X ω‖₊ ∂μ) ≠ 0 := by
     intro H
@@ -210,20 +211,20 @@ theorem IndepFunCat.integrableRightOfIntegrableMul {β : Type _} [MeasurableSpac
   simp only [nnnorm_mul, ENNReal.coe_mul] at A
   rw [lintegral_mul_eq_lintegral_mul_lintegral_of_indep_fun'' hX.ennnorm hY.ennnorm J, H] at A
   simpa [ENNReal.top_mul', I] using A
-#align probability_theory.indep_fun.integrable_right_of_integrable_mul ProbabilityTheory.IndepFunCat.integrableRightOfIntegrableMul
+#align probability_theory.indep_fun.integrable_right_of_integrable_mul ProbabilityTheory.IndepFunCat.integrable_right_of_integrable_mul
 
 /-- The (Bochner) integral of the product of two independent, nonnegative random
   variables is the product of their integrals. The proof is just plumbing around
   `lintegral_mul_eq_lintegral_mul_lintegral_of_indep_fun'`. -/
 theorem IndepFunCat.integral_mul_of_nonneg (hXY : IndepFunCat X Y μ) (hXp : 0 ≤ X) (hYp : 0 ≤ Y)
-    (hXm : AeMeasurable X μ) (hYm : AeMeasurable Y μ) :
+    (hXm : AEMeasurable X μ) (hYm : AEMeasurable Y μ) :
     integral μ (X * Y) = integral μ X * integral μ Y :=
   by
-  have h1 : AeMeasurable (fun a => ENNReal.ofReal (X a)) μ :=
+  have h1 : AEMeasurable (fun a => ENNReal.ofReal (X a)) μ :=
     ennreal.measurable_of_real.comp_ae_measurable hXm
-  have h2 : AeMeasurable (fun a => ENNReal.ofReal (Y a)) μ :=
+  have h2 : AEMeasurable (fun a => ENNReal.ofReal (Y a)) μ :=
     ennreal.measurable_of_real.comp_ae_measurable hYm
-  have h3 : AeMeasurable (X * Y) μ := hXm.mul hYm
+  have h3 : AEMeasurable (X * Y) μ := hXm.mul hYm
   have h4 : 0 ≤ᵐ[μ] X * Y := ae_of_all _ fun ω => mul_nonneg (hXp ω) (hYp ω)
   rw [integral_eq_lintegral_of_nonneg_ae (ae_of_all _ hXp) hXm.ae_strongly_measurable,
     integral_eq_lintegral_of_nonneg_ae (ae_of_all _ hYp) hYm.ae_strongly_measurable,
@@ -256,10 +257,10 @@ theorem IndepFunCat.integral_mul_of_integrable (hXY : IndepFunCat X Y μ) (hX :
   have hp2 : 0 ≤ Xp := fun ω => le_max_right _ _
   have hp3 : 0 ≤ Ym := fun ω => le_max_right _ _
   have hp4 : 0 ≤ Yp := fun ω => le_max_right _ _
-  have hm1 : AeMeasurable Xm μ := hX.1.AeMeasurable.neg.max aeMeasurableConst
-  have hm2 : AeMeasurable Xp μ := hX.1.AeMeasurable.max aeMeasurableConst
-  have hm3 : AeMeasurable Ym μ := hY.1.AeMeasurable.neg.max aeMeasurableConst
-  have hm4 : AeMeasurable Yp μ := hY.1.AeMeasurable.max aeMeasurableConst
+  have hm1 : AEMeasurable Xm μ := hX.1.AEMeasurable.neg.max aemeasurable_const
+  have hm2 : AEMeasurable Xp μ := hX.1.AEMeasurable.max aemeasurable_const
+  have hm3 : AEMeasurable Ym μ := hY.1.AEMeasurable.neg.max aemeasurable_const
+  have hm4 : AEMeasurable Yp μ := hY.1.AEMeasurable.max aemeasurable_const
   have hv1 : integrable Xm μ := hX.neg_part
   have hv2 : integrable Xp μ := hX.pos_part
   have hv3 : integrable Ym μ := hY.neg_part

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

@@ -292,13 +292,13 @@ theorem IndepFunCat.integral_mul (hXY : IndepFunCat X Y μ) (hX : AeStronglyMeas
       filter_upwards [h'X]with ω hω
       simp [hω]
     simp only [integral_congr_ae h'X, integral_congr_ae h', Pi.zero_apply, integral_const,
-      Algebra.id.smul_eq_mul, mul_zero, zero_mul]
+      Algebra.id.smul_eq_mul, MulZeroClass.mul_zero, MulZeroClass.zero_mul]
   by_cases h'Y : Y =ᵐ[μ] 0
   · have h' : X * Y =ᵐ[μ] 0 := by
       filter_upwards [h'Y]with ω hω
       simp [hω]
     simp only [integral_congr_ae h'Y, integral_congr_ae h', Pi.zero_apply, integral_const,
-      Algebra.id.smul_eq_mul, mul_zero, zero_mul]
+      Algebra.id.smul_eq_mul, MulZeroClass.mul_zero, MulZeroClass.zero_mul]
   by_cases h : integrable (X * Y) μ
   · have HX : integrable X μ := hXY.integrable_left_of_integrable_mul h hX hY h'Y
     have HY : integrable Y μ := hXY.integrable_right_of_integrable_mul h hX hY h'X

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

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Martin Zinkevich, Vincent Beffara
 
