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

@@ -200,7 +200,7 @@ theorem nonempty (μ : ProbabilityMeasure Ω) : Nonempty Ω :=
   by_contra maybe_empty
   have zero : (μ : Measure Ω) univ = 0 := by
     rw [univ_eq_empty_iff.mpr (not_nonempty_iff.mp maybe_empty), measure_empty]
-  rw [measure_univ] at zero 
+  rw [measure_univ] at zero
   exact zero_ne_one zero.symm
 #align measure_theory.probability_measure.nonempty_of_probability_measure MeasureTheory.ProbabilityMeasure.nonempty
 -/
@@ -499,8 +499,8 @@ theorem tendsto_testAgainstNN_of_tendsto_normalize_testAgainstNN_of_tendsto_mass
       eq_self_iff_true] at *
     exact tendsto_zero_test_against_nn_of_tendsto_zero_mass mass_lim f
   simp_rw [fun i => (μs i).testAgainstNN_eq_mass_mul f, μ.test_against_nn_eq_mass_mul f]
-  rw [probability_measure.tendsto_nhds_iff_to_finite_measures_tendsto_nhds] at μs_lim 
-  rw [tendsto_iff_forall_test_against_nn_tendsto] at μs_lim 
+  rw [probability_measure.tendsto_nhds_iff_to_finite_measures_tendsto_nhds] at μs_lim
+  rw [tendsto_iff_forall_test_against_nn_tendsto] at μs_lim
   have lim_pair :
     tendsto (fun i => (⟨(μs i).mass, (μs i).normalize.toFiniteMeasure.testAgainstNN f⟩ : ℝ≥0 × ℝ≥0))
       F (𝓝 ⟨μ.mass, μ.normalize.to_finite_measure.test_against_nn f⟩) :=

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

@@ -3,8 +3,8 @@ Copyright (c) 2021 Kalle Kytölä. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kalle Kytölä
 -/
-import Mathbin.MeasureTheory.Measure.FiniteMeasure
-import Mathbin.MeasureTheory.Integral.Average
+import MeasureTheory.Measure.FiniteMeasure
+import MeasureTheory.Integral.Average
 
 #align_import measure_theory.measure.probability_measure from "leanprover-community/mathlib"@"7e5137f579de09a059a5ce98f364a04e221aabf0"
 

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

@@ -2,15 +2,12 @@
 Copyright (c) 2021 Kalle Kytölä. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kalle Kytölä
-
-! This file was ported from Lean 3 source module measure_theory.measure.probability_measure
-! 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.Measure.FiniteMeasure
 import Mathbin.MeasureTheory.Integral.Average
 
+#align_import measure_theory.measure.probability_measure from "leanprover-community/mathlib"@"7e5137f579de09a059a5ce98f364a04e221aabf0"
+
 /-!
 # Probability measures
 

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

@@ -151,9 +151,11 @@ theorem coeFn_univ (ν : ProbabilityMeasure Ω) : ν univ = 1 :=
 #align measure_theory.probability_measure.coe_fn_univ MeasureTheory.ProbabilityMeasure.coeFn_univ
 -/
 
+#print MeasureTheory.ProbabilityMeasure.coeFn_univ_ne_zero /-
 theorem coeFn_univ_ne_zero (ν : ProbabilityMeasure Ω) : ν univ ≠ 0 := by
   simp only [coe_fn_univ, Ne.def, one_ne_zero, not_false_iff]
 #align measure_theory.probability_measure.coe_fn_univ_ne_zero MeasureTheory.ProbabilityMeasure.coeFn_univ_ne_zero
+-/
 
 #print MeasureTheory.ProbabilityMeasure.toFiniteMeasure /-
 /-- A probability measure can be interpreted as a finite measure. -/
@@ -240,10 +242,12 @@ theorem toFiniteMeasure_nonzero (μ : ProbabilityMeasure Ω) : μ.toFiniteMeasur
 
 variable [TopologicalSpace Ω] [OpensMeasurableSpace Ω]
 
+#print MeasureTheory.ProbabilityMeasure.testAgainstNN_lipschitz /-
 theorem testAgainstNN_lipschitz (μ : ProbabilityMeasure Ω) :
     LipschitzWith 1 fun f : Ω →ᵇ ℝ≥0 => μ.toFiniteMeasure.testAgainstNN f :=
   μ.mass_toFiniteMeasure ▸ μ.toFiniteMeasure.testAgainstNN_lipschitz
 #align measure_theory.probability_measure.test_against_nn_lipschitz MeasureTheory.ProbabilityMeasure.testAgainstNN_lipschitz
+-/
 
