probability.kernel.invariance ⟷ Mathlib.Probability.Kernel.Invariance

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

@@ -92,10 +92,10 @@ def Invariant (κ : kernel α α) (μ : Measure α) : Prop :=
 
 variable {κ η : kernel α α} {μ : Measure α}
 
-#print ProbabilityTheory.kernel.Invariant.def' /-
-theorem Invariant.def' (hκ : Invariant κ μ) : μ.bind κ = μ :=
+#print ProbabilityTheory.kernel.Invariant.def /-
+theorem Invariant.def (hκ : Invariant κ μ) : μ.bind κ = μ :=
   hκ
-#align probability_theory.kernel.invariant.def ProbabilityTheory.kernel.Invariant.def'
+#align probability_theory.kernel.invariant.def ProbabilityTheory.kernel.Invariant.def
 -/
 
 #print ProbabilityTheory.kernel.Invariant.comp_const /-

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

@@ -92,10 +92,10 @@ def Invariant (κ : kernel α α) (μ : Measure α) : Prop :=
 
 variable {κ η : kernel α α} {μ : Measure α}
 
-#print ProbabilityTheory.kernel.Invariant.def /-
-theorem Invariant.def (hκ : Invariant κ μ) : μ.bind κ = μ :=
+#print ProbabilityTheory.kernel.Invariant.def' /-
+theorem Invariant.def' (hκ : Invariant κ μ) : μ.bind κ = μ :=
   hκ
-#align probability_theory.kernel.invariant.def ProbabilityTheory.kernel.Invariant.def
+#align probability_theory.kernel.invariant.def ProbabilityTheory.kernel.Invariant.def'
 -/
 
 #print ProbabilityTheory.kernel.Invariant.comp_const /-

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

@@ -3,7 +3,7 @@ Copyright (c) 2023 Kexing Ying. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kexing Ying
 -/
-import Mathbin.Probability.Kernel.Composition
+import Probability.Kernel.Composition
 
 #align_import probability.kernel.invariance from "leanprover-community/mathlib"@"2a0ce625dbb0ffbc7d1316597de0b25c1ec75303"
 

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

@@ -2,14 +2,11 @@
 Copyright (c) 2023 Kexing Ying. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kexing Ying
-
-! This file was ported from Lean 3 source module probability.kernel.invariance
-! leanprover-community/mathlib commit 2a0ce625dbb0ffbc7d1316597de0b25c1ec75303
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Probability.Kernel.Composition
 
+#align_import probability.kernel.invariance from "leanprover-community/mathlib"@"2a0ce625dbb0ffbc7d1316597de0b25c1ec75303"
+
 /-!
 # Invariance of measures along a kernel
 

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

@@ -70,7 +70,7 @@ theorem bind_smul (κ : kernel α β) (μ : Measure α) (r : ℝ≥0∞) : (r 
 theorem const_bind_eq_comp_const (κ : kernel α β) (μ : Measure α) :
     const α (μ.bind κ) = κ ∘ₖ const α μ :=
   by
-  ext (a s hs) : 2
+  ext a s hs : 2
   simp_rw [comp_apply' _ _ _ hs, const_apply, measure.bind_apply hs (kernel.measurable _)]
 #align probability_theory.kernel.const_bind_eq_comp_const ProbabilityTheory.kernel.const_bind_eq_comp_const
 -/

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

@@ -45,6 +45,7 @@ namespace Kernel
 /-! ### Push-forward of measures along a kernel -/
 
 
+#print ProbabilityTheory.kernel.bind_add /-
 @[simp]
 theorem bind_add (μ ν : Measure α) (κ : kernel α β) : (μ + ν).bind κ = μ.bind κ + ν.bind κ :=
   by
@@ -53,7 +54,9 @@ theorem bind_add (μ ν : Measure α) (κ : kernel α β) : (μ + ν).bind κ =
     Pi.add_apply, measure.bind_apply hs (kernel.measurable _),
     measure.bind_apply hs (kernel.measurable _)]
 #align probability_theory.kernel.bind_add ProbabilityTheory.kernel.bind_add
+-/
 