 ! This file was ported from Lean 3 source module probability.integration
-! leanprover-community/mathlib commit 17ef379e997badd73e5eabb4d38f11919ab3c4b3
+! leanprover-community/mathlib commit 57ac39bd365c2f80589a700f9fbb664d3a1a30c2
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -76,7 +76,7 @@ theorem lintegral_mul_indicator_eq_lintegral_mul_lintegral_indicator {Mf mΩ : M
     rw [lintegral_supr h_measM_f h_mono_f, lintegral_supr, ENNReal.supᵢ_mul]
     · simp_rw [← h_ind_f]
     · exact fun n => h_mul_indicator _ (h_measM_f n)
-    · exact fun m n h_le a => ENNReal.mul_le_mul (h_mono_f h_le a) le_rfl
+    · exact fun m n h_le a => mul_le_mul_right' (h_mono_f h_le a) _
 #align probability_theory.lintegral_mul_indicator_eq_lintegral_mul_lintegral_indicator ProbabilityTheory.lintegral_mul_indicator_eq_lintegral_mul_lintegral_indicator
 
 /-- If `f` and `g` are independent random variables with values in `ℝ≥0∞`,
@@ -109,7 +109,7 @@ theorem lintegral_mul_eq_lintegral_mul_lintegral_of_independent_measurableSpace
     rw [lintegral_supr, lintegral_supr h_measM_f' h_mono_f', ENNReal.mul_supᵢ]
     · simp_rw [← h_ind_f']
     · exact fun n => h_measM_f.mul (h_measM_f' n)
-    · exact fun n m (h_le : n ≤ m) a => ENNReal.mul_le_mul le_rfl (h_mono_f' h_le a)
+    · exact fun n m (h_le : n ≤ m) a => mul_le_mul_left' (h_mono_f' h_le a) _
 #align probability_theory.lintegral_mul_eq_lintegral_mul_lintegral_of_independent_measurable_space ProbabilityTheory.lintegral_mul_eq_lintegral_mul_lintegral_of_independent_measurableSpace
 
 /-- If `f` and `g` are independent random variables with values in `ℝ≥0∞`,

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

@@ -36,7 +36,7 @@ noncomputable section
 
 open Set MeasureTheory
 
-open Ennreal MeasureTheory
+open ENNReal MeasureTheory
 
 variable {Ω : Type _} {mΩ : MeasurableSpace Ω} {μ : Measure Ω} {f g : Ω → ℝ≥0∞} {X Y : Ω → ℝ}
 
@@ -54,7 +54,7 @@ theorem lintegral_mul_indicator_eq_lintegral_mul_lintegral_indicator {Mf mΩ : M
   revert f
   have h_mul_indicator : ∀ g, Measurable g → Measurable fun a => g a * T.indicator (fun x => c) a :=
     fun g h_mg => h_mg.mul (measurable_const.indicator h_meas_T)
-  apply Measurable.ennreal_induction
+  apply Measurable.eNNReal_induction
   · intro c' s' h_meas_s'
     simp_rw [← inter_indicator_mul]
     rw [lintegral_indicator _ (MeasurableSet.inter (hMf _ h_meas_s') h_meas_T),
@@ -72,11 +72,11 @@ theorem lintegral_mul_indicator_eq_lintegral_mul_lintegral_indicator {Mf mΩ : M
       right_distrib, h_ind_f', h_ind_g]
   · intro f h_meas_f h_mono_f h_ind_f
     have h_measM_f : ∀ n, Measurable (f n) := fun n => (h_meas_f n).mono hMf le_rfl
-    simp_rw [Ennreal.supᵢ_mul]
-    rw [lintegral_supr h_measM_f h_mono_f, lintegral_supr, Ennreal.supᵢ_mul]
+    simp_rw [ENNReal.supᵢ_mul]
+    rw [lintegral_supr h_measM_f h_mono_f, lintegral_supr, ENNReal.supᵢ_mul]
     · simp_rw [← h_ind_f]
     · exact fun n => h_mul_indicator _ (h_measM_f n)
-    · exact fun m n h_le a => Ennreal.mul_le_mul (h_mono_f h_le a) le_rfl
+    · exact fun m n h_le a => ENNReal.mul_le_mul (h_mono_f h_le a) le_rfl
 #align probability_theory.lintegral_mul_indicator_eq_lintegral_mul_lintegral_indicator ProbabilityTheory.lintegral_mul_indicator_eq_lintegral_mul_lintegral_indicator
 
 /-- If `f` and `g` are independent random variables with values in `ℝ≥0∞`,
@@ -92,7 +92,7 @@ theorem lintegral_mul_eq_lintegral_mul_lintegral_of_independent_measurableSpace
   by
   revert g
   have h_measM_f : Measurable f := h_meas_f.mono hMf le_rfl
-  apply Measurable.ennreal_induction
+  apply Measurable.eNNReal_induction
   · intro c s h_s
     apply lintegral_mul_indicator_eq_lintegral_mul_lintegral_indicator hMf _ (hMg _ h_s) _ h_meas_f
     apply indep_sets_of_indep_sets_of_le_right h_ind
@@ -105,11 +105,11 @@ theorem lintegral_mul_eq_lintegral_mul_lintegral_of_independent_measurableSpace
       h_ind_f', h_ind_g']
   · intro f' h_meas_f' h_mono_f' h_ind_f'
     have h_measM_f' : ∀ n, Measurable (f' n) := fun n => (h_meas_f' n).mono hMg le_rfl
-    simp_rw [Ennreal.mul_supᵢ]
-    rw [lintegral_supr, lintegral_supr h_measM_f' h_mono_f', Ennreal.mul_supᵢ]
+    simp_rw [ENNReal.mul_supᵢ]
+    rw [lintegral_supr, lintegral_supr h_measM_f' h_mono_f', ENNReal.mul_supᵢ]
     · simp_rw [← h_ind_f']
     · exact fun n => h_measM_f.mul (h_measM_f' n)
-    · exact fun n m (h_le : n ≤ m) a => Ennreal.mul_le_mul le_rfl (h_mono_f' h_le a)
+    · exact fun n m (h_le : n ≤ m) a => ENNReal.mul_le_mul le_rfl (h_mono_f' h_le a)
 #align probability_theory.lintegral_mul_eq_lintegral_mul_lintegral_of_independent_measurable_space ProbabilityTheory.lintegral_mul_eq_lintegral_mul_lintegral_of_independent_measurableSpace
 