 /-- The topology of weak convergence on `measure_theory.probability_measure Ω`. This is inherited
 (induced) from the topology of weak convergence of finite measures via the inclusion
@@ -251,40 +255,53 @@ theorem testAgainstNN_lipschitz (μ : ProbabilityMeasure Ω) :
 instance : TopologicalSpace (ProbabilityMeasure Ω) :=
   TopologicalSpace.induced toFiniteMeasure inferInstance
 
+#print MeasureTheory.ProbabilityMeasure.toFiniteMeasure_continuous /-
 theorem toFiniteMeasure_continuous :
     Continuous (toFiniteMeasure : ProbabilityMeasure Ω → FiniteMeasure Ω) :=
   continuous_induced_dom
 #align measure_theory.probability_measure.to_finite_measure_continuous MeasureTheory.ProbabilityMeasure.toFiniteMeasure_continuous
+-/
 
+#print MeasureTheory.ProbabilityMeasure.toWeakDualBCNN /-
 /-- Probability measures yield elements of the `weak_dual` of bounded continuous nonnegative
 functions via `measure_theory.finite_measure.test_against_nn`, i.e., integration. -/
 def toWeakDualBCNN : ProbabilityMeasure Ω → WeakDual ℝ≥0 (Ω →ᵇ ℝ≥0) :=
   FiniteMeasure.toWeakDualBCNN ∘ toFiniteMeasure
 #align measure_theory.probability_measure.to_weak_dual_bcnn MeasureTheory.ProbabilityMeasure.toWeakDualBCNN
+-/
 
+#print MeasureTheory.ProbabilityMeasure.coe_toWeakDualBCNN /-
 @[simp]
 theorem coe_toWeakDualBCNN (μ : ProbabilityMeasure Ω) :
     ⇑μ.toWeakDualBCNN = μ.toFiniteMeasure.testAgainstNN :=
   rfl
 #align measure_theory.probability_measure.coe_to_weak_dual_bcnn MeasureTheory.ProbabilityMeasure.coe_toWeakDualBCNN
+-/
 
+#print MeasureTheory.ProbabilityMeasure.toWeakDualBCNN_apply /-
 @[simp]
 theorem toWeakDualBCNN_apply (μ : ProbabilityMeasure Ω) (f : Ω →ᵇ ℝ≥0) :
     μ.toWeakDualBCNN f = (∫⁻ ω, f ω ∂(μ : Measure Ω)).toNNReal :=
   rfl
 #align measure_theory.probability_measure.to_weak_dual_bcnn_apply MeasureTheory.ProbabilityMeasure.toWeakDualBCNN_apply
+-/
 
+#print MeasureTheory.ProbabilityMeasure.toWeakDualBCNN_continuous /-
 theorem toWeakDualBCNN_continuous : Continuous fun μ : ProbabilityMeasure Ω => μ.toWeakDualBCNN :=
   FiniteMeasure.toWeakDualBCNN_continuous.comp toFiniteMeasure_continuous
 #align measure_theory.probability_measure.to_weak_dual_bcnn_continuous MeasureTheory.ProbabilityMeasure.toWeakDualBCNN_continuous
+-/
 
+#print MeasureTheory.ProbabilityMeasure.continuous_testAgainstNN_eval /-
 /- Integration of (nonnegative bounded continuous) test functions against Borel probability
 measures depends continuously on the measure. -/
 theorem continuous_testAgainstNN_eval (f : Ω →ᵇ ℝ≥0) :
     Continuous fun μ : ProbabilityMeasure Ω => μ.toFiniteMeasure.testAgainstNN f :=
   (FiniteMeasure.continuous_testAgainstNN_eval f).comp toFiniteMeasure_continuous
 #align measure_theory.probability_measure.continuous_test_against_nn_eval MeasureTheory.ProbabilityMeasure.continuous_testAgainstNN_eval
+-/
 