+#print ProbabilityTheory.kernel.bind_smul /-
 @[simp]
 theorem bind_smul (κ : kernel α β) (μ : Measure α) (r : ℝ≥0∞) : (r • μ).bind κ = r • μ.bind κ :=
   by
@@ -61,38 +64,50 @@ theorem bind_smul (κ : kernel α β) (μ : Measure α) (r : ℝ≥0∞) : (r 
   rw [measure.bind_apply hs (kernel.measurable _), lintegral_smul_measure, measure.coe_smul,
     Pi.smul_apply, measure.bind_apply hs (kernel.measurable _), smul_eq_mul]
 #align probability_theory.kernel.bind_smul ProbabilityTheory.kernel.bind_smul
+-/
 
+#print ProbabilityTheory.kernel.const_bind_eq_comp_const /-
 theorem const_bind_eq_comp_const (κ : kernel α β) (μ : Measure α) :
     const α (μ.bind κ) = κ ∘ₖ const α μ :=
   by
   ext (a s hs) : 2
   simp_rw [comp_apply' _ _ _ hs, const_apply, measure.bind_apply hs (kernel.measurable _)]
 #align probability_theory.kernel.const_bind_eq_comp_const ProbabilityTheory.kernel.const_bind_eq_comp_const
+-/
 
+#print ProbabilityTheory.kernel.comp_const_apply_eq_bind /-
 theorem comp_const_apply_eq_bind (κ : kernel α β) (μ : Measure α) (a : α) :
     (κ ∘ₖ const α μ) a = μ.bind κ := by
   rw [← const_apply (μ.bind κ) a, const_bind_eq_comp_const κ μ]
 #align probability_theory.kernel.comp_const_apply_eq_bind ProbabilityTheory.kernel.comp_const_apply_eq_bind
+-/
 
 /-! ### Invariant measures of kernels -/
 
 
+#print ProbabilityTheory.kernel.Invariant /-
 /-- A measure `μ` is invariant with respect to the kernel `κ` if the push-forward measure of `μ`
 along `κ` equals `μ`. -/
 def Invariant (κ : kernel α α) (μ : Measure α) : Prop :=
   μ.bind κ = μ
 #align probability_theory.kernel.invariant ProbabilityTheory.kernel.Invariant
+-/
 
 variable {κ η : kernel α α} {μ : Measure α}
 
+#print ProbabilityTheory.kernel.Invariant.def /-
 theorem Invariant.def (hκ : Invariant κ μ) : μ.bind κ = μ :=
   hκ
 #align probability_theory.kernel.invariant.def ProbabilityTheory.kernel.Invariant.def
+-/
 
+#print ProbabilityTheory.kernel.Invariant.comp_const /-
 theorem Invariant.comp_const (hκ : Invariant κ μ) : κ ∘ₖ const α μ = const α μ := by
   rw [← const_bind_eq_comp_const κ μ, hκ.def]
 #align probability_theory.kernel.invariant.comp_const ProbabilityTheory.kernel.Invariant.comp_const
+-/
 
+#print ProbabilityTheory.kernel.Invariant.comp /-
 theorem Invariant.comp [IsSFiniteKernel κ] (hκ : Invariant κ μ) (hη : Invariant η μ) :
     Invariant (κ ∘ₖ η) μ := by
   cases' isEmpty_or_nonempty α with _ hα
@@ -101,6 +116,7 @@ theorem Invariant.comp [IsSFiniteKernel κ] (hκ : Invariant κ μ) (hη : Invar
     simp_rw [invariant, ← comp_const_apply_eq_bind (κ ∘ₖ η) μ hα.some, comp_assoc, hη.comp_const,
       hκ.comp_const, const_apply]
 #align probability_theory.kernel.invariant.comp ProbabilityTheory.kernel.Invariant.comp
+-/
 
 end Kernel
 

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

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kexing Ying
 
 ! This file was ported from Lean 3 source module probability.kernel.invariance
-! leanprover-community/mathlib commit 3b92d54a05ee592aa2c6181a4e76b1bb7cc45d0b
+! leanprover-community/mathlib commit 2a0ce625dbb0ffbc7d1316597de0b25c1ec75303
 ! 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.Composition
 /-!
 # Invariance of measures along a kernel
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 We say that a measure `μ` is invariant with respect to a kernel `κ` if its push-forward along the
 kernel `μ.bind κ` is the same measure.
 

