probability.kernel.condexp ⟷ Mathlib.Probability.Kernel.Condexp

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

@@ -64,7 +64,7 @@ theorem MeasureTheory.AEStronglyMeasurable.comp_snd_map_prod_id [TopologicalSpac
     AEStronglyMeasurable (fun x : Ω × Ω => f x.2)
       (@Measure.map Ω (Ω × Ω) (m.Prod mΩ) mΩ (fun ω => (id ω, id ω)) μ) :=
   by
-  rw [← ae_strongly_measurable_comp_snd_map_prod_mk_iff (measurable_id'' hm)] at hf 
+  rw [← ae_strongly_measurable_comp_snd_map_prod_mk_iff (measurable_id'' hm)] at hf
   simp_rw [id.def] at hf ⊢
   exact hf
 #align measure_theory.ae_strongly_measurable.comp_snd_map_prod_id MeasureTheory.AEStronglyMeasurable.comp_snd_map_prod_id
@@ -76,7 +76,7 @@ theorem MeasureTheory.Integrable.comp_snd_map_prod_id [NormedAddCommGroup F] (hm
     Integrable (fun x : Ω × Ω => f x.2)
       (@Measure.map Ω (Ω × Ω) (m.Prod mΩ) mΩ (fun ω => (id ω, id ω)) μ) :=
   by
-  rw [← integrable_comp_snd_map_prod_mk_iff (measurable_id'' hm)] at hf 
+  rw [← integrable_comp_snd_map_prod_mk_iff (measurable_id'' hm)] at hf
   simp_rw [id.def] at hf ⊢
   exact hf
 #align measure_theory.integrable.comp_snd_map_prod_id MeasureTheory.Integrable.comp_snd_map_prod_id
@@ -129,7 +129,7 @@ theorem aestronglyMeasurable'_integral_condexpKernel [NormedSpace ℝ F] [Comple
   have h :=
     ae_strongly_measurable'_integral_cond_distrib (ae_measurable_id'' μ hm) aemeasurable_id
       (hf.comp_snd_map_prod_id hm)
-  rwa [MeasurableSpace.comap_id] at h 
+  rwa [MeasurableSpace.comap_id] at h
 #align probability_theory.ae_strongly_measurable'_integral_condexp_kernel ProbabilityTheory.aestronglyMeasurable'_integral_condexpKernel
 -/
 

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

@@ -3,7 +3,7 @@ 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.CondDistrib
+import Probability.Kernel.CondDistrib
 
 #align_import probability.kernel.condexp from "leanprover-community/mathlib"@"1b089e3bdc3ce6b39cd472543474a0a137128c6c"
 

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

@@ -44,18 +44,18 @@ section AuxLemmas
 
 variable {Ω F : Type _} {m mΩ : MeasurableSpace Ω} {μ : Measure Ω} {f : Ω → F}
 
-#print ProbabilityTheory.measurable_id'' /-
+#print measurable_id'' /-
 -- todo after the port: move to measure_theory/measurable_space, after measurable.mono
 theorem measurable_id'' (hm : m ≤ mΩ) : @Measurable Ω Ω mΩ m id :=
   measurable_id.mono le_rfl hm
-#align probability_theory.measurable_id'' ProbabilityTheory.measurable_id''
+#align probability_theory.measurable_id'' measurable_id''
 -/
 
-#print ProbabilityTheory.aemeasurable_id'' /-
+#print aemeasurable_id'' /-
 -- todo after the port: move to measure_theory/measurable_space, after measurable.mono
 theorem aemeasurable_id'' (μ : Measure Ω) (hm : m ≤ mΩ) : @AEMeasurable Ω Ω m mΩ id μ :=
   @Measurable.aemeasurable Ω Ω mΩ m id μ (measurable_id'' hm)
-#align probability_theory.ae_measurable_id'' ProbabilityTheory.aemeasurable_id''
+#align probability_theory.ae_measurable_id'' aemeasurable_id''
 -/
 
 #print MeasureTheory.AEStronglyMeasurable.comp_snd_map_prod_id /-

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

@@ -2,14 +2,11 @@
 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.condexp
-! leanprover-community/mathlib commit 1b089e3bdc3ce6b39cd472543474a0a137128c6c
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Probability.Kernel.CondDistrib
 
+#align_import probability.kernel.condexp from "leanprover-community/mathlib"@"1b089e3bdc3ce6b39cd472543474a0a137128c6c"
+
 /-!
 # Kernel associated with a conditional expectation
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/d30d31261cdb4d2f5e612eabc3c4bf45556350d5

@@ -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.condexp
-! leanprover-community/mathlib commit 00abe0695d8767201e6d008afa22393978bb324d
+! leanprover-community/mathlib commit 1b089e3bdc3ce6b39cd472543474a0a137128c6c
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -13,6 +13,9 @@ import Mathbin.Probability.Kernel.CondDistrib
 /-!
 # Kernel associated with a conditional expectation
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 We define `condexp_kernel μ m`, a kernel from `Ω` to `Ω` such that for all integrable functions `f`,
 `μ[f | m] =ᵐ[μ] λ ω, ∫ y, f y ∂(condexp_kernel μ m ω)`.
 

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

@@ -44,16 +44,21 @@ section AuxLemmas
 
 variable {Ω F : Type _} {m mΩ : MeasurableSpace Ω} {μ : Measure Ω} {f : Ω → F}
 
+#print ProbabilityTheory.measurable_id'' /-
 -- todo after the port: move to measure_theory/measurable_space, after measurable.mono
 theorem measurable_id'' (hm : m ≤ mΩ) : @Measurable Ω Ω mΩ m id :=
   measurable_id.mono le_rfl hm
 #align probability_theory.measurable_id'' ProbabilityTheory.measurable_id''
+-/
 
+#print ProbabilityTheory.aemeasurable_id'' /-
 -- todo after the port: move to measure_theory/measurable_space, after measurable.mono
-theorem aEMeasurable_id'' (μ : Measure Ω) (hm : m ≤ mΩ) : @AEMeasurable Ω Ω m mΩ id μ :=
+theorem aemeasurable_id'' (μ : Measure Ω) (hm : m ≤ mΩ) : @AEMeasurable Ω Ω m mΩ id μ :=
   @Measurable.aemeasurable Ω Ω mΩ m id μ (measurable_id'' hm)
-#align probability_theory.ae_measurable_id'' ProbabilityTheory.aEMeasurable_id''
+#align probability_theory.ae_measurable_id'' ProbabilityTheory.aemeasurable_id''
+-/
 