+#print MeasureTheory.ProbabilityMeasure.toFiniteMeasure_embedding /-
 -- The canonical mapping from probability measures to finite measures is an embedding.
 theorem toFiniteMeasure_embedding (Ω : Type _) [MeasurableSpace Ω] [TopologicalSpace Ω]
     [OpensMeasurableSpace Ω] :
@@ -292,13 +309,17 @@ theorem toFiniteMeasure_embedding (Ω : Type _) [MeasurableSpace Ω] [Topologica
   { induced := rfl
     inj := fun μ ν h => Subtype.eq (by convert congr_arg coe h) }
 #align measure_theory.probability_measure.to_finite_measure_embedding MeasureTheory.ProbabilityMeasure.toFiniteMeasure_embedding
+-/
 
+#print MeasureTheory.ProbabilityMeasure.tendsto_nhds_iff_toFiniteMeasure_tendsto_nhds /-
 theorem tendsto_nhds_iff_toFiniteMeasure_tendsto_nhds {δ : Type _} (F : Filter δ)
     {μs : δ → ProbabilityMeasure Ω} {μ₀ : ProbabilityMeasure Ω} :
     Tendsto μs F (𝓝 μ₀) ↔ Tendsto (toFiniteMeasure ∘ μs) F (𝓝 μ₀.toFiniteMeasure) :=
   Embedding.tendsto_nhds_iff (toFiniteMeasure_embedding Ω)
 #align measure_theory.probability_measure.tendsto_nhds_iff_to_finite_measures_tendsto_nhds MeasureTheory.ProbabilityMeasure.tendsto_nhds_iff_toFiniteMeasure_tendsto_nhds
+-/
 
+#print MeasureTheory.ProbabilityMeasure.tendsto_iff_forall_lintegral_tendsto /-
 /-- A characterization of weak convergence of probability measures by the condition that the
 integrals of every continuous bounded nonnegative function converge to the integral of the function
 against the limit measure. -/
@@ -311,7 +332,9 @@ theorem tendsto_iff_forall_lintegral_tendsto {γ : Type _} {F : Filter γ}
   rw [tendsto_nhds_iff_to_finite_measures_tendsto_nhds]
   exact finite_measure.tendsto_iff_forall_lintegral_tendsto
 #align measure_theory.probability_measure.tendsto_iff_forall_lintegral_tendsto MeasureTheory.ProbabilityMeasure.tendsto_iff_forall_lintegral_tendsto
+-/
 
+#print MeasureTheory.ProbabilityMeasure.tendsto_iff_forall_integral_tendsto /-
 /-- The characterization of weak convergence of probability measures by the usual (defining)
 condition that the integrals of every continuous bounded function converge to the integral of the
 function against the limit measure. -/
@@ -325,6 +348,7 @@ theorem tendsto_iff_forall_integral_tendsto {γ : Type _} {F : Filter γ}
   rw [finite_measure.tendsto_iff_forall_integral_tendsto]
   simp only [coe_comp_to_finite_measure_eq_coe]
 #align measure_theory.probability_measure.tendsto_iff_forall_integral_tendsto MeasureTheory.ProbabilityMeasure.tendsto_iff_forall_integral_tendsto
+-/
 
 end ProbabilityMeasure
 
@@ -364,6 +388,7 @@ def normalize : ProbabilityMeasure Ω :=
 #align measure_theory.finite_measure.normalize MeasureTheory.FiniteMeasure.normalize
 -/
 
+#print MeasureTheory.FiniteMeasure.self_eq_mass_mul_normalize /-
 @[simp]
 theorem self_eq_mass_mul_normalize (s : Set Ω) : μ s = μ.mass * μ.normalize s :=
   by
@@ -375,6 +400,7 @@ theorem self_eq_mass_mul_normalize (s : Set Ω) : μ s = μ.mass * μ.normalize
     MeasureTheory.Measure.coe_nnreal_smul_apply, mul_inv_cancel_left₀ mass_nonzero,
     finite_measure.coe_fn_eq_to_nnreal_coe_fn_to_measure]
 #align measure_theory.finite_measure.self_eq_mass_mul_normalize MeasureTheory.FiniteMeasure.self_eq_mass_mul_normalize
+-/
 
 #print MeasureTheory.FiniteMeasure.self_eq_mass_smul_normalize /-
 theorem self_eq_mass_smul_normalize : μ = μ.mass • μ.normalize.toFiniteMeasure :=
@@ -386,10 +412,12 @@ theorem self_eq_mass_smul_normalize : μ = μ.mass • μ.normalize.toFiniteMeas
 #align measure_theory.finite_measure.self_eq_mass_smul_normalize MeasureTheory.FiniteMeasure.self_eq_mass_smul_normalize
 -/
 