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

@@ -37,8 +37,6 @@ namespace ProbabilityTheory
 
 variable {α β γ : Type _} {mα : MeasurableSpace α} {mβ : MeasurableSpace β} {mγ : MeasurableSpace γ}
 
-include mα mβ
-
 namespace Kernel
 
 /-! ### Push-forward of measures along a kernel -/
@@ -73,8 +71,6 @@ theorem comp_const_apply_eq_bind (κ : kernel α β) (μ : Measure α) (a : α)
   rw [← const_apply (μ.bind κ) a, const_bind_eq_comp_const κ μ]
 #align probability_theory.kernel.comp_const_apply_eq_bind ProbabilityTheory.kernel.comp_const_apply_eq_bind
 
-omit mβ
-
 /-! ### Invariant measures of kernels -/
 
 

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

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kexing Ying
 
 ! This file was ported from Lean 3 source module probability.kernel.invariance
-! leanprover-community/mathlib commit a9545e8a564bac7f24637443f52ae955474e4991
+! leanprover-community/mathlib commit 3b92d54a05ee592aa2c6181a4e76b1bb7cc45d0b
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -13,20 +13,17 @@ import Mathbin.Probability.Kernel.Composition
 /-!
 # Invariance of measures along a kernel
 
-We define the push-forward of a measure along a kernel which results in another measure. In the
-case that the push-forward measure is the same as the original measure, we say that the measure is
-invariant with respect to the kernel.
+We say that a measure `μ` is invariant with respect to a kernel `κ` if its push-forward along the
+kernel `μ.bind κ` is the same measure.
 
 ## Main definitions
 
-* `probability_theory.kernel.map_measure`: the push-forward of a measure along a kernel.
 * `probability_theory.kernel.invariant`: invariance of a given measure with respect to a kernel.
 
 ## Useful lemmas
 
-* `probability_theory.kernel.comp_apply_eq_map_measure`,
-  `probability_theory.kernel.const_map_measure_eq_comp_const`, and
-  `probability_theory.kernel.comp_const_apply_eq_map_measure` established the relationship between
+* `probability_theory.kernel.const_bind_eq_comp_const`, and
+  `probability_theory.kernel.comp_const_apply_eq_bind` established the relationship between
   the push-forward measure and the composition of kernels.
 
 -/
@@ -47,81 +44,34 @@ namespace Kernel
 /-! ### Push-forward of measures along a kernel -/
 
 
-/-- The push-forward of a measure along a kernel. -/
-noncomputable def mapMeasure (κ : kernel α β) (μ : Measure α) : Measure β :=
-  Measure.ofMeasurable (fun s hs => ∫⁻ x, κ x s ∂μ)
-    (by simp only [measure_empty, MeasureTheory.lintegral_const, MulZeroClass.zero_mul])
-    (by
-      intro f hf₁ hf₂
-      simp_rw [measure_Union hf₂ hf₁,
-        lintegral_tsum fun i => (kernel.measurable_coe κ (hf₁ i)).AEMeasurable])
-#align probability_theory.kernel.map_measure ProbabilityTheory.kernel.mapMeasure
-
-@[simp]
-theorem mapMeasure_apply (κ : kernel α β) (μ : Measure α) {s : Set β} (hs : MeasurableSet s) :
-    mapMeasure κ μ s = ∫⁻ x, κ x s ∂μ := by rw [map_measure, measure.of_measurable_apply s hs]
-#align probability_theory.kernel.map_measure_apply ProbabilityTheory.kernel.mapMeasure_apply
-
 @[simp]
-theorem mapMeasure_zero (κ : kernel α β) : mapMeasure κ 0 = 0 :=
+theorem bind_add (μ ν : Measure α) (κ : kernel α β) : (μ + ν).bind κ = μ.bind κ + ν.bind κ :=
   by
   ext1 s hs
-  rw [map_measure_apply κ 0 hs, lintegral_zero_measure, measure.coe_zero, Pi.zero_apply]
-#align probability_theory.kernel.map_measure_zero ProbabilityTheory.kernel.mapMeasure_zero
+  rw [measure.bind_apply hs (kernel.measurable _), lintegral_add_measure, measure.coe_add,
+    Pi.add_apply, measure.bind_apply hs (kernel.measurable _),
+    measure.bind_apply hs (kernel.measurable _)]
+#align probability_theory.kernel.bind_add ProbabilityTheory.kernel.bind_add
 