+#print MeasureTheory.AEStronglyMeasurable.comp_snd_map_prod_id /-
 theorem MeasureTheory.AEStronglyMeasurable.comp_snd_map_prod_id [TopologicalSpace F] (hm : m ≤ mΩ)
     (hf : AEStronglyMeasurable f μ) :
     AEStronglyMeasurable (fun x : Ω × Ω => f x.2)
@@ -63,7 +68,9 @@ theorem MeasureTheory.AEStronglyMeasurable.comp_snd_map_prod_id [TopologicalSpac
   simp_rw [id.def] at hf ⊢
   exact hf
 #align measure_theory.ae_strongly_measurable.comp_snd_map_prod_id MeasureTheory.AEStronglyMeasurable.comp_snd_map_prod_id
+-/
 
+#print MeasureTheory.Integrable.comp_snd_map_prod_id /-
 theorem MeasureTheory.Integrable.comp_snd_map_prod_id [NormedAddCommGroup F] (hm : m ≤ mΩ)
     (hf : Integrable f μ) :
     Integrable (fun x : Ω × Ω => f x.2)
@@ -73,6 +80,7 @@ theorem MeasureTheory.Integrable.comp_snd_map_prod_id [NormedAddCommGroup F] (hm
   simp_rw [id.def] at hf ⊢
   exact hf
 #align measure_theory.integrable.comp_snd_map_prod_id MeasureTheory.Integrable.comp_snd_map_prod_id
+-/
 
 end AuxLemmas
 
@@ -80,6 +88,7 @@ variable {Ω F : Type _} [TopologicalSpace Ω] {m : MeasurableSpace Ω} [mΩ : M
   [PolishSpace Ω] [BorelSpace Ω] [Nonempty Ω] {μ : Measure Ω} [IsFiniteMeasure μ]
   [NormedAddCommGroup F] {f : Ω → F}
 
+#print ProbabilityTheory.condexpKernel /-
 /-- Kernel associated with the conditional expectation with respect to a σ-algebra. It satisfies
 `μ[f | m] =ᵐ[μ] λ ω, ∫ y, f y ∂(condexp_kernel μ m ω)`.
 It is defined as the conditional distribution of the identity given the identity, where the second
@@ -88,14 +97,18 @@ noncomputable irreducible_def condexpKernel (μ : Measure Ω) [IsFiniteMeasure 
     (m : MeasurableSpace Ω) : @kernel Ω Ω m mΩ :=
   @condDistrib Ω Ω Ω _ mΩ _ _ _ mΩ m id id μ _
 #align probability_theory.condexp_kernel ProbabilityTheory.condexpKernel
+-/
 
 section Measurability
 
+#print ProbabilityTheory.measurable_condexpKernel /-
 theorem measurable_condexpKernel {s : Set Ω} (hs : MeasurableSet s) :
     measurable[m] fun ω => condexpKernel μ m ω s := by rw [condexp_kernel];
   convert measurable_cond_distrib hs; rw [MeasurableSpace.comap_id]
 #align probability_theory.measurable_condexp_kernel ProbabilityTheory.measurable_condexpKernel
+-/
 
+#print MeasureTheory.AEStronglyMeasurable.integral_condexpKernel /-
 theorem MeasureTheory.AEStronglyMeasurable.integral_condexpKernel [NormedSpace ℝ F]
     [CompleteSpace F] (hm : m ≤ mΩ) (hf : AEStronglyMeasurable f μ) :
     AEStronglyMeasurable (fun ω => ∫ y, f y ∂condexpKernel μ m ω) μ :=
@@ -105,8 +118,10 @@ theorem MeasureTheory.AEStronglyMeasurable.integral_condexpKernel [NormedSpace 
     ae_strongly_measurable.integral_cond_distrib (ae_measurable_id'' μ hm) aemeasurable_id
       (hf.comp_snd_map_prod_id hm)
 #align measure_theory.ae_strongly_measurable.integral_condexp_kernel MeasureTheory.AEStronglyMeasurable.integral_condexpKernel
+-/
 
-theorem aEStronglyMeasurable'_integral_condexpKernel [NormedSpace ℝ F] [CompleteSpace F]
+#print ProbabilityTheory.aestronglyMeasurable'_integral_condexpKernel /-
+theorem aestronglyMeasurable'_integral_condexpKernel [NormedSpace ℝ F] [CompleteSpace F]
     (hm : m ≤ mΩ) (hf : AEStronglyMeasurable f μ) :
     AEStronglyMeasurable' m (fun ω => ∫ y, f y ∂condexpKernel μ m ω) μ :=
   by
@@ -115,12 +130,14 @@ theorem aEStronglyMeasurable'_integral_condexpKernel [NormedSpace ℝ F] [Comple
     ae_strongly_measurable'_integral_cond_distrib (ae_measurable_id'' μ hm) aemeasurable_id
       (hf.comp_snd_map_prod_id hm)
   rwa [MeasurableSpace.comap_id] at h 
-#align probability_theory.ae_strongly_measurable'_integral_condexp_kernel ProbabilityTheory.aEStronglyMeasurable'_integral_condexpKernel
+#align probability_theory.ae_strongly_measurable'_integral_condexp_kernel ProbabilityTheory.aestronglyMeasurable'_integral_condexpKernel
+-/
 
 end Measurability
 
 section Integrability
 
+#print MeasureTheory.Integrable.condexpKernel_ae /-
 theorem MeasureTheory.Integrable.condexpKernel_ae (hm : m ≤ mΩ) (hf_int : Integrable f μ) :
     ∀ᵐ ω ∂μ, Integrable f (condexpKernel μ m ω) :=
   by
@@ -129,7 +146,9 @@ theorem MeasureTheory.Integrable.condexpKernel_ae (hm : m ≤ mΩ) (hf_int : Int
     integrable.cond_distrib_ae (ae_measurable_id'' μ hm) aemeasurable_id
       (hf_int.comp_snd_map_prod_id hm)
 #align measure_theory.integrable.condexp_kernel_ae MeasureTheory.Integrable.condexpKernel_ae
+-/
 