+#print MeasureTheory.FiniteMeasure.normalize_eq_of_nonzero /-
 theorem normalize_eq_of_nonzero (nonzero : μ ≠ 0) (s : Set Ω) : μ.normalize s = μ.mass⁻¹ * μ s := by
   simp only [μ.self_eq_mass_mul_normalize, μ.mass_nonzero_iff.mpr nonzero, inv_mul_cancel_left₀,
     Ne.def, not_false_iff]
 #align measure_theory.finite_measure.normalize_eq_of_nonzero MeasureTheory.FiniteMeasure.normalize_eq_of_nonzero
+-/
 
 #print MeasureTheory.FiniteMeasure.normalize_eq_inv_mass_smul_of_nonzero /-
 theorem normalize_eq_inv_mass_smul_of_nonzero (nonzero : μ ≠ 0) :
@@ -402,6 +430,7 @@ theorem normalize_eq_inv_mass_smul_of_nonzero (nonzero : μ ≠ 0) :
 #align measure_theory.finite_measure.normalize_eq_inv_mass_smul_of_nonzero MeasureTheory.FiniteMeasure.normalize_eq_inv_mass_smul_of_nonzero
 -/
 
+#print MeasureTheory.FiniteMeasure.toMeasure_normalize_eq_of_nonzero /-
 theorem toMeasure_normalize_eq_of_nonzero (nonzero : μ ≠ 0) :
     (μ.normalize : Measure Ω) = μ.mass⁻¹ • μ :=
   by
@@ -410,6 +439,7 @@ theorem toMeasure_normalize_eq_of_nonzero (nonzero : μ ≠ 0) :
     μ.normalize_eq_of_nonzero nonzero s, ENNReal.coe_mul, ennreal_coe_fn_eq_coe_fn_to_measure,
     measure.coe_nnreal_smul_apply]
 #align measure_theory.finite_measure.coe_normalize_eq_of_nonzero MeasureTheory.FiniteMeasure.toMeasure_normalize_eq_of_nonzero
+-/
 
 #print ProbabilityMeasure.toFiniteMeasure_normalize_eq_self /-
 @[simp]
@@ -440,22 +470,27 @@ theorem average_eq_integral_normalize {E : Type _} [NormedAddCommGroup E] [Norme
 
 variable [TopologicalSpace Ω]
 
+#print MeasureTheory.FiniteMeasure.testAgainstNN_eq_mass_mul /-
 theorem testAgainstNN_eq_mass_mul (f : Ω →ᵇ ℝ≥0) :
     μ.testAgainstNN f = μ.mass * μ.normalize.toFiniteMeasure.testAgainstNN f :=
   by
   nth_rw 1 [μ.self_eq_mass_smul_normalize]
   rw [μ.normalize.to_finite_measure.smul_test_against_nn_apply μ.mass f, smul_eq_mul]
 #align measure_theory.finite_measure.test_against_nn_eq_mass_mul MeasureTheory.FiniteMeasure.testAgainstNN_eq_mass_mul
+-/
 
+#print MeasureTheory.FiniteMeasure.normalize_testAgainstNN /-
 theorem normalize_testAgainstNN (nonzero : μ ≠ 0) (f : Ω →ᵇ ℝ≥0) :
     μ.normalize.toFiniteMeasure.testAgainstNN f = μ.mass⁻¹ * μ.testAgainstNN f := by
   simp [μ.test_against_nn_eq_mass_mul, μ.mass_nonzero_iff.mpr nonzero]
 #align measure_theory.finite_measure.normalize_test_against_nn MeasureTheory.FiniteMeasure.normalize_testAgainstNN
+-/
 
 variable [OpensMeasurableSpace Ω]
 
 variable {μ}
 
+#print MeasureTheory.FiniteMeasure.tendsto_testAgainstNN_of_tendsto_normalize_testAgainstNN_of_tendsto_mass /-
 theorem tendsto_testAgainstNN_of_tendsto_normalize_testAgainstNN_of_tendsto_mass {γ : Type _}
     {F : Filter γ} {μs : γ → FiniteMeasure Ω}
     (μs_lim : Tendsto (fun i => (μs i).normalize) F (𝓝 μ.normalize))
@@ -475,7 +510,9 @@ theorem tendsto_testAgainstNN_of_tendsto_normalize_testAgainstNN_of_tendsto_mass
     (Prod.tendsto_iff _ _).mpr ⟨mass_lim, μs_lim f⟩
   exact tendsto_mul.comp lim_pair
 #align measure_theory.finite_measure.tendsto_test_against_nn_of_tendsto_normalize_test_against_nn_of_tendsto_mass MeasureTheory.FiniteMeasure.tendsto_testAgainstNN_of_tendsto_normalize_testAgainstNN_of_tendsto_mass
+-/
 