 @[simp]
-theorem mapMeasure_add (κ : kernel α β) (μ ν : Measure α) :
-    mapMeasure κ (μ + ν) = mapMeasure κ μ + mapMeasure κ ν :=
+theorem bind_smul (κ : kernel α β) (μ : Measure α) (r : ℝ≥0∞) : (r • μ).bind κ = r • μ.bind κ :=
   by
   ext1 s hs
-  rw [map_measure_apply κ (μ + ν) hs, lintegral_add_measure, measure.coe_add, Pi.add_apply,
-    map_measure_apply κ μ hs, map_measure_apply κ ν hs]
-#align probability_theory.kernel.map_measure_add ProbabilityTheory.kernel.mapMeasure_add
+  rw [measure.bind_apply hs (kernel.measurable _), lintegral_smul_measure, measure.coe_smul,
+    Pi.smul_apply, measure.bind_apply hs (kernel.measurable _), smul_eq_mul]
+#align probability_theory.kernel.bind_smul ProbabilityTheory.kernel.bind_smul
 
-@[simp]
-theorem mapMeasure_smul (κ : kernel α β) (μ : Measure α) (r : ℝ≥0∞) :
-    mapMeasure κ (r • μ) = r • mapMeasure κ μ :=
+theorem const_bind_eq_comp_const (κ : kernel α β) (μ : Measure α) :
+    const α (μ.bind κ) = κ ∘ₖ const α μ :=
   by
-  ext1 s hs
-  rw [map_measure_apply κ (r • μ) hs, lintegral_smul_measure, measure.coe_smul, Pi.smul_apply,
-    map_measure_apply κ μ hs, smul_eq_mul]
-#align probability_theory.kernel.map_measure_smul ProbabilityTheory.kernel.mapMeasure_smul
+  ext (a s hs) : 2
+  simp_rw [comp_apply' _ _ _ hs, const_apply, measure.bind_apply hs (kernel.measurable _)]
+#align probability_theory.kernel.const_bind_eq_comp_const ProbabilityTheory.kernel.const_bind_eq_comp_const
 
-include mγ
-
-theorem comp_apply_eq_mapMeasure (η : kernel β γ) [IsSFiniteKernel η] (κ : kernel α β)
-    [IsSFiniteKernel κ] (a : α) : (η ∘ₖ κ) a = mapMeasure η (κ a) :=
-  by
-  ext1 s hs
-  rw [comp_apply η κ a hs, map_measure_apply η _ hs]
-#align probability_theory.kernel.comp_apply_eq_map_measure ProbabilityTheory.kernel.comp_apply_eq_mapMeasure
-
-omit mγ
-
-theorem const_mapMeasure_eq_comp_const (κ : kernel α β) [IsSFiniteKernel κ] (μ : Measure α)
-    [IsFiniteMeasure μ] : const α (mapMeasure κ μ) = κ ∘ₖ const α μ :=
-  by
-  ext1 a; ext1 s hs
-  rw [const_apply, map_measure_apply _ _ hs, comp_apply _ _ _ hs, const_apply]
-#align probability_theory.kernel.const_map_measure_eq_comp_const ProbabilityTheory.kernel.const_mapMeasure_eq_comp_const
-
-theorem comp_const_apply_eq_mapMeasure (κ : kernel α β) [IsSFiniteKernel κ] (μ : Measure α)
-    [IsFiniteMeasure μ] (a : α) : (κ ∘ₖ const α μ) a = mapMeasure κ μ := by
-  rw [← const_apply (map_measure κ μ) a, const_map_measure_eq_comp_const κ μ]
-#align probability_theory.kernel.comp_const_apply_eq_map_measure ProbabilityTheory.kernel.comp_const_apply_eq_mapMeasure
-
-theorem lintegral_mapMeasure (κ : kernel α β) [IsSFiniteKernel κ] (μ : Measure α)
-    [IsFiniteMeasure μ] {f : β → ℝ≥0∞} (hf : Measurable f) :
-    (∫⁻ b, f b ∂mapMeasure κ μ) = ∫⁻ a, ∫⁻ b, f b ∂κ a ∂μ :=
-  by
-  by_cases hα : Nonempty α
-  · have := const_apply μ hα.some
-    swap; infer_instance
-    conv_rhs => rw [← this]
-    rw [← lintegral_comp _ _ _ hf, ← comp_const_apply_eq_map_measure κ μ hα.some]
-  · haveI := not_nonempty_iff.1 hα
-    rw [μ.eq_zero_of_is_empty, map_measure_zero, lintegral_zero_measure, lintegral_zero_measure]
-#align probability_theory.kernel.lintegral_map_measure ProbabilityTheory.kernel.lintegral_mapMeasure
+theorem comp_const_apply_eq_bind (κ : kernel α β) (μ : Measure α) (a : α) :
+    (κ ∘ₖ const α μ) a = μ.bind κ := by
+  rw [← const_apply (μ.bind κ) a, const_bind_eq_comp_const κ μ]
+#align probability_theory.kernel.comp_const_apply_eq_bind ProbabilityTheory.kernel.comp_const_apply_eq_bind
 