+#print MeasureTheory.Integrable.integral_norm_condexpKernel /-
 theorem MeasureTheory.Integrable.integral_norm_condexpKernel (hm : m ≤ mΩ)
     (hf_int : Integrable f μ) : Integrable (fun ω => ∫ y, ‖f y‖ ∂condexpKernel μ m ω) μ :=
   by
@@ -138,7 +157,9 @@ theorem MeasureTheory.Integrable.integral_norm_condexpKernel (hm : m ≤ mΩ)
     integrable.integral_norm_cond_distrib (ae_measurable_id'' μ hm) aemeasurable_id
       (hf_int.comp_snd_map_prod_id hm)
 #align measure_theory.integrable.integral_norm_condexp_kernel MeasureTheory.Integrable.integral_norm_condexpKernel
+-/
 
+#print MeasureTheory.Integrable.norm_integral_condexpKernel /-
 theorem MeasureTheory.Integrable.norm_integral_condexpKernel [NormedSpace ℝ F] [CompleteSpace F]
     (hm : m ≤ mΩ) (hf_int : Integrable f μ) :
     Integrable (fun ω => ‖∫ y, f y ∂condexpKernel μ m ω‖) μ :=
@@ -148,7 +169,9 @@ theorem MeasureTheory.Integrable.norm_integral_condexpKernel [NormedSpace ℝ F]
     integrable.norm_integral_cond_distrib (ae_measurable_id'' μ hm) aemeasurable_id
       (hf_int.comp_snd_map_prod_id hm)
 #align measure_theory.integrable.norm_integral_condexp_kernel MeasureTheory.Integrable.norm_integral_condexpKernel
+-/
 
+#print MeasureTheory.Integrable.integral_condexpKernel /-
 theorem MeasureTheory.Integrable.integral_condexpKernel [NormedSpace ℝ F] [CompleteSpace F]
     (hm : m ≤ mΩ) (hf_int : Integrable f μ) :
     Integrable (fun ω => ∫ y, f y ∂condexpKernel μ m ω) μ :=
@@ -158,16 +181,20 @@ theorem MeasureTheory.Integrable.integral_condexpKernel [NormedSpace ℝ F] [Com
     integrable.integral_cond_distrib (ae_measurable_id'' μ hm) aemeasurable_id
       (hf_int.comp_snd_map_prod_id hm)
 #align measure_theory.integrable.integral_condexp_kernel MeasureTheory.Integrable.integral_condexpKernel
+-/
 
+#print ProbabilityTheory.integrable_toReal_condexpKernel /-
 theorem integrable_toReal_condexpKernel (hm : m ≤ mΩ) {s : Set Ω} (hs : MeasurableSet s) :
     Integrable (fun ω => (condexpKernel μ m ω s).toReal) μ :=
   by
   rw [condexp_kernel]
   exact integrable_to_real_cond_distrib (ae_measurable_id'' μ hm) hs
 #align probability_theory.integrable_to_real_condexp_kernel ProbabilityTheory.integrable_toReal_condexpKernel
+-/
 
 end Integrability
 
+#print ProbabilityTheory.condexp_ae_eq_integral_condexpKernel /-
 /-- The conditional expectation of `f` with respect to a σ-algebra `m` is almost everywhere equal to
 the integral `∫ y, f y ∂(condexp_kernel μ m ω)`. -/
 theorem condexp_ae_eq_integral_condexpKernel [NormedSpace ℝ F] [CompleteSpace F] (hm : m ≤ mΩ)
@@ -178,6 +205,7 @@ theorem condexp_ae_eq_integral_condexpKernel [NormedSpace ℝ F] [CompleteSpace
   refine' eventually_eq.trans _ (condexp_ae_eq_integral_cond_distrib_id hX hf_int)
   simp only [MeasurableSpace.comap_id, id.def]
 #align probability_theory.condexp_ae_eq_integral_condexp_kernel ProbabilityTheory.condexp_ae_eq_integral_condexpKernel
+-/
 
 end ProbabilityTheory
 

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

@@ -106,16 +106,16 @@ theorem MeasureTheory.AEStronglyMeasurable.integral_condexpKernel [NormedSpace 
       (hf.comp_snd_map_prod_id hm)
 #align measure_theory.ae_strongly_measurable.integral_condexp_kernel MeasureTheory.AEStronglyMeasurable.integral_condexpKernel
 
-theorem aeStronglyMeasurable'_integral_condexpKernel [NormedSpace ℝ F] [CompleteSpace F]
+theorem aEStronglyMeasurable'_integral_condexpKernel [NormedSpace ℝ F] [CompleteSpace F]
     (hm : m ≤ mΩ) (hf : AEStronglyMeasurable f μ) :
-    AeStronglyMeasurable' m (fun ω => ∫ y, f y ∂condexpKernel μ m ω) μ :=
+    AEStronglyMeasurable' m (fun ω => ∫ y, f y ∂condexpKernel μ m ω) μ :=
   by
   rw [condexp_kernel]
   have h :=
     ae_strongly_measurable'_integral_cond_distrib (ae_measurable_id'' μ hm) aemeasurable_id
       (hf.comp_snd_map_prod_id hm)
   rwa [MeasurableSpace.comap_id] at h 
-#align probability_theory.ae_strongly_measurable'_integral_condexp_kernel ProbabilityTheory.aeStronglyMeasurable'_integral_condexpKernel
+#align probability_theory.ae_strongly_measurable'_integral_condexp_kernel ProbabilityTheory.aEStronglyMeasurable'_integral_condexpKernel
 
 end Measurability
 

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

@@ -77,15 +77,15 @@ theorem MeasureTheory.Integrable.comp_snd_map_prod_id [NormedAddCommGroup F] (hm
 end AuxLemmas
 
 variable {Ω F : Type _} [TopologicalSpace Ω] {m : MeasurableSpace Ω} [mΩ : MeasurableSpace Ω]
-  [PolishSpace Ω] [BorelSpace Ω] [Nonempty Ω] {μ : Measure Ω} [FiniteMeasure μ]
+  [PolishSpace Ω] [BorelSpace Ω] [Nonempty Ω] {μ : Measure Ω} [IsFiniteMeasure μ]
   [NormedAddCommGroup F] {f : Ω → F}
 