+#print MeasureTheory.FiniteMeasure.tendsto_normalize_testAgainstNN_of_tendsto /-
 theorem tendsto_normalize_testAgainstNN_of_tendsto {γ : Type _} {F : Filter γ}
     {μs : γ → FiniteMeasure Ω} (μs_lim : Tendsto μs F (𝓝 μ)) (nonzero : μ ≠ 0) (f : Ω →ᵇ ℝ≥0) :
     Tendsto (fun i => (μs i).normalize.toFiniteMeasure.testAgainstNN f) F
@@ -505,7 +542,9 @@ theorem tendsto_normalize_testAgainstNN_of_tendsto {γ : Type _} {F : Filter γ}
     · exact tendsto_iff_forall_test_against_nn_tendsto.mp μs_lim f
   exact tendsto_mul.comp lim_pair
 #align measure_theory.finite_measure.tendsto_normalize_test_against_nn_of_tendsto MeasureTheory.FiniteMeasure.tendsto_normalize_testAgainstNN_of_tendsto
+-/
 
+#print MeasureTheory.FiniteMeasure.tendsto_of_tendsto_normalize_testAgainstNN_of_tendsto_mass /-
 /-- If the normalized versions of finite measures converge weakly and their total masses
 also converge, then the finite measures themselves converge weakly. -/
 theorem tendsto_of_tendsto_normalize_testAgainstNN_of_tendsto_mass {γ : Type _} {F : Filter γ}
@@ -516,7 +555,9 @@ theorem tendsto_of_tendsto_normalize_testAgainstNN_of_tendsto_mass {γ : Type _}
   exact fun f =>
     tendsto_test_against_nn_of_tendsto_normalize_test_against_nn_of_tendsto_mass μs_lim mass_lim f
 #align measure_theory.finite_measure.tendsto_of_tendsto_normalize_test_against_nn_of_tendsto_mass MeasureTheory.FiniteMeasure.tendsto_of_tendsto_normalize_testAgainstNN_of_tendsto_mass
+-/
 
+#print MeasureTheory.FiniteMeasure.tendsto_normalize_of_tendsto /-
 /-- If finite measures themselves converge weakly to a nonzero limit measure, then their
 normalized versions also converge weakly. -/
 theorem tendsto_normalize_of_tendsto {γ : Type _} {F : Filter γ} {μs : γ → FiniteMeasure Ω}
@@ -527,7 +568,9 @@ theorem tendsto_normalize_of_tendsto {γ : Type _} {F : Filter γ} {μs : γ →
     tendsto_iff_forall_test_against_nn_tendsto]
   exact fun f => tendsto_normalize_test_against_nn_of_tendsto μs_lim nonzero f
 #align measure_theory.finite_measure.tendsto_normalize_of_tendsto MeasureTheory.FiniteMeasure.tendsto_normalize_of_tendsto
+-/
 
+#print MeasureTheory.FiniteMeasure.tendsto_normalize_iff_tendsto /-
 /-- The weak convergence of finite measures to a nonzero limit can be characterized by the weak
 convergence of both their normalized versions (probability measures) and their total masses. -/
 theorem tendsto_normalize_iff_tendsto {γ : Type _} {F : Filter γ} {μs : γ → FiniteMeasure Ω}
@@ -542,6 +585,7 @@ theorem tendsto_normalize_iff_tendsto {γ : Type _} {F : Filter γ} {μs : γ 
   · intro μs_lim
     refine' ⟨tendsto_normalize_of_tendsto μs_lim nonzero, μs_lim.mass⟩
 #align measure_theory.finite_measure.tendsto_normalize_iff_tendsto MeasureTheory.FiniteMeasure.tendsto_normalize_iff_tendsto
+-/
 
 end FiniteMeasure
 

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: Kalle Kytölä
 
 ! This file was ported from Lean 3 source module measure_theory.measure.probability_measure
-! leanprover-community/mathlib commit f0c8bf9245297a541f468be517f1bde6195105e9
+! 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.MeasureTheory.Integral.Average
 /-!
 # Probability measures
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 This file defines the type of probability measures on a given measurable space. When the underlying
 space has a topology and the measurable space structure (sigma algebra) is finer than the Borel
 sigma algebra, then the type of probability measures is equipped with the topology of convergence