 /-- If `f` and `g` are independent random variables with values in `ℝ≥0∞`,
@@ -149,18 +149,18 @@ theorem IndepFunCat.integrableMul {β : Type _} [MeasurableSpace β] {X Y : Ω 
     [NormedDivisionRing β] [BorelSpace β] (hXY : IndepFunCat X Y μ) (hX : Integrable X μ)
     (hY : Integrable Y μ) : Integrable (X * Y) μ :=
   by
-  let nX : Ω → Ennreal := fun a => ‖X a‖₊
-  let nY : Ω → Ennreal := fun a => ‖Y a‖₊
+  let nX : Ω → ENNReal := fun a => ‖X a‖₊
+  let nY : Ω → ENNReal := fun a => ‖Y a‖₊
   have hXY' : indep_fun (fun a => ‖X a‖₊) (fun a => ‖Y a‖₊) μ :=
     hXY.comp measurable_nnnorm measurable_nnnorm
   have hXY'' : indep_fun nX nY μ :=
-    hXY'.comp measurable_coe_nNReal_ennreal measurable_coe_nNReal_ennreal
-  have hnX : AeMeasurable nX μ := hX.1.AeMeasurable.nnnorm.coe_nNReal_ennreal
-  have hnY : AeMeasurable nY μ := hY.1.AeMeasurable.nnnorm.coe_nNReal_ennreal
+    hXY'.comp measurable_coe_nNReal_eNNReal measurable_coe_nNReal_eNNReal
+  have hnX : AeMeasurable nX μ := hX.1.AeMeasurable.nnnorm.coe_nNReal_eNNReal
+  have hnY : AeMeasurable nY μ := hY.1.AeMeasurable.nnnorm.coe_nNReal_eNNReal
   have hmul : (∫⁻ a, nX a * nY a ∂μ) = (∫⁻ a, nX a ∂μ) * ∫⁻ a, nY a ∂μ := by
     convert lintegral_mul_eq_lintegral_mul_lintegral_of_indep_fun' hnX hnY hXY''
   refine' ⟨hX.1.mul hY.1, _⟩
-  simp_rw [has_finite_integral, Pi.mul_apply, nnnorm_mul, Ennreal.coe_mul, hmul]
+  simp_rw [has_finite_integral, Pi.mul_apply, nnnorm_mul, ENNReal.coe_mul, hmul]
   exact ennreal.mul_lt_top_iff.mpr (Or.inl ⟨hX.2, hY.2⟩)
 #align probability_theory.indep_fun.integrable_mul ProbabilityTheory.IndepFunCat.integrableMul
 
@@ -183,9 +183,9 @@ theorem IndepFunCat.integrableLeftOfIntegrableMul {β : Type _} [MeasurableSpace
     have M : Measurable fun x : β => (‖x‖₊ : ℝ≥0∞) := measurable_nnnorm.coe_nnreal_ennreal
     apply indep_fun.comp hXY M M
   have A : (∫⁻ ω, ‖X ω * Y ω‖₊ ∂μ) < ∞ := h'XY.2
-  simp only [nnnorm_mul, Ennreal.coe_mul] at A
+  simp only [nnnorm_mul, ENNReal.coe_mul] at A
   rw [lintegral_mul_eq_lintegral_mul_lintegral_of_indep_fun'' hX.ennnorm hY.ennnorm J, H] at A
-  simpa [Ennreal.top_mul, I] using A
+  simpa [ENNReal.top_mul', I] using A
 #align probability_theory.indep_fun.integrable_left_of_integrable_mul ProbabilityTheory.IndepFunCat.integrableLeftOfIntegrableMul
 
 /-- If the product of two independent real_valued random variables is integrable and the
@@ -207,9 +207,9 @@ theorem IndepFunCat.integrableRightOfIntegrableMul {β : Type _} [MeasurableSpac
     have M : Measurable fun x : β => (‖x‖₊ : ℝ≥0∞) := measurable_nnnorm.coe_nnreal_ennreal
     apply indep_fun.comp hXY M M
   have A : (∫⁻ ω, ‖X ω * Y ω‖₊ ∂μ) < ∞ := h'XY.2
-  simp only [nnnorm_mul, Ennreal.coe_mul] at A
+  simp only [nnnorm_mul, ENNReal.coe_mul] at A
   rw [lintegral_mul_eq_lintegral_mul_lintegral_of_indep_fun'' hX.ennnorm hY.ennnorm J, H] at A
-  simpa [Ennreal.top_mul, I] using A
+  simpa [ENNReal.top_mul', I] using A
 #align probability_theory.indep_fun.integrable_right_of_integrable_mul ProbabilityTheory.IndepFunCat.integrableRightOfIntegrableMul
 