 /-- Kernel associated with the conditional expectation with respect to a σ-algebra. It satisfies
 `μ[f | m] =ᵐ[μ] λ ω, ∫ y, f y ∂(condexp_kernel μ m ω)`.
 It is defined as the conditional distribution of the identity given the identity, where the second
 identity is understood as a map from `Ω` with the σ-algebra `mΩ` to `Ω` with σ-algebra `m`. -/
-noncomputable irreducible_def condexpKernel (μ : Measure Ω) [FiniteMeasure μ]
-  (m : MeasurableSpace Ω) : @kernel Ω Ω m mΩ :=
+noncomputable irreducible_def condexpKernel (μ : Measure Ω) [IsFiniteMeasure μ]
+    (m : MeasurableSpace Ω) : @kernel Ω Ω m mΩ :=
   @condDistrib Ω Ω Ω _ mΩ _ _ _ mΩ m id id μ _
 #align probability_theory.condexp_kernel ProbabilityTheory.condexpKernel
 

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

@@ -59,8 +59,8 @@ theorem MeasureTheory.AEStronglyMeasurable.comp_snd_map_prod_id [TopologicalSpac
     AEStronglyMeasurable (fun x : Ω × Ω => f x.2)
       (@Measure.map Ω (Ω × Ω) (m.Prod mΩ) mΩ (fun ω => (id ω, id ω)) μ) :=
   by
-  rw [← ae_strongly_measurable_comp_snd_map_prod_mk_iff (measurable_id'' hm)] at hf
-  simp_rw [id.def] at hf⊢
+  rw [← ae_strongly_measurable_comp_snd_map_prod_mk_iff (measurable_id'' hm)] at hf 
+  simp_rw [id.def] at hf ⊢
   exact hf
 #align measure_theory.ae_strongly_measurable.comp_snd_map_prod_id MeasureTheory.AEStronglyMeasurable.comp_snd_map_prod_id
 
@@ -69,8 +69,8 @@ theorem MeasureTheory.Integrable.comp_snd_map_prod_id [NormedAddCommGroup F] (hm
     Integrable (fun x : Ω × Ω => f x.2)
       (@Measure.map Ω (Ω × Ω) (m.Prod mΩ) mΩ (fun ω => (id ω, id ω)) μ) :=
   by
-  rw [← integrable_comp_snd_map_prod_mk_iff (measurable_id'' hm)] at hf
-  simp_rw [id.def] at hf⊢
+  rw [← integrable_comp_snd_map_prod_mk_iff (measurable_id'' hm)] at hf 
+  simp_rw [id.def] at hf ⊢
   exact hf
 #align measure_theory.integrable.comp_snd_map_prod_id MeasureTheory.Integrable.comp_snd_map_prod_id
 
@@ -114,7 +114,7 @@ theorem aeStronglyMeasurable'_integral_condexpKernel [NormedSpace ℝ F] [Comple
   have h :=
     ae_strongly_measurable'_integral_cond_distrib (ae_measurable_id'' μ hm) aemeasurable_id
       (hf.comp_snd_map_prod_id hm)
-  rwa [MeasurableSpace.comap_id] at h
+  rwa [MeasurableSpace.comap_id] at h 
 #align probability_theory.ae_strongly_measurable'_integral_condexp_kernel ProbabilityTheory.aeStronglyMeasurable'_integral_condexpKernel
 
 end Measurability

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

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>

@@ -97,7 +97,7 @@ theorem stronglyMeasurable_condexpKernel {s : Set Ω} (hs : MeasurableSet s) :
   Measurable.stronglyMeasurable (measurable_condexpKernel hs)
 
 theorem _root_.MeasureTheory.AEStronglyMeasurable.integral_condexpKernel [NormedSpace ℝ F]
-    [CompleteSpace F] (hf : AEStronglyMeasurable f μ) :
+    (hf : AEStronglyMeasurable f μ) :
     AEStronglyMeasurable (fun ω => ∫ y, f y ∂condexpKernel μ m ω) μ := by
   simp_rw [condexpKernel_apply_eq_condDistrib]
   exact AEStronglyMeasurable.integral_condDistrib
@@ -105,7 +105,7 @@ theorem _root_.MeasureTheory.AEStronglyMeasurable.integral_condexpKernel [Normed
     (hf.comp_snd_map_prod_id inf_le_right)
 #align measure_theory.ae_strongly_measurable.integral_condexp_kernel MeasureTheory.AEStronglyMeasurable.integral_condexpKernel
 
-theorem aestronglyMeasurable'_integral_condexpKernel [NormedSpace ℝ F] [CompleteSpace F]
+theorem aestronglyMeasurable'_integral_condexpKernel [NormedSpace ℝ F]
     (hf : AEStronglyMeasurable f μ) :
     AEStronglyMeasurable' m (fun ω => ∫ y, f y ∂condexpKernel μ m ω) μ := by
   rw [condexpKernel]
@@ -139,7 +139,7 @@ theorem _root_.MeasureTheory.Integrable.integral_norm_condexpKernel (hf_int : In
 #align measure_theory.integrable.integral_norm_condexp_kernel MeasureTheory.Integrable.integral_norm_condexpKernel
 
 theorem _root_.MeasureTheory.Integrable.norm_integral_condexpKernel [NormedSpace ℝ F]
-    [CompleteSpace F] (hf_int : Integrable f μ) :
+    (hf_int : Integrable f μ) :
     Integrable (fun ω => ‖∫ y, f y ∂condexpKernel μ m ω‖) μ := by
   rw [condexpKernel]
   exact Integrable.norm_integral_condDistrib
@@ -147,7 +147,7 @@ theorem _root_.MeasureTheory.Integrable.norm_integral_condexpKernel [NormedSpace
     (hf_int.comp_snd_map_prod_id (inf_le_right : m ⊓ mΩ ≤ mΩ))
 #align measure_theory.integrable.norm_integral_condexp_kernel MeasureTheory.Integrable.norm_integral_condexpKernel
 
-theorem _root_.MeasureTheory.Integrable.integral_condexpKernel [NormedSpace ℝ F] [CompleteSpace F]
+theorem _root_.MeasureTheory.Integrable.integral_condexpKernel [NormedSpace ℝ F]
     (hf_int : Integrable f μ) :
     Integrable (fun ω => ∫ y, f y ∂condexpKernel μ m ω) μ := by
   rw [condexpKernel]

Co-authored-by: Ruben Van de Velde <65514131+Ruben-VandeVelde@users.noreply.github.com>