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

@@ -98,11 +98,13 @@ finite measure, this is implemented as the induced topology from the mapping
 -/
 
 
+#print MeasureTheory.ProbabilityMeasure /-
 /-- Probability measures are defined as the subtype of measures that have the property of being
 probability measures (i.e., their total mass is one). -/
 def ProbabilityMeasure (Ω : Type _) [MeasurableSpace Ω] : Type _ :=
   { μ : Measure Ω // IsProbabilityMeasure μ }
 #align measure_theory.probability_measure MeasureTheory.ProbabilityMeasure
+-/
 
 namespace ProbabilityMeasure
 
@@ -126,86 +128,112 @@ theorem coeFn_eq_toNNReal_coeFn_to_measure (ν : ProbabilityMeasure Ω) :
   rfl
 #align measure_theory.probability_measure.coe_fn_eq_to_nnreal_coe_fn_to_measure MeasureTheory.ProbabilityMeasure.coeFn_eq_toNNReal_coeFn_to_measure
 
+#print MeasureTheory.ProbabilityMeasure.val_eq_to_measure /-
 @[simp]
 theorem val_eq_to_measure (ν : ProbabilityMeasure Ω) : ν.val = (ν : Measure Ω) :=
   rfl
 #align measure_theory.probability_measure.val_eq_to_measure MeasureTheory.ProbabilityMeasure.val_eq_to_measure
+-/
 
-theorem coe_injective : Function.Injective (coe : ProbabilityMeasure Ω → Measure Ω) :=
+#print MeasureTheory.ProbabilityMeasure.toMeasure_injective /-
+theorem toMeasure_injective : Function.Injective (coe : ProbabilityMeasure Ω → Measure Ω) :=
   Subtype.coe_injective
-#align measure_theory.probability_measure.coe_injective MeasureTheory.ProbabilityMeasure.coe_injective
+#align measure_theory.probability_measure.coe_injective MeasureTheory.ProbabilityMeasure.toMeasure_injective
+-/
 
+#print MeasureTheory.ProbabilityMeasure.coeFn_univ /-
 @[simp]
 theorem coeFn_univ (ν : ProbabilityMeasure Ω) : ν univ = 1 :=
   congr_arg ENNReal.toNNReal ν.Prop.measure_univ
 #align measure_theory.probability_measure.coe_fn_univ MeasureTheory.ProbabilityMeasure.coeFn_univ
+-/
 
 theorem coeFn_univ_ne_zero (ν : ProbabilityMeasure Ω) : ν univ ≠ 0 := by
   simp only [coe_fn_univ, Ne.def, one_ne_zero, not_false_iff]
 #align measure_theory.probability_measure.coe_fn_univ_ne_zero MeasureTheory.ProbabilityMeasure.coeFn_univ_ne_zero
 
+#print MeasureTheory.ProbabilityMeasure.toFiniteMeasure /-
 /-- A probability measure can be interpreted as a finite measure. -/
 def toFiniteMeasure (μ : ProbabilityMeasure Ω) : FiniteMeasure Ω :=
   ⟨μ, inferInstance⟩
 #align measure_theory.probability_measure.to_finite_measure MeasureTheory.ProbabilityMeasure.toFiniteMeasure
+-/
 
+#print MeasureTheory.ProbabilityMeasure.toMeasure_comp_toFiniteMeasure_eq_toMeasure /-
 @[simp]
-theorem coe_comp_toFiniteMeasure_eq_coe (ν : ProbabilityMeasure Ω) :
+theorem toMeasure_comp_toFiniteMeasure_eq_toMeasure (ν : ProbabilityMeasure Ω) :
     (ν.toFiniteMeasure : Measure Ω) = (ν : Measure Ω) :=
   rfl
-#align measure_theory.probability_measure.coe_comp_to_finite_measure_eq_coe MeasureTheory.ProbabilityMeasure.coe_comp_toFiniteMeasure_eq_coe
+#align measure_theory.probability_measure.coe_comp_to_finite_measure_eq_coe MeasureTheory.ProbabilityMeasure.toMeasure_comp_toFiniteMeasure_eq_toMeasure
+-/
 