 /-- The (Bochner) integral of the product of two independent, nonnegative random
@@ -219,19 +219,19 @@ theorem IndepFunCat.integral_mul_of_nonneg (hXY : IndepFunCat X Y μ) (hXp : 0 
     (hXm : AeMeasurable X μ) (hYm : AeMeasurable Y μ) :
     integral μ (X * Y) = integral μ X * integral μ Y :=
   by
-  have h1 : AeMeasurable (fun a => Ennreal.ofReal (X a)) μ :=
+  have h1 : AeMeasurable (fun a => ENNReal.ofReal (X a)) μ :=
     ennreal.measurable_of_real.comp_ae_measurable hXm
-  have h2 : AeMeasurable (fun a => Ennreal.ofReal (Y a)) μ :=
+  have h2 : AeMeasurable (fun a => ENNReal.ofReal (Y a)) μ :=
     ennreal.measurable_of_real.comp_ae_measurable hYm
   have h3 : AeMeasurable (X * Y) μ := hXm.mul hYm
   have h4 : 0 ≤ᵐ[μ] X * Y := ae_of_all _ fun ω => mul_nonneg (hXp ω) (hYp ω)
   rw [integral_eq_lintegral_of_nonneg_ae (ae_of_all _ hXp) hXm.ae_strongly_measurable,
     integral_eq_lintegral_of_nonneg_ae (ae_of_all _ hYp) hYm.ae_strongly_measurable,
     integral_eq_lintegral_of_nonneg_ae h4 h3.ae_strongly_measurable]
-  simp_rw [← Ennreal.toReal_mul, Pi.mul_apply, Ennreal.ofReal_mul (hXp _)]
+  simp_rw [← ENNReal.toReal_mul, Pi.mul_apply, ENNReal.ofReal_mul (hXp _)]
   congr
   apply lintegral_mul_eq_lintegral_mul_lintegral_of_indep_fun' h1 h2
-  exact hXY.comp Ennreal.measurable_ofReal Ennreal.measurable_ofReal
+  exact hXY.comp ENNReal.measurable_ofReal ENNReal.measurable_ofReal
 #align probability_theory.indep_fun.integral_mul_of_nonneg ProbabilityTheory.IndepFunCat.integral_mul_of_nonneg
 
 /-- The (Bochner) integral of the product of two independent, integrable random
@@ -337,10 +337,10 @@ theorem indepFunCat_iff_integral_comp_mul [IsFiniteMeasure μ] {β β' : Type _}
     h (measurable_one.indicator hA) (measurable_one.indicator hB)
       ((integrable_const 1).indicator (hfm.comp measurable_id hA))
       ((integrable_const 1).indicator (hgm.comp measurable_id hB))
-  rwa [← Ennreal.toReal_eq_toReal (measure_ne_top μ _), Ennreal.toReal_mul, ←
+  rwa [← ENNReal.toReal_eq_toReal (measure_ne_top μ _), ENNReal.toReal_mul, ←
     integral_indicator_one ((hfm hA).inter (hgm hB)), ← integral_indicator_one (hfm hA), ←
     integral_indicator_one (hgm hB), Set.inter_indicator_one]
-  exact Ennreal.mul_ne_top (measure_ne_top μ _) (measure_ne_top μ _)
+  exact ENNReal.mul_ne_top (measure_ne_top μ _) (measure_ne_top μ _)
 #align probability_theory.indep_fun_iff_integral_comp_mul ProbabilityTheory.indepFunCat_iff_integral_comp_mul
 
 end ProbabilityTheory

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

PR contents

This is the supremum of

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

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

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

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

Lean PRs involved in this bump

In particular this includes adjustments for the Lean PRs

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

leanprover/lean4#2778

We can get rid of all the

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

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

leanprover/lean4#2722

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

leanprover/lean4#2783

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

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

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

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

@@ -172,7 +172,7 @@ theorem IndepFun.integrable_left_of_integrable_mul {β : Type*} [MeasurableSpace
   have A : (∫⁻ ω, ‖X ω * Y ω‖₊ ∂μ) < ∞ := h'XY.2
   simp only [nnnorm_mul, ENNReal.coe_mul] at A
   rw [lintegral_mul_eq_lintegral_mul_lintegral_of_indepFun'' hX.ennnorm hY.ennnorm J, H] at A
-  simp only [ENNReal.top_mul I] at A
+  simp only [ENNReal.top_mul I, lt_self_iff_false] at A
 #align probability_theory.indep_fun.integrable_left_of_integrable_mul ProbabilityTheory.IndepFun.integrable_left_of_integrable_mul
 
 /-- If the product of two independent real-valued random variables is integrable and the
@@ -194,7 +194,7 @@ theorem IndepFun.integrable_right_of_integrable_mul {β : Type*} [MeasurableSpac
   have A : (∫⁻ ω, ‖X ω * Y ω‖₊ ∂μ) < ∞ := h'XY.2
   simp only [nnnorm_mul, ENNReal.coe_mul] at A
   rw [lintegral_mul_eq_lintegral_mul_lintegral_of_indepFun'' hX.ennnorm hY.ennnorm J, H] at A
-  simp only [ENNReal.mul_top I] at A
+  simp only [ENNReal.mul_top I, lt_self_iff_false] at A
 #align probability_theory.indep_fun.integrable_right_of_integrable_mul ProbabilityTheory.IndepFun.integrable_right_of_integrable_mul
 