@@ -45,7 +45,7 @@ theorem _root_.MeasureTheory.AEStronglyMeasurable.comp_snd_map_prod_id [Topologi
     (hm : m ≤ mΩ) (hf : AEStronglyMeasurable f μ) : AEStronglyMeasurable (fun x : Ω × Ω => f x.2)
       (@Measure.map Ω (Ω × Ω) (m.prod mΩ) mΩ (fun ω => (id ω, id ω)) μ) := by
   rw [← aestronglyMeasurable_comp_snd_map_prod_mk_iff (measurable_id'' hm)] at hf
-  simp_rw [id.def] at hf ⊢
+  simp_rw [id] at hf ⊢
   exact hf
 #align measure_theory.ae_strongly_measurable.comp_snd_map_prod_id MeasureTheory.AEStronglyMeasurable.comp_snd_map_prod_id
 
@@ -53,7 +53,7 @@ theorem _root_.MeasureTheory.Integrable.comp_snd_map_prod_id [NormedAddCommGroup
     (hf : Integrable f μ) : Integrable (fun x : Ω × Ω => f x.2)
       (@Measure.map Ω (Ω × Ω) (m.prod mΩ) mΩ (fun ω => (id ω, id ω)) μ) := by
   rw [← integrable_comp_snd_map_prod_mk_iff (measurable_id'' hm)] at hf
-  simp_rw [id.def] at hf ⊢
+  simp_rw [id] at hf ⊢
   exact hf
 #align measure_theory.integrable.comp_snd_map_prod_id MeasureTheory.Integrable.comp_snd_map_prod_id
 

@@ -59,8 +59,8 @@ theorem _root_.MeasureTheory.Integrable.comp_snd_map_prod_id [NormedAddCommGroup
 
 end AuxLemmas
 
-variable {Ω F : Type*} [TopologicalSpace Ω] {m : MeasurableSpace Ω} [mΩ : MeasurableSpace Ω]
-  [PolishSpace Ω] [BorelSpace Ω] [Nonempty Ω] {μ : Measure Ω} [IsFiniteMeasure μ]
+variable {Ω F : Type*} {m : MeasurableSpace Ω} [mΩ : MeasurableSpace Ω]
+  [StandardBorelSpace Ω] [Nonempty Ω] {μ : Measure Ω} [IsFiniteMeasure μ]
 
 /-- Kernel associated with the conditional expectation with respect to a σ-algebra. It satisfies
 `μ[f | m] =ᵐ[μ] fun ω => ∫ y, f y ∂(condexpKernel μ m ω)`.
@@ -70,13 +70,12 @@ We use `m ⊓ mΩ` instead of `m` to ensure that it is a sub-σ-algebra of `mΩ`
 `kernel.comap` to get a kernel from `m` to `mΩ` instead of from `m ⊓ mΩ` to `mΩ`. -/
 noncomputable irreducible_def condexpKernel (μ : Measure Ω) [IsFiniteMeasure μ]
     (m : MeasurableSpace Ω) : @kernel Ω Ω m mΩ :=
-  kernel.comap (@condDistrib Ω Ω Ω _ mΩ _ _ _ mΩ (m ⊓ mΩ) id id μ _) id
+  kernel.comap (@condDistrib Ω Ω Ω mΩ _ _ mΩ (m ⊓ mΩ) id id μ _) id
     (measurable_id'' (inf_le_left : m ⊓ mΩ ≤ m))
 #align probability_theory.condexp_kernel ProbabilityTheory.condexpKernel
 
-set_option autoImplicit true in
-lemma condexpKernel_apply_eq_condDistrib :
-    condexpKernel μ m ω = @condDistrib Ω Ω Ω _ mΩ _ _ _ mΩ (m ⊓ mΩ) id id μ _ (id ω) := by
+lemma condexpKernel_apply_eq_condDistrib {ω : Ω} :
+    condexpKernel μ m ω = @condDistrib Ω Ω Ω mΩ _ _ mΩ (m ⊓ mΩ) id id μ _ (id ω) := by
   simp_rw [condexpKernel, kernel.comap_apply]
 
 instance : IsMarkovKernel (condexpKernel μ m) := by simp only [condexpKernel]; infer_instance

Autoimplicits are highly controversial and also defeat the performance-improving work in #6474.

The intent of this PR is to make autoImplicit opt-in on a per-file basis, by disabling it in the lakefile and enabling it again with set_option autoImplicit true in the few files that rely on it.

That also keeps this PR small, as opposed to attempting to "fix" files to not need it any more.

I claim that many of the uses of autoImplicit in these files are accidental; situations such as:

• Assuming variables are in scope, but pasting the lemma in the wrong section
• Pasting in a lemma from a scratch file without checking to see if the variable names are consistent with the rest of the file
• Making a copy-paste error between lemmas and forgetting to add an explicit arguments.

Having set_option autoImplicit false as the default prevents these types of mistake being made in the 90% of files where autoImplicits are not used at all, and causes them to be caught by CI during review.

I think there were various points during the port where we encouraged porters to delete the universes u v lines; I think having autoparams for universe variables only would cover a lot of the cases we actually use them, while avoiding any real shortcomings.

A Zulip poll (after combining overlapping votes accordingly) was in favor of this change with 5:5:18 as the no:dontcare:yes vote ratio.

While this PR was being reviewed, a handful of files gained some more likely-accidental autoImplicits. In these places, set_option autoImplicit true has been placed locally within a section, rather than at the top of the file.

@@ -74,6 +74,7 @@ noncomputable irreducible_def condexpKernel (μ : Measure Ω) [IsFiniteMeasure 
     (measurable_id'' (inf_le_left : m ⊓ mΩ ≤ m))
 #align probability_theory.condexp_kernel ProbabilityTheory.condexpKernel
 
+set_option autoImplicit true in
 lemma condexpKernel_apply_eq_condDistrib :
     condexpKernel μ m ω = @condDistrib Ω Ω Ω _ mΩ _ _ _ mΩ (m ⊓ mΩ) id id μ _ (id ω) := by
   simp_rw [condexpKernel, kernel.comap_apply]

condexpKernel is a Markov kernel, is strongly measurable and is a.e. equal to the conditional expectation.