 omit mβ
 
@@ -131,28 +81,26 @@ omit mβ
 /-- A measure `μ` is invariant with respect to the kernel `κ` if the push-forward measure of `μ`
 along `κ` equals `μ`. -/
 def Invariant (κ : kernel α α) (μ : Measure α) : Prop :=
-  mapMeasure κ μ = μ
+  μ.bind κ = μ
 #align probability_theory.kernel.invariant ProbabilityTheory.kernel.Invariant
 
 variable {κ η : kernel α α} {μ : Measure α}
 
-theorem Invariant.def (hκ : Invariant κ μ) : mapMeasure κ μ = μ :=
+theorem Invariant.def (hκ : Invariant κ μ) : μ.bind κ = μ :=
   hκ
 #align probability_theory.kernel.invariant.def ProbabilityTheory.kernel.Invariant.def
 
-theorem Invariant.comp_const [IsSFiniteKernel κ] [IsFiniteMeasure μ] (hκ : Invariant κ μ) :
-    κ ∘ₖ const α μ = const α μ := by rw [← const_map_measure_eq_comp_const κ μ, hκ.def]
+theorem Invariant.comp_const (hκ : Invariant κ μ) : κ ∘ₖ const α μ = const α μ := by
+  rw [← const_bind_eq_comp_const κ μ, hκ.def]
 #align probability_theory.kernel.invariant.comp_const ProbabilityTheory.kernel.Invariant.comp_const
 
-theorem Invariant.comp [IsSFiniteKernel κ] [IsSFiniteKernel η] [IsFiniteMeasure μ]
-    (hκ : Invariant κ μ) (hη : Invariant η μ) : Invariant (κ ∘ₖ η) μ :=
-  by
-  by_cases hα : Nonempty α
+theorem Invariant.comp [IsSFiniteKernel κ] (hκ : Invariant κ μ) (hη : Invariant η μ) :
+    Invariant (κ ∘ₖ η) μ := by
+  cases' isEmpty_or_nonempty α with _ hα
+  · exact Subsingleton.elim _ _
   ·
-    simp_rw [invariant, ← comp_const_apply_eq_map_measure (κ ∘ₖ η) μ hα.some, comp_assoc,
-      hη.comp_const, hκ.comp_const, const_apply]
-  · haveI := not_nonempty_iff.1 hα
-    exact Subsingleton.elim _ _
+    simp_rw [invariant, ← comp_const_apply_eq_bind (κ ∘ₖ η) μ hα.some, comp_assoc, hη.comp_const,
+      hκ.comp_const, const_apply]
 #align probability_theory.kernel.invariant.comp ProbabilityTheory.kernel.Invariant.comp
 
 end Kernel

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

@@ -99,19 +99,20 @@ theorem comp_apply_eq_mapMeasure (η : kernel β γ) [IsSFiniteKernel η] (κ :
 omit mγ
 
 theorem const_mapMeasure_eq_comp_const (κ : kernel α β) [IsSFiniteKernel κ] (μ : Measure α)
-    [FiniteMeasure μ] : const α (mapMeasure κ μ) = κ ∘ₖ const α μ :=
+    [IsFiniteMeasure μ] : const α (mapMeasure κ μ) = κ ∘ₖ const α μ :=
   by
   ext1 a; ext1 s hs
   rw [const_apply, map_measure_apply _ _ hs, comp_apply _ _ _ hs, const_apply]
 #align probability_theory.kernel.const_map_measure_eq_comp_const ProbabilityTheory.kernel.const_mapMeasure_eq_comp_const
 
 theorem comp_const_apply_eq_mapMeasure (κ : kernel α β) [IsSFiniteKernel κ] (μ : Measure α)
-    [FiniteMeasure μ] (a : α) : (κ ∘ₖ const α μ) a = mapMeasure κ μ := by
+    [IsFiniteMeasure μ] (a : α) : (κ ∘ₖ const α μ) a = mapMeasure κ μ := by
   rw [← const_apply (map_measure κ μ) a, const_map_measure_eq_comp_const κ μ]
 #align probability_theory.kernel.comp_const_apply_eq_map_measure ProbabilityTheory.kernel.comp_const_apply_eq_mapMeasure
 