 /-- The (Bochner) integral of the product of two independent, nonnegative random

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

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

@@ -274,13 +274,13 @@ theorem IndepFun.integral_mul (hXY : IndepFun X Y μ) (hX : AEStronglyMeasurable
       filter_upwards [h'X] with ω hω
       simp [hω]
     simp only [integral_congr_ae h'X, integral_congr_ae h', Pi.zero_apply, integral_const,
-      Algebra.id.smul_eq_mul, MulZeroClass.mul_zero, MulZeroClass.zero_mul]
+      Algebra.id.smul_eq_mul, mul_zero, zero_mul]
   by_cases h'Y : Y =ᵐ[μ] 0
   · have h' : X * Y =ᵐ[μ] 0 := by
       filter_upwards [h'Y] with ω hω
       simp [hω]
     simp only [integral_congr_ae h'Y, integral_congr_ae h', Pi.zero_apply, integral_const,
-      Algebra.id.smul_eq_mul, MulZeroClass.mul_zero, MulZeroClass.zero_mul]
+      Algebra.id.smul_eq_mul, mul_zero, zero_mul]
   by_cases h : Integrable (X * Y) μ
   · have HX : Integrable X μ := hXY.integrable_left_of_integrable_mul h hX hY h'Y
     have HY : Integrable Y μ := hXY.integrable_right_of_integrable_mul h hX hY h'X

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

This has nice performance benefits.

@@ -35,7 +35,7 @@ open Set MeasureTheory
 
 open scoped ENNReal MeasureTheory
 
-variable {Ω : Type _} {mΩ : MeasurableSpace Ω} {μ : Measure Ω} {f g : Ω → ℝ≥0∞} {X Y : Ω → ℝ}
+variable {Ω : Type*} {mΩ : MeasurableSpace Ω} {μ : Measure Ω} {f g : Ω → ℝ≥0∞} {X Y : Ω → ℝ}
 
 namespace ProbabilityTheory
 
@@ -135,7 +135,7 @@ theorem lintegral_mul_eq_lintegral_mul_lintegral_of_indepFun'' (h_meas_f : AEMea
 #align probability_theory.lintegral_mul_eq_lintegral_mul_lintegral_of_indep_fun'' ProbabilityTheory.lintegral_mul_eq_lintegral_mul_lintegral_of_indepFun''
 
 /-- The product of two independent, integrable, real-valued random variables is integrable. -/
-theorem IndepFun.integrable_mul {β : Type _} [MeasurableSpace β] {X Y : Ω → β}
+theorem IndepFun.integrable_mul {β : Type*} [MeasurableSpace β] {X Y : Ω → β}
     [NormedDivisionRing β] [BorelSpace β] (hXY : IndepFun X Y μ) (hX : Integrable X μ)
     (hY : Integrable Y μ) : Integrable (X * Y) μ := by
   let nX : Ω → ENNReal := fun a => ‖X a‖₊
@@ -155,7 +155,7 @@ theorem IndepFun.integrable_mul {β : Type _} [MeasurableSpace β] {X Y : Ω →
 
 /-- If the product of two independent real-valued random variables is integrable and
 the second one is not almost everywhere zero, then the first one is integrable. -/
-theorem IndepFun.integrable_left_of_integrable_mul {β : Type _} [MeasurableSpace β] {X Y : Ω → β}
+theorem IndepFun.integrable_left_of_integrable_mul {β : Type*} [MeasurableSpace β] {X Y : Ω → β}
     [NormedDivisionRing β] [BorelSpace β] (hXY : IndepFun X Y μ) (h'XY : Integrable (X * Y) μ)
     (hX : AEStronglyMeasurable X μ) (hY : AEStronglyMeasurable Y μ) (h'Y : ¬Y =ᵐ[μ] 0) :
     Integrable X μ := by
@@ -177,7 +177,7 @@ theorem IndepFun.integrable_left_of_integrable_mul {β : Type _} [MeasurableSpac
 
 /-- If the product of two independent real-valued random variables is integrable and the
 first one is not almost everywhere zero, then the second one is integrable. -/
-theorem IndepFun.integrable_right_of_integrable_mul {β : Type _} [MeasurableSpace β] {X Y : Ω → β}
+theorem IndepFun.integrable_right_of_integrable_mul {β : Type*} [MeasurableSpace β] {X Y : Ω → β}
     [NormedDivisionRing β] [BorelSpace β] (hXY : IndepFun X Y μ) (h'XY : Integrable (X * Y) μ)
     (hX : AEStronglyMeasurable X μ) (hY : AEStronglyMeasurable Y μ) (h'X : ¬X =ᵐ[μ] 0) :
     Integrable Y μ := by
@@ -302,7 +302,7 @@ theorem IndepFun.integral_mul' (hXY : IndepFun X Y μ) (hX : AEStronglyMeasurabl
 /-- Independence of functions `f` and `g` into arbitrary types is characterized by the relation
   `E[(φ ∘ f) * (ψ ∘ g)] = E[φ ∘ f] * E[ψ ∘ g]` for all measurable `φ` and `ψ` with values in `ℝ`
   satisfying appropriate integrability conditions. -/
-theorem indepFun_iff_integral_comp_mul [IsFiniteMeasure μ] {β β' : Type _} {mβ : MeasurableSpace β}
+theorem indepFun_iff_integral_comp_mul [IsFiniteMeasure μ] {β β' : Type*} {mβ : MeasurableSpace β}
     {mβ' : MeasurableSpace β'} {f : Ω → β} {g : Ω → β'} {hfm : Measurable f} {hgm : Measurable g} :
     IndepFun f g μ ↔ ∀ {φ : β → ℝ} {ψ : β' → ℝ}, Measurable φ → Measurable ψ →
       Integrable (φ ∘ f) μ → Integrable (ψ ∘ g) μ →

Independence is the special case of independence with respect to a kernel and a measure where the kernel is constant.