Co-authored-by: RemyDegenne <Remydegenne@gmail.com>

@@ -41,16 +41,6 @@ section AuxLemmas
 
 variable {Ω F : Type*} {m mΩ : MeasurableSpace Ω} {μ : Measure Ω} {f : Ω → F}
 
--- Porting note: todo: move to `MeasureTheory/MeasurableSpace`, after `Measurable.mono`
-theorem measurable_id'' (hm : m ≤ mΩ) : @Measurable Ω Ω mΩ m id :=
-  measurable_id.mono le_rfl hm
-#align probability_theory.measurable_id'' ProbabilityTheory.measurable_id''
-
--- Porting note: todo: move to `MeasureTheory/MeasurableSpace`, after `Measurable.mono`
-theorem aemeasurable_id'' (μ : Measure Ω) (hm : m ≤ mΩ) : @AEMeasurable Ω Ω m mΩ id μ :=
-  @Measurable.aemeasurable Ω Ω mΩ m id μ (measurable_id'' hm)
-#align probability_theory.ae_measurable_id'' ProbabilityTheory.aemeasurable_id''
-
 theorem _root_.MeasureTheory.AEStronglyMeasurable.comp_snd_map_prod_id [TopologicalSpace F]
     (hm : m ≤ mΩ) (hf : AEStronglyMeasurable f μ) : AEStronglyMeasurable (fun x : Ω × Ω => f x.2)
       (@Measure.map Ω (Ω × Ω) (m.prod mΩ) mΩ (fun ω => (id ω, id ω)) μ) := by
@@ -71,91 +61,144 @@ end AuxLemmas
 
 variable {Ω F : Type*} [TopologicalSpace Ω] {m : MeasurableSpace Ω} [mΩ : MeasurableSpace Ω]
   [PolishSpace Ω] [BorelSpace Ω] [Nonempty Ω] {μ : Measure Ω} [IsFiniteMeasure μ]
-  [NormedAddCommGroup F] {f : Ω → F}
 
 /-- Kernel associated with the conditional expectation with respect to a σ-algebra. It satisfies
 `μ[f | m] =ᵐ[μ] fun ω => ∫ y, f y ∂(condexpKernel μ m ω)`.
 It is defined as the conditional distribution of the identity given the identity, where the second
-identity is understood as a map from `Ω` with the σ-algebra `mΩ` to `Ω` with σ-algebra `m`. -/
+identity is understood as a map from `Ω` with the σ-algebra `mΩ` to `Ω` with σ-algebra `m ⊓ mΩ`.
+We use `m ⊓ mΩ` instead of `m` to ensure that it is a sub-σ-algebra of `mΩ`. We then use
+`kernel.comap` to get a kernel from `m` to `mΩ` instead of from `m ⊓ mΩ` to `mΩ`. -/
 noncomputable irreducible_def condexpKernel (μ : Measure Ω) [IsFiniteMeasure μ]
     (m : MeasurableSpace Ω) : @kernel Ω Ω m mΩ :=
-  @condDistrib Ω Ω Ω _ mΩ _ _ _ mΩ m id id μ _
+  kernel.comap (@condDistrib Ω Ω Ω _ mΩ _ _ _ mΩ (m ⊓ mΩ) id id μ _) id
+    (measurable_id'' (inf_le_left : m ⊓ mΩ ≤ m))
 #align probability_theory.condexp_kernel ProbabilityTheory.condexpKernel
 
+lemma condexpKernel_apply_eq_condDistrib :
+    condexpKernel μ m ω = @condDistrib Ω Ω Ω _ mΩ _ _ _ mΩ (m ⊓ mΩ) id id μ _ (id ω) := by
+  simp_rw [condexpKernel, kernel.comap_apply]
+
+instance : IsMarkovKernel (condexpKernel μ m) := by simp only [condexpKernel]; infer_instance
+
 section Measurability
 
+variable [NormedAddCommGroup F] {f : Ω → F}
+
 theorem measurable_condexpKernel {s : Set Ω} (hs : MeasurableSet s) :
     Measurable[m] fun ω => condexpKernel μ m ω s := by
-  rw [condexpKernel]; convert measurable_condDistrib (μ := μ) hs; rw [MeasurableSpace.comap_id]
+  simp_rw [condexpKernel_apply_eq_condDistrib]
+  refine Measurable.mono ?_ (inf_le_left : m ⊓ mΩ ≤ m) le_rfl
+  convert measurable_condDistrib (μ := μ) hs
+  rw [MeasurableSpace.comap_id]
 #align probability_theory.measurable_condexp_kernel ProbabilityTheory.measurable_condexpKernel
 
+theorem stronglyMeasurable_condexpKernel {s : Set Ω} (hs : MeasurableSet s) :
+    StronglyMeasurable[m] fun ω => condexpKernel μ m ω s :=
+  Measurable.stronglyMeasurable (measurable_condexpKernel hs)
+
 theorem _root_.MeasureTheory.AEStronglyMeasurable.integral_condexpKernel [NormedSpace ℝ F]
-    [CompleteSpace F] (hm : m ≤ mΩ) (hf : AEStronglyMeasurable f μ) :
+    [CompleteSpace F] (hf : AEStronglyMeasurable f μ) :
     AEStronglyMeasurable (fun ω => ∫ y, f y ∂condexpKernel μ m ω) μ := by
-  rw [condexpKernel]
-  exact AEStronglyMeasurable.integral_condDistrib (aemeasurable_id'' μ hm) aemeasurable_id
-    (hf.comp_snd_map_prod_id hm)
+  simp_rw [condexpKernel_apply_eq_condDistrib]
+  exact AEStronglyMeasurable.integral_condDistrib
+    (aemeasurable_id'' μ (inf_le_right : m ⊓ mΩ ≤ mΩ)) aemeasurable_id
+    (hf.comp_snd_map_prod_id inf_le_right)
 #align measure_theory.ae_strongly_measurable.integral_condexp_kernel MeasureTheory.AEStronglyMeasurable.integral_condexpKernel
 