-theorem lintegral_mapMeasure (κ : kernel α β) [IsSFiniteKernel κ] (μ : Measure α) [FiniteMeasure μ]
-    {f : β → ℝ≥0∞} (hf : Measurable f) : (∫⁻ b, f b ∂mapMeasure κ μ) = ∫⁻ a, ∫⁻ b, f b ∂κ a ∂μ :=
+theorem lintegral_mapMeasure (κ : kernel α β) [IsSFiniteKernel κ] (μ : Measure α)
+    [IsFiniteMeasure μ] {f : β → ℝ≥0∞} (hf : Measurable f) :
+    (∫⁻ b, f b ∂mapMeasure κ μ) = ∫⁻ a, ∫⁻ b, f b ∂κ a ∂μ :=
   by
   by_cases hα : Nonempty α
   · have := const_apply μ hα.some
@@ -139,11 +140,11 @@ theorem Invariant.def (hκ : Invariant κ μ) : mapMeasure κ μ = μ :=
   hκ
 #align probability_theory.kernel.invariant.def ProbabilityTheory.kernel.Invariant.def
 
-theorem Invariant.comp_const [IsSFiniteKernel κ] [FiniteMeasure μ] (hκ : Invariant κ μ) :
+theorem Invariant.comp_const [IsSFiniteKernel κ] [IsFiniteMeasure μ] (hκ : Invariant κ μ) :
     κ ∘ₖ const α μ = const α μ := by rw [← const_map_measure_eq_comp_const κ μ, hκ.def]
 #align probability_theory.kernel.invariant.comp_const ProbabilityTheory.kernel.Invariant.comp_const
 
-theorem Invariant.comp [IsSFiniteKernel κ] [IsSFiniteKernel η] [FiniteMeasure μ]
+theorem Invariant.comp [IsSFiniteKernel κ] [IsSFiniteKernel η] [IsFiniteMeasure μ]
     (hκ : Invariant κ μ) (hη : Invariant η μ) : Invariant (κ ∘ₖ η) μ :=
   by
   by_cases hα : Nonempty α

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

@@ -34,7 +34,7 @@ invariant with respect to the kernel.
 
 open MeasureTheory
 
-open MeasureTheory ENNReal ProbabilityTheory
+open scoped MeasureTheory ENNReal ProbabilityTheory
 
 namespace ProbabilityTheory
 

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

@@ -115,8 +115,7 @@ theorem lintegral_mapMeasure (κ : kernel α β) [IsSFiniteKernel κ] (μ : Meas
   by
   by_cases hα : Nonempty α
   · have := const_apply μ hα.some
-    swap
-    infer_instance
+    swap; infer_instance
     conv_rhs => rw [← this]
     rw [← lintegral_comp _ _ _ hf, ← comp_const_apply_eq_map_measure κ μ hα.some]
   · haveI := not_nonempty_iff.1 hα

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

@@ -99,20 +99,19 @@ theorem comp_apply_eq_mapMeasure (η : kernel β γ) [IsSFiniteKernel η] (κ :
 omit mγ
 
 theorem const_mapMeasure_eq_comp_const (κ : kernel α β) [IsSFiniteKernel κ] (μ : Measure α)
-    [IsFiniteMeasure μ] : const α (mapMeasure κ μ) = κ ∘ₖ const α μ :=
+    [FiniteMeasure μ] : const α (mapMeasure κ μ) = κ ∘ₖ const α μ :=
   by
   ext1 a; ext1 s hs
   rw [const_apply, map_measure_apply _ _ hs, comp_apply _ _ _ hs, const_apply]
 #align probability_theory.kernel.const_map_measure_eq_comp_const ProbabilityTheory.kernel.const_mapMeasure_eq_comp_const
 