@@ -57,6 +57,7 @@ theorem lintegral_mul_indicator_eq_lintegral_mul_lintegral_indicator {Mf mΩ : M
       lintegral_indicator _ (hMf _ h_meas_s'), lintegral_indicator _ h_meas_T]
     simp only [measurable_const, lintegral_const, univ_inter, lintegral_const_mul,
       MeasurableSet.univ, Measure.restrict_apply]
+    rw [IndepSets_iff] at h_ind
     rw [mul_mul_mul_comm, h_ind s' T h_meas_s' (Set.mem_singleton _)]
   · intro f' g _ h_meas_f' _ h_ind_f' h_ind_g
     have h_measM_f' : Measurable f' := h_meas_f'.mono hMf le_rfl
@@ -307,6 +308,7 @@ theorem indepFun_iff_integral_comp_mul [IsFiniteMeasure μ] {β β' : Type _} {m
       Integrable (φ ∘ f) μ → Integrable (ψ ∘ g) μ →
         integral μ (φ ∘ f * ψ ∘ g) = integral μ (φ ∘ f) * integral μ (ψ ∘ g) := by
   refine' ⟨fun hfg _ _ hφ hψ => IndepFun.integral_mul_of_integrable (hfg.comp hφ hψ), _⟩
+  rw [IndepFun_iff]
   rintro h _ _ ⟨A, hA, rfl⟩ ⟨B, hB, rfl⟩
   specialize
     h (measurable_one.indicator hA) (measurable_one.indicator hB)

• depends on: #5966

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

@@ -2,15 +2,12 @@
 Copyright (c) 2021 Martin Zinkevich. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Martin Zinkevich, Vincent Beffara
-
-! This file was ported from Lean 3 source module probability.integration
-! leanprover-community/mathlib commit 2f8347015b12b0864dfaf366ec4909eb70c78740
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.MeasureTheory.Integral.SetIntegral
 import Mathlib.Probability.Independence.Basic
 
+#align_import probability.integration from "leanprover-community/mathlib"@"2f8347015b12b0864dfaf366ec4909eb70c78740"
+
 /-!
 # Integration in Probability Theory
 

@@ -84,7 +84,7 @@ theorem lintegral_mul_indicator_eq_lintegral_mul_lintegral_indicator {Mf mΩ : M
 theorem lintegral_mul_eq_lintegral_mul_lintegral_of_independent_measurableSpace
     {Mf Mg mΩ : MeasurableSpace Ω} {μ : Measure Ω} (hMf : Mf ≤ mΩ) (hMg : Mg ≤ mΩ)
     (h_ind : Indep Mf Mg μ) (h_meas_f : Measurable[Mf] f) (h_meas_g : Measurable[Mg] g) :
-    (∫⁻ ω, f ω * g ω ∂μ) = (∫⁻ ω, f ω ∂μ) * ∫⁻ ω, g ω ∂μ := by
+    ∫⁻ ω, f ω * g ω ∂μ = (∫⁻ ω, f ω ∂μ) * ∫⁻ ω, g ω ∂μ := by
   revert g
   have h_measM_f : Measurable f := h_meas_f.mono hMf le_rfl
   apply @Measurable.ennreal_induction _ Mg
@@ -132,7 +132,7 @@ theorem lintegral_mul_eq_lintegral_mul_lintegral_of_indepFun' (h_meas_f : AEMeas
 
 theorem lintegral_mul_eq_lintegral_mul_lintegral_of_indepFun'' (h_meas_f : AEMeasurable f μ)
     (h_meas_g : AEMeasurable g μ) (h_indep_fun : IndepFun f g μ) :
-    (∫⁻ ω, f ω * g ω ∂μ) = (∫⁻ ω, f ω ∂μ) * ∫⁻ ω, g ω ∂μ :=
+    ∫⁻ ω, f ω * g ω ∂μ = (∫⁻ ω, f ω ∂μ) * ∫⁻ ω, g ω ∂μ :=
   lintegral_mul_eq_lintegral_mul_lintegral_of_indepFun' h_meas_f h_meas_g h_indep_fun
 #align probability_theory.lintegral_mul_eq_lintegral_mul_lintegral_of_indep_fun'' ProbabilityTheory.lintegral_mul_eq_lintegral_mul_lintegral_of_indepFun''
 
@@ -148,7 +148,7 @@ theorem IndepFun.integrable_mul {β : Type _} [MeasurableSpace β] {X Y : Ω →
     hXY'.comp measurable_coe_nnreal_ennreal measurable_coe_nnreal_ennreal
   have hnX : AEMeasurable nX μ := hX.1.aemeasurable.nnnorm.coe_nnreal_ennreal
   have hnY : AEMeasurable nY μ := hY.1.aemeasurable.nnnorm.coe_nnreal_ennreal
-  have hmul : (∫⁻ a, nX a * nY a ∂μ) = (∫⁻ a, nX a ∂μ) * ∫⁻ a, nY a ∂μ :=
+  have hmul : ∫⁻ a, nX a * nY a ∂μ = (∫⁻ a, nX a ∂μ) * ∫⁻ a, nY a ∂μ :=
     lintegral_mul_eq_lintegral_mul_lintegral_of_indepFun' hnX hnY hXY''
   refine' ⟨hX.1.mul hY.1, _⟩
   simp_rw [HasFiniteIntegral, Pi.mul_apply, nnnorm_mul, ENNReal.coe_mul, hmul]