 theorem aestronglyMeasurable'_integral_condexpKernel [NormedSpace ℝ F] [CompleteSpace F]
-    (hm : m ≤ mΩ) (hf : AEStronglyMeasurable f μ) :
+    (hf : AEStronglyMeasurable f μ) :
     AEStronglyMeasurable' m (fun ω => ∫ y, f y ∂condexpKernel μ m ω) μ := by
   rw [condexpKernel]
-  have h := aestronglyMeasurable'_integral_condDistrib (aemeasurable_id'' μ hm) aemeasurable_id
-    (hf.comp_snd_map_prod_id hm)
-  rwa [MeasurableSpace.comap_id] at h
+  have h := aestronglyMeasurable'_integral_condDistrib
+    (aemeasurable_id'' μ (inf_le_right : m ⊓ mΩ ≤ mΩ)) aemeasurable_id
+    (hf.comp_snd_map_prod_id (inf_le_right : m ⊓ mΩ ≤ mΩ))
+  rw [MeasurableSpace.comap_id] at h
+  exact AEStronglyMeasurable'.mono h inf_le_left
 #align probability_theory.ae_strongly_measurable'_integral_condexp_kernel ProbabilityTheory.aestronglyMeasurable'_integral_condexpKernel
 
 end Measurability
 
 section Integrability
 
-theorem _root_.MeasureTheory.Integrable.condexpKernel_ae (hm : m ≤ mΩ) (hf_int : Integrable f μ) :
+variable [NormedAddCommGroup F] {f : Ω → F}
+
+theorem _root_.MeasureTheory.Integrable.condexpKernel_ae (hf_int : Integrable f μ) :
     ∀ᵐ ω ∂μ, Integrable f (condexpKernel μ m ω) := by
   rw [condexpKernel]
-  exact Integrable.condDistrib_ae (aemeasurable_id'' μ hm) aemeasurable_id
-    (hf_int.comp_snd_map_prod_id hm)
+  exact Integrable.condDistrib_ae
+    (aemeasurable_id'' μ (inf_le_right : m ⊓ mΩ ≤ mΩ)) aemeasurable_id
+    (hf_int.comp_snd_map_prod_id (inf_le_right : m ⊓ mΩ ≤ mΩ))
 #align measure_theory.integrable.condexp_kernel_ae MeasureTheory.Integrable.condexpKernel_ae
 
-theorem _root_.MeasureTheory.Integrable.integral_norm_condexpKernel (hm : m ≤ mΩ)
-    (hf_int : Integrable f μ) : Integrable (fun ω => ∫ y, ‖f y‖ ∂condexpKernel μ m ω) μ := by
+theorem _root_.MeasureTheory.Integrable.integral_norm_condexpKernel (hf_int : Integrable f μ) :
+    Integrable (fun ω => ∫ y, ‖f y‖ ∂condexpKernel μ m ω) μ := by
   rw [condexpKernel]
-  exact Integrable.integral_norm_condDistrib (aemeasurable_id'' μ hm) aemeasurable_id
-    (hf_int.comp_snd_map_prod_id hm)
+  exact Integrable.integral_norm_condDistrib
+    (aemeasurable_id'' μ (inf_le_right : m ⊓ mΩ ≤ mΩ)) aemeasurable_id
+    (hf_int.comp_snd_map_prod_id (inf_le_right : m ⊓ mΩ ≤ mΩ))
 #align measure_theory.integrable.integral_norm_condexp_kernel MeasureTheory.Integrable.integral_norm_condexpKernel
 
 theorem _root_.MeasureTheory.Integrable.norm_integral_condexpKernel [NormedSpace ℝ F]
-    [CompleteSpace F] (hm : m ≤ mΩ) (hf_int : Integrable f μ) :
+    [CompleteSpace F] (hf_int : Integrable f μ) :
     Integrable (fun ω => ‖∫ y, f y ∂condexpKernel μ m ω‖) μ := by
   rw [condexpKernel]
-  exact Integrable.norm_integral_condDistrib (aemeasurable_id'' μ hm) aemeasurable_id
-    (hf_int.comp_snd_map_prod_id hm)
+  exact Integrable.norm_integral_condDistrib
+    (aemeasurable_id'' μ (inf_le_right : m ⊓ mΩ ≤ mΩ)) aemeasurable_id
+    (hf_int.comp_snd_map_prod_id (inf_le_right : m ⊓ mΩ ≤ mΩ))
 #align measure_theory.integrable.norm_integral_condexp_kernel MeasureTheory.Integrable.norm_integral_condexpKernel
 
 theorem _root_.MeasureTheory.Integrable.integral_condexpKernel [NormedSpace ℝ F] [CompleteSpace F]
-    (hm : m ≤ mΩ) (hf_int : Integrable f μ) :
+    (hf_int : Integrable f μ) :
     Integrable (fun ω => ∫ y, f y ∂condexpKernel μ m ω) μ := by
   rw [condexpKernel]
-  exact Integrable.integral_condDistrib (aemeasurable_id'' μ hm) aemeasurable_id
-    (hf_int.comp_snd_map_prod_id hm)
+  exact Integrable.integral_condDistrib
+    (aemeasurable_id'' μ (inf_le_right : m ⊓ mΩ ≤ mΩ)) aemeasurable_id
+    (hf_int.comp_snd_map_prod_id (inf_le_right : m ⊓ mΩ ≤ mΩ))
 #align measure_theory.integrable.integral_condexp_kernel MeasureTheory.Integrable.integral_condexpKernel
 
-theorem integrable_toReal_condexpKernel (hm : m ≤ mΩ) {s : Set Ω} (hs : MeasurableSet s) :
+theorem integrable_toReal_condexpKernel {s : Set Ω} (hs : MeasurableSet s) :
     Integrable (fun ω => (condexpKernel μ m ω s).toReal) μ := by
   rw [condexpKernel]
-  exact integrable_toReal_condDistrib (aemeasurable_id'' μ hm) hs
+  exact integrable_toReal_condDistrib (aemeasurable_id'' μ (inf_le_right : m ⊓ mΩ ≤ mΩ)) hs
 #align probability_theory.integrable_to_real_condexp_kernel ProbabilityTheory.integrable_toReal_condexpKernel
 