+#print MeasureTheory.ProbabilityMeasure.coeFn_comp_toFiniteMeasure_eq_coeFn /-
 @[simp]
 theorem coeFn_comp_toFiniteMeasure_eq_coeFn (ν : ProbabilityMeasure Ω) :
     (ν.toFiniteMeasure : Set Ω → ℝ≥0) = (ν : Set Ω → ℝ≥0) :=
   rfl
 #align measure_theory.probability_measure.coe_fn_comp_to_finite_measure_eq_coe_fn MeasureTheory.ProbabilityMeasure.coeFn_comp_toFiniteMeasure_eq_coeFn
+-/
 
+#print MeasureTheory.ProbabilityMeasure.ennreal_coeFn_eq_coeFn_toMeasure /-
 @[simp]
-theorem eNNReal_coeFn_eq_coeFn_to_measure (ν : ProbabilityMeasure Ω) (s : Set Ω) :
+theorem ennreal_coeFn_eq_coeFn_toMeasure (ν : ProbabilityMeasure Ω) (s : Set Ω) :
     (ν s : ℝ≥0∞) = (ν : Measure Ω) s := by
   rw [← coe_fn_comp_to_finite_measure_eq_coe_fn, finite_measure.ennreal_coe_fn_eq_coe_fn_to_measure,
     coe_comp_to_finite_measure_eq_coe]
-#align measure_theory.probability_measure.ennreal_coe_fn_eq_coe_fn_to_measure MeasureTheory.ProbabilityMeasure.eNNReal_coeFn_eq_coeFn_to_measure
+#align measure_theory.probability_measure.ennreal_coe_fn_eq_coe_fn_to_measure MeasureTheory.ProbabilityMeasure.ennreal_coeFn_eq_coeFn_toMeasure
+-/
 
+#print MeasureTheory.ProbabilityMeasure.apply_mono /-
 theorem apply_mono (μ : ProbabilityMeasure Ω) {s₁ s₂ : Set Ω} (h : s₁ ⊆ s₂) : μ s₁ ≤ μ s₂ :=
   by
   rw [← coe_fn_comp_to_finite_measure_eq_coe_fn]
   exact MeasureTheory.FiniteMeasure.apply_mono _ h
 #align measure_theory.probability_measure.apply_mono MeasureTheory.ProbabilityMeasure.apply_mono
+-/
 
-theorem nonempty_of_probabilityMeasure (μ : ProbabilityMeasure Ω) : Nonempty Ω :=
+#print MeasureTheory.ProbabilityMeasure.nonempty /-
+theorem nonempty (μ : ProbabilityMeasure Ω) : Nonempty Ω :=
   by
   by_contra maybe_empty
   have zero : (μ : Measure Ω) univ = 0 := by
     rw [univ_eq_empty_iff.mpr (not_nonempty_iff.mp maybe_empty), measure_empty]
   rw [measure_univ] at zero 
   exact zero_ne_one zero.symm
-#align measure_theory.probability_measure.nonempty_of_probability_measure MeasureTheory.ProbabilityMeasure.nonempty_of_probabilityMeasure
+#align measure_theory.probability_measure.nonempty_of_probability_measure MeasureTheory.ProbabilityMeasure.nonempty
+-/
 
+#print MeasureTheory.ProbabilityMeasure.eq_of_forall_toMeasure_apply_eq /-
 @[ext]
-theorem eq_of_forall_measure_apply_eq (μ ν : ProbabilityMeasure Ω)
+theorem eq_of_forall_toMeasure_apply_eq (μ ν : ProbabilityMeasure Ω)
     (h : ∀ s : Set Ω, MeasurableSet s → (μ : Measure Ω) s = (ν : Measure Ω) s) : μ = ν := by ext1;
   ext1 s s_mble; exact h s s_mble
-#align measure_theory.probability_measure.eq_of_forall_measure_apply_eq MeasureTheory.ProbabilityMeasure.eq_of_forall_measure_apply_eq
+#align measure_theory.probability_measure.eq_of_forall_measure_apply_eq MeasureTheory.ProbabilityMeasure.eq_of_forall_toMeasure_apply_eq
+-/
 