@@ -25,8 +25,8 @@ will always pick the later typeclass in this situation, and does not care whethe
 `[]`, `{}`, or `()`. All of these use the `MeasurableSpace` `M2` to define `μ`:
 
 ```lean
-example {M1 : MeasurableSpace Ω} [M2 : MeasurableSpace Ω] {μ : measure Ω} : sorry := sorry
-example [M1 : MeasurableSpace Ω] {M2 : MeasurableSpace Ω} {μ : measure Ω} : sorry := sorry
+example {M1 : MeasurableSpace Ω} [M2 : MeasurableSpace Ω] {μ : Measure Ω} : sorry := sorry
+example [M1 : MeasurableSpace Ω] {M2 : MeasurableSpace Ω} {μ : Measure Ω} : sorry := sorry
 ```
 
 -/
@@ -44,7 +44,7 @@ namespace ProbabilityTheory
 
 /-- If a random variable `f` in `ℝ≥0∞` is independent of an event `T`, then if you restrict the
   random variable to `T`, then `E[f * indicator T c 0]=E[f] * E[indicator T c 0]`. It is useful for
-  `lintegral_mul_eq_lintegral_mul_lintegral_of_independent_measurable_space`. -/
+  `lintegral_mul_eq_lintegral_mul_lintegral_of_independent_measurableSpace`. -/
 theorem lintegral_mul_indicator_eq_lintegral_mul_lintegral_indicator {Mf mΩ : MeasurableSpace Ω}
     {μ : Measure Ω} (hMf : Mf ≤ mΩ) (c : ℝ≥0∞) {T : Set Ω} (h_meas_T : MeasurableSet T)
     (h_ind : IndepSets {s | MeasurableSet[Mf] s} {T} μ) (h_meas_f : Measurable[Mf] f) :
@@ -79,7 +79,7 @@ theorem lintegral_mul_indicator_eq_lintegral_mul_lintegral_indicator {Mf mΩ : M
    then `E[f * g] = E[f] * E[g]`. However, instead of directly using the independence
    of the random variables, it uses the independence of measurable spaces for the
    domains of `f` and `g`. This is similar to the sigma-algebra approach to
-   independence. See `lintegral_mul_eq_lintegral_mul_lintegral_of_independent_fn` for
+   independence. See `lintegral_mul_eq_lintegral_mul_lintegral_of_indepFun` for
    a more common variant of the product of independent variables. -/
 theorem lintegral_mul_eq_lintegral_mul_lintegral_of_independent_measurableSpace
     {Mf Mg mΩ : MeasurableSpace Ω} {μ : Measure Ω} (hMf : Mf ≤ mΩ) (hMg : Mg ≤ mΩ)
@@ -118,7 +118,7 @@ theorem lintegral_mul_eq_lintegral_mul_lintegral_of_indepFun (h_meas_f : Measura
 
 /-- If `f` and `g` with values in `ℝ≥0∞` are independent and almost everywhere measurable,
    then `E[f * g] = E[f] * E[g]` (slightly generalizing
-   `lintegral_mul_eq_lintegral_mul_lintegral_of_indep_fun`). -/
+   `lintegral_mul_eq_lintegral_mul_lintegral_of_indepFun`). -/
 theorem lintegral_mul_eq_lintegral_mul_lintegral_of_indepFun' (h_meas_f : AEMeasurable f μ)
     (h_meas_g : AEMeasurable g μ) (h_indep_fun : IndepFun f g μ) :
     (∫⁻ ω, (f * g) ω ∂μ) = (∫⁻ ω, f ω ∂μ) * ∫⁻ ω, g ω ∂μ := by
@@ -136,7 +136,7 @@ theorem lintegral_mul_eq_lintegral_mul_lintegral_of_indepFun'' (h_meas_f : AEMea
   lintegral_mul_eq_lintegral_mul_lintegral_of_indepFun' h_meas_f h_meas_g h_indep_fun
 #align probability_theory.lintegral_mul_eq_lintegral_mul_lintegral_of_indep_fun'' ProbabilityTheory.lintegral_mul_eq_lintegral_mul_lintegral_of_indepFun''
 
-/-- The product of two independent, integrable, real_valued random variables is integrable. -/
+/-- The product of two independent, integrable, real-valued random variables is integrable. -/
 theorem IndepFun.integrable_mul {β : Type _} [MeasurableSpace β] {X Y : Ω → β}
     [NormedDivisionRing β] [BorelSpace β] (hXY : IndepFun X Y μ) (hX : Integrable X μ)
     (hY : Integrable Y μ) : Integrable (X * Y) μ := by
@@ -155,7 +155,7 @@ theorem IndepFun.integrable_mul {β : Type _} [MeasurableSpace β] {X Y : Ω →
   exact ENNReal.mul_lt_top hX.2.ne hY.2.ne
 #align probability_theory.indep_fun.integrable_mul ProbabilityTheory.IndepFun.integrable_mul
 