 end Integrability
 
+lemma condexpKernel_ae_eq_condexp' [IsFiniteMeasure μ] {s : Set Ω} (hs : MeasurableSet s) :
+    (fun ω ↦ (condexpKernel μ m ω s).toReal) =ᵐ[μ] μ⟦s | m ⊓ mΩ⟧ := by
+  have h := condDistrib_ae_eq_condexp (μ := μ)
+    (measurable_id'' (inf_le_right : m ⊓ mΩ ≤ mΩ)) measurable_id hs
+  simp only [id_eq, ge_iff_le, MeasurableSpace.comap_id, preimage_id_eq] at h
+  simp_rw [condexpKernel_apply_eq_condDistrib]
+  exact h
+
+lemma condexpKernel_ae_eq_condexp [IsFiniteMeasure μ]
+    (hm : m ≤ mΩ) {s : Set Ω} (hs : MeasurableSet s) :
+    (fun ω ↦ (condexpKernel μ m ω s).toReal) =ᵐ[μ] μ⟦s | m⟧ :=
+  (condexpKernel_ae_eq_condexp' hs).trans (by rw [inf_of_le_left hm])
+
+lemma condexpKernel_ae_eq_trim_condexp [IsFiniteMeasure μ]
+    (hm : m ≤ mΩ) {s : Set Ω} (hs : MeasurableSet s) :
+    (fun ω ↦ (condexpKernel μ m ω s).toReal) =ᵐ[μ.trim hm] μ⟦s | m⟧ := by
+  rw [ae_eq_trim_iff hm _ stronglyMeasurable_condexp]
+  · exact condexpKernel_ae_eq_condexp hm hs
+  · refine Measurable.stronglyMeasurable ?_
+    exact @Measurable.ennreal_toReal _ m _ (measurable_condexpKernel hs)
+
+theorem condexp_ae_eq_integral_condexpKernel' [NormedAddCommGroup F] {f : Ω → F}
+    [NormedSpace ℝ F] [CompleteSpace F] (hf_int : Integrable f μ) :
+    μ[f|m ⊓ mΩ] =ᵐ[μ] fun ω => ∫ y, f y ∂condexpKernel μ m ω := by
+  have hX : @Measurable Ω Ω mΩ (m ⊓ mΩ) id := measurable_id.mono le_rfl (inf_le_right : m ⊓ mΩ ≤ mΩ)
+  simp_rw [condexpKernel_apply_eq_condDistrib]
+  have h := condexp_ae_eq_integral_condDistrib_id hX hf_int
+  simpa only [MeasurableSpace.comap_id, id_eq] using h
+
 /-- The conditional expectation of `f` with respect to a σ-algebra `m` is almost everywhere equal to
 the integral `∫ y, f y ∂(condexpKernel μ m ω)`. -/
-theorem condexp_ae_eq_integral_condexpKernel [NormedSpace ℝ F] [CompleteSpace F] (hm : m ≤ mΩ)
-    (hf_int : Integrable f μ) : μ[f|m] =ᵐ[μ] fun ω => ∫ y, f y ∂condexpKernel μ m ω := by
-  have hX : @Measurable Ω Ω mΩ m id := measurable_id.mono le_rfl hm
-  rw [condexpKernel]
-  refine' EventuallyEq.trans _ (condexp_ae_eq_integral_condDistrib_id hX hf_int)
-  simp only [MeasurableSpace.comap_id, id.def]; rfl
+theorem condexp_ae_eq_integral_condexpKernel [NormedAddCommGroup F] {f : Ω → F}
+    [NormedSpace ℝ F] [CompleteSpace F] (hm : m ≤ mΩ) (hf_int : Integrable f μ) :
+    μ[f|m] =ᵐ[μ] fun ω => ∫ y, f y ∂condexpKernel μ m ω :=
+  ((condexp_ae_eq_integral_condexpKernel' hf_int).symm.trans (by rw [inf_of_le_left hm])).symm
 #align probability_theory.condexp_ae_eq_integral_condexp_kernel ProbabilityTheory.condexp_ae_eq_integral_condexpKernel
 
 end ProbabilityTheory

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

This has nice performance benefits.

@@ -39,7 +39,7 @@ namespace ProbabilityTheory
 
 section AuxLemmas
 
-variable {Ω F : Type _} {m mΩ : MeasurableSpace Ω} {μ : Measure Ω} {f : Ω → F}
+variable {Ω F : Type*} {m mΩ : MeasurableSpace Ω} {μ : Measure Ω} {f : Ω → F}
 
 -- Porting note: todo: move to `MeasureTheory/MeasurableSpace`, after `Measurable.mono`
 theorem measurable_id'' (hm : m ≤ mΩ) : @Measurable Ω Ω mΩ m id :=
@@ -69,7 +69,7 @@ theorem _root_.MeasureTheory.Integrable.comp_snd_map_prod_id [NormedAddCommGroup
 
 end AuxLemmas
 
-variable {Ω F : Type _} [TopologicalSpace Ω] {m : MeasurableSpace Ω} [mΩ : MeasurableSpace Ω]
+variable {Ω F : Type*} [TopologicalSpace Ω] {m : MeasurableSpace Ω} [mΩ : MeasurableSpace Ω]
   [PolishSpace Ω] [BorelSpace Ω] [Nonempty Ω] {μ : Measure Ω} [IsFiniteMeasure μ]
   [NormedAddCommGroup F] {f : Ω → F}
 

• depends on: #5966

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

@@ -2,14 +2,11 @@
 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.condexp
-! leanprover-community/mathlib commit 00abe0695d8767201e6d008afa22393978bb324d
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Probability.Kernel.CondDistrib
 
+#align_import probability.kernel.condexp from "leanprover-community/mathlib"@"00abe0695d8767201e6d008afa22393978bb324d"
+
 /-!
 # Kernel associated with a conditional expectation
 

@@ -44,12 +44,12 @@ section AuxLemmas
 
 variable {Ω F : Type _} {m mΩ : MeasurableSpace Ω} {μ : Measure Ω} {f : Ω → F}
 
--- todo after the port: move to `MeasureTheory/MeasurableSpace`, after `Measurable.mono`
+-- Porting note: todo: move to `MeasureTheory/MeasurableSpace`, after `Measurable.mono`
 theorem measurable_id'' (hm : m ≤ mΩ) : @Measurable Ω Ω mΩ m id :=
   measurable_id.mono le_rfl hm
 #align probability_theory.measurable_id'' ProbabilityTheory.measurable_id''
 
--- todo after the port: move to `MeasureTheory/MeasurableSpace`, after `Measurable.mono`
+-- Porting note: todo: move to `MeasureTheory/MeasurableSpace`, after `Measurable.mono`
 theorem aemeasurable_id'' (μ : Measure Ω) (hm : m ≤ mΩ) : @AEMeasurable Ω Ω m mΩ id μ :=
   @Measurable.aemeasurable Ω Ω mΩ m id μ (measurable_id'' hm)
 #align probability_theory.ae_measurable_id'' ProbabilityTheory.aemeasurable_id''