 theorem comp_const_apply_eq_mapMeasure (κ : kernel α β) [IsSFiniteKernel κ] (μ : Measure α)
-    [IsFiniteMeasure μ] (a : α) : (κ ∘ₖ const α μ) a = mapMeasure κ μ := by
+    [FiniteMeasure μ] (a : α) : (κ ∘ₖ const α μ) a = mapMeasure κ μ := by
   rw [← const_apply (map_measure κ μ) a, const_map_measure_eq_comp_const κ μ]
 #align probability_theory.kernel.comp_const_apply_eq_map_measure ProbabilityTheory.kernel.comp_const_apply_eq_mapMeasure
 
-theorem lintegral_mapMeasure (κ : kernel α β) [IsSFiniteKernel κ] (μ : Measure α)
-    [IsFiniteMeasure μ] {f : β → ℝ≥0∞} (hf : Measurable f) :
-    (∫⁻ b, f b ∂mapMeasure κ μ) = ∫⁻ a, ∫⁻ b, f b ∂κ a ∂μ :=
+theorem lintegral_mapMeasure (κ : kernel α β) [IsSFiniteKernel κ] (μ : Measure α) [FiniteMeasure μ]
+    {f : β → ℝ≥0∞} (hf : Measurable f) : (∫⁻ b, f b ∂mapMeasure κ μ) = ∫⁻ a, ∫⁻ b, f b ∂κ a ∂μ :=
   by
   by_cases hα : Nonempty α
   · have := const_apply μ hα.some
@@ -141,11 +140,11 @@ theorem Invariant.def (hκ : Invariant κ μ) : mapMeasure κ μ = μ :=
   hκ
 #align probability_theory.kernel.invariant.def ProbabilityTheory.kernel.Invariant.def
 
-theorem Invariant.comp_const [IsSFiniteKernel κ] [IsFiniteMeasure μ] (hκ : Invariant κ μ) :
+theorem Invariant.comp_const [IsSFiniteKernel κ] [FiniteMeasure μ] (hκ : Invariant κ μ) :
     κ ∘ₖ const α μ = const α μ := by rw [← const_map_measure_eq_comp_const κ μ, hκ.def]
 #align probability_theory.kernel.invariant.comp_const ProbabilityTheory.kernel.Invariant.comp_const
 
-theorem Invariant.comp [IsSFiniteKernel κ] [IsSFiniteKernel η] [IsFiniteMeasure μ]
+theorem Invariant.comp [IsSFiniteKernel κ] [IsSFiniteKernel η] [FiniteMeasure μ]
     (hκ : Invariant κ μ) (hη : Invariant η μ) : Invariant (κ ∘ₖ η) μ :=
   by
   by_cases hα : Nonempty α

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

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kexing Ying
 
 ! This file was ported from Lean 3 source module probability.kernel.invariance
-! leanprover-community/mathlib commit 97d1aa955750bd57a7eeef91de310e633881670b
+! leanprover-community/mathlib commit a9545e8a564bac7f24637443f52ae955474e4991
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -50,7 +50,7 @@ namespace Kernel
 /-- The push-forward of a measure along a kernel. -/
 noncomputable def mapMeasure (κ : kernel α β) (μ : Measure α) : Measure β :=
   Measure.ofMeasurable (fun s hs => ∫⁻ x, κ x s ∂μ)
-    (by simp only [measure_empty, lintegral_const, MulZeroClass.zero_mul])
+    (by simp only [measure_empty, MeasureTheory.lintegral_const, MulZeroClass.zero_mul])
     (by
       intro f hf₁ hf₂
       simp_rw [measure_Union hf₂ hf₁,

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

@@ -54,7 +54,7 @@ noncomputable def mapMeasure (κ : kernel α β) (μ : Measure α) : Measure β
     (by
       intro f hf₁ hf₂
       simp_rw [measure_Union hf₂ hf₁,
-        lintegral_tsum fun i => (kernel.measurable_coe κ (hf₁ i)).AeMeasurable])
+        lintegral_tsum fun i => (kernel.measurable_coe κ (hf₁ i)).AEMeasurable])
 #align probability_theory.kernel.map_measure ProbabilityTheory.kernel.mapMeasure
 
 @[simp]

mathlib commit https://github.com/leanprover-community/mathlib/commit/da3fc4a33ff6bc75f077f691dc94c217b8d41559