-/-- If the product of two independent real_valued random variables is integrable and
+/-- If the product of two independent real-valued random variables is integrable and
 the second one is not almost everywhere zero, then the first one is integrable. -/
 theorem IndepFun.integrable_left_of_integrable_mul {β : Type _} [MeasurableSpace β] {X Y : Ω → β}
     [NormedDivisionRing β] [BorelSpace β] (hXY : IndepFun X Y μ) (h'XY : Integrable (X * Y) μ)
@@ -172,12 +172,12 @@ theorem IndepFun.integrable_left_of_integrable_mul {β : Type _} [MeasurableSpac
     have M : Measurable fun x : β => (‖x‖₊ : ℝ≥0∞) := measurable_nnnorm.coe_nnreal_ennreal
     apply IndepFun.comp hXY M M
   have A : (∫⁻ ω, ‖X ω * Y ω‖₊ ∂μ) < ∞ := h'XY.2
-  simp only [nnnorm_mul, ENNReal.coe_mul] at A 
-  rw [lintegral_mul_eq_lintegral_mul_lintegral_of_indepFun'' hX.ennnorm hY.ennnorm J, H] at A 
+  simp only [nnnorm_mul, ENNReal.coe_mul] at A
+  rw [lintegral_mul_eq_lintegral_mul_lintegral_of_indepFun'' hX.ennnorm hY.ennnorm J, H] at A
   simp only [ENNReal.top_mul I] at A
 #align probability_theory.indep_fun.integrable_left_of_integrable_mul ProbabilityTheory.IndepFun.integrable_left_of_integrable_mul
 
-/-- If the product of two independent real_valued random variables is integrable and the
+/-- If the product of two independent real-valued random variables is integrable and the
 first one is not almost everywhere zero, then the second one is integrable. -/
 theorem IndepFun.integrable_right_of_integrable_mul {β : Type _} [MeasurableSpace β] {X Y : Ω → β}
     [NormedDivisionRing β] [BorelSpace β] (hXY : IndepFun X Y μ) (h'XY : Integrable (X * Y) μ)
@@ -194,14 +194,14 @@ theorem IndepFun.integrable_right_of_integrable_mul {β : Type _} [MeasurableSpa
     have M : Measurable fun x : β => (‖x‖₊ : ℝ≥0∞) := measurable_nnnorm.coe_nnreal_ennreal
     apply IndepFun.comp hXY M M
   have A : (∫⁻ ω, ‖X ω * Y ω‖₊ ∂μ) < ∞ := h'XY.2
-  simp only [nnnorm_mul, ENNReal.coe_mul] at A 
-  rw [lintegral_mul_eq_lintegral_mul_lintegral_of_indepFun'' hX.ennnorm hY.ennnorm J, H] at A 
+  simp only [nnnorm_mul, ENNReal.coe_mul] at A
+  rw [lintegral_mul_eq_lintegral_mul_lintegral_of_indepFun'' hX.ennnorm hY.ennnorm J, H] at A
   simp only [ENNReal.mul_top I] at A
 #align probability_theory.indep_fun.integrable_right_of_integrable_mul ProbabilityTheory.IndepFun.integrable_right_of_integrable_mul
 
 /-- The (Bochner) integral of the product of two independent, nonnegative random
   variables is the product of their integrals. The proof is just plumbing around
-  `lintegral_mul_eq_lintegral_mul_lintegral_of_indep_fun'`. -/
+  `lintegral_mul_eq_lintegral_mul_lintegral_of_indepFun'`. -/
 theorem IndepFun.integral_mul_of_nonneg (hXY : IndepFun X Y μ) (hXp : 0 ≤ X) (hYp : 0 ≤ Y)
     (hXm : AEMeasurable X μ) (hYm : AEMeasurable Y μ) :
     integral μ (X * Y) = integral μ X * integral μ Y := by
@@ -222,7 +222,7 @@ theorem IndepFun.integral_mul_of_nonneg (hXY : IndepFun X Y μ) (hXp : 0 ≤ X)
 
 /-- The (Bochner) integral of the product of two independent, integrable random
   variables is the product of their integrals. The proof is pedestrian decomposition
-  into their positive and negative parts in order to apply `indep_fun.integral_mul_of_nonneg`
+  into their positive and negative parts in order to apply `IndepFun.integral_mul_of_nonneg`
   four times. -/
 theorem IndepFun.integral_mul_of_integrable (hXY : IndepFun X Y μ) (hX : Integrable X μ)
     (hY : Integrable Y μ) : integral μ (X * Y) = integral μ X * integral μ Y := by
@@ -291,7 +291,7 @@ theorem IndepFun.integral_mul (hXY : IndepFun X Y μ) (hX : AEStronglyMeasurable
     have I : ¬(Integrable X μ ∧ Integrable Y μ) := by
       rintro ⟨HX, HY⟩
       exact h (hXY.integrable_mul HX HY)
-    rw [not_and_or] at I 
+    rw [not_and_or] at I
     cases' I with I I <;> simp [integral_undef I]
 #align probability_theory.indep_fun.integral_mul ProbabilityTheory.IndepFun.integral_mul
 
@@ -322,4 +322,3 @@ theorem indepFun_iff_integral_comp_mul [IsFiniteMeasure μ] {β β' : Type _} {m
 #align probability_theory.indep_fun_iff_integral_comp_mul ProbabilityTheory.indepFun_iff_integral_comp_mul
 
 end ProbabilityTheory
-