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

@@ -76,14 +76,12 @@ def Invariant (κ : kernel α α) (μ : Measure α) : Prop :=
 
 variable {κ η : kernel α α} {μ : Measure α}
 
--- Adaptation note: 2024-03-15
--- Renamed to avoid the reserved name `Invariant.def`.
-theorem Invariant.def' (hκ : Invariant κ μ) : μ.bind κ = μ :=
+theorem Invariant.def (hκ : Invariant κ μ) : μ.bind κ = μ :=
   hκ
-#align probability_theory.kernel.invariant.def ProbabilityTheory.kernel.Invariant.def'
+#align probability_theory.kernel.invariant.def ProbabilityTheory.kernel.Invariant.def
 
 theorem Invariant.comp_const (hκ : Invariant κ μ) : κ ∘ₖ const α μ = const α μ := by
-  rw [← const_bind_eq_comp_const κ μ, hκ.def']
+  rw [← const_bind_eq_comp_const κ μ, hκ.def]
 #align probability_theory.kernel.invariant.comp_const ProbabilityTheory.kernel.Invariant.comp_const
 
 theorem Invariant.comp [IsSFiniteKernel κ] (hκ : Invariant κ μ) (hη : Invariant η μ) :

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

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

@@ -76,12 +76,14 @@ def Invariant (κ : kernel α α) (μ : Measure α) : Prop :=
 
 variable {κ η : kernel α α} {μ : Measure α}
 
-theorem Invariant.def (hκ : Invariant κ μ) : μ.bind κ = μ :=
+-- Adaptation note: 2024-03-15
+-- Renamed to avoid the reserved name `Invariant.def`.
+theorem Invariant.def' (hκ : Invariant κ μ) : μ.bind κ = μ :=
   hκ
-#align probability_theory.kernel.invariant.def ProbabilityTheory.kernel.Invariant.def
+#align probability_theory.kernel.invariant.def ProbabilityTheory.kernel.Invariant.def'
 
 theorem Invariant.comp_const (hκ : Invariant κ μ) : κ ∘ₖ const α μ = const α μ := by
-  rw [← const_bind_eq_comp_const κ μ, hκ.def]
+  rw [← const_bind_eq_comp_const κ μ, hκ.def']
 #align probability_theory.kernel.invariant.comp_const ProbabilityTheory.kernel.Invariant.comp_const
 
 theorem Invariant.comp [IsSFiniteKernel κ] (hκ : Invariant κ μ) (hη : Invariant η μ) :

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

This has nice performance benefits.

@@ -32,7 +32,7 @@ open scoped MeasureTheory ENNReal ProbabilityTheory
 
 namespace ProbabilityTheory
 
-variable {α β γ : Type _} {mα : MeasurableSpace α} {mβ : MeasurableSpace β} {mγ : MeasurableSpace γ}
+variable {α β γ : Type*} {mα : MeasurableSpace α} {mβ : MeasurableSpace β} {mγ : MeasurableSpace γ}
 
 namespace kernel
 

• 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 Kexing Ying. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kexing Ying
-
-! This file was ported from Lean 3 source module probability.kernel.invariance
-! leanprover-community/mathlib commit 3b92d54a05ee592aa2c6181a4e76b1bb7cc45d0b
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Probability.Kernel.Composition
 
+#align_import probability.kernel.invariance from "leanprover-community/mathlib"@"3b92d54a05ee592aa2c6181a4e76b1bb7cc45d0b"
+
 /-!
 # Invariance of measures along a kernel
 

Co-authored-by: Scott Morrison <scott.morrison@anu.edu.au> Co-authored-by: Mario Carneiro <di.gama@gmail.com>

@@ -59,7 +59,7 @@ theorem bind_smul (κ : kernel α β) (μ : Measure α) (r : ℝ≥0∞) : (r 
 
 theorem const_bind_eq_comp_const (κ : kernel α β) (μ : Measure α) :
     const α (μ.bind κ) = κ ∘ₖ const α μ := by
-  ext a s; intro hs
+  ext a s hs
   simp_rw [comp_apply' _ _ _ hs, const_apply, Measure.bind_apply hs (kernel.measurable _)]
 #align probability_theory.kernel.const_bind_eq_comp_const ProbabilityTheory.kernel.const_bind_eq_comp_const