+#print MeasureTheory.ProbabilityMeasure.eq_of_forall_apply_eq /-
 theorem eq_of_forall_apply_eq (μ ν : ProbabilityMeasure Ω)
     (h : ∀ s : Set Ω, MeasurableSet s → μ s = ν s) : μ = ν :=
   by
   ext1 s s_mble
   simpa [ennreal_coe_fn_eq_coe_fn_to_measure] using congr_arg (coe : ℝ≥0 → ℝ≥0∞) (h s s_mble)
 #align measure_theory.probability_measure.eq_of_forall_apply_eq MeasureTheory.ProbabilityMeasure.eq_of_forall_apply_eq
+-/
 
+#print MeasureTheory.ProbabilityMeasure.mass_toFiniteMeasure /-
 @[simp]
 theorem mass_toFiniteMeasure (μ : ProbabilityMeasure Ω) : μ.toFiniteMeasure.mass = 1 :=
   μ.coeFn_univ
 #align measure_theory.probability_measure.mass_to_finite_measure MeasureTheory.ProbabilityMeasure.mass_toFiniteMeasure
+-/
 
+#print MeasureTheory.ProbabilityMeasure.toFiniteMeasure_nonzero /-
 theorem toFiniteMeasure_nonzero (μ : ProbabilityMeasure Ω) : μ.toFiniteMeasure ≠ 0 :=
   by
   rw [← finite_measure.mass_nonzero_iff, μ.mass_to_finite_measure]
   exact one_ne_zero
 #align measure_theory.probability_measure.to_finite_measure_nonzero MeasureTheory.ProbabilityMeasure.toFiniteMeasure_nonzero
+-/
 
 variable [TopologicalSpace Ω] [OpensMeasurableSpace Ω]
 
@@ -227,25 +255,25 @@ theorem toFiniteMeasure_continuous :
 
 /-- Probability measures yield elements of the `weak_dual` of bounded continuous nonnegative
 functions via `measure_theory.finite_measure.test_against_nn`, i.e., integration. -/
-def toWeakDualBcnn : ProbabilityMeasure Ω → WeakDual ℝ≥0 (Ω →ᵇ ℝ≥0) :=
+def toWeakDualBCNN : ProbabilityMeasure Ω → WeakDual ℝ≥0 (Ω →ᵇ ℝ≥0) :=
   FiniteMeasure.toWeakDualBCNN ∘ toFiniteMeasure
-#align measure_theory.probability_measure.to_weak_dual_bcnn MeasureTheory.ProbabilityMeasure.toWeakDualBcnn
+#align measure_theory.probability_measure.to_weak_dual_bcnn MeasureTheory.ProbabilityMeasure.toWeakDualBCNN
 
 @[simp]
-theorem coe_toWeakDualBcnn (μ : ProbabilityMeasure Ω) :
+theorem coe_toWeakDualBCNN (μ : ProbabilityMeasure Ω) :
     ⇑μ.toWeakDualBCNN = μ.toFiniteMeasure.testAgainstNN :=
   rfl
-#align measure_theory.probability_measure.coe_to_weak_dual_bcnn MeasureTheory.ProbabilityMeasure.coe_toWeakDualBcnn
+#align measure_theory.probability_measure.coe_to_weak_dual_bcnn MeasureTheory.ProbabilityMeasure.coe_toWeakDualBCNN
 
 @[simp]
-theorem toWeakDualBcnn_apply (μ : ProbabilityMeasure Ω) (f : Ω →ᵇ ℝ≥0) :
+theorem toWeakDualBCNN_apply (μ : ProbabilityMeasure Ω) (f : Ω →ᵇ ℝ≥0) :
     μ.toWeakDualBCNN f = (∫⁻ ω, f ω ∂(μ : Measure Ω)).toNNReal :=
   rfl
-#align measure_theory.probability_measure.to_weak_dual_bcnn_apply MeasureTheory.ProbabilityMeasure.toWeakDualBcnn_apply
+#align measure_theory.probability_measure.to_weak_dual_bcnn_apply MeasureTheory.ProbabilityMeasure.toWeakDualBCNN_apply
 
-theorem toWeakDualBcnn_continuous : Continuous fun μ : ProbabilityMeasure Ω => μ.toWeakDualBCNN :=
+theorem toWeakDualBCNN_continuous : Continuous fun μ : ProbabilityMeasure Ω => μ.toWeakDualBCNN :=
   FiniteMeasure.toWeakDualBCNN_continuous.comp toFiniteMeasure_continuous
-#align measure_theory.probability_measure.to_weak_dual_bcnn_continuous MeasureTheory.ProbabilityMeasure.toWeakDualBcnn_continuous
+#align measure_theory.probability_measure.to_weak_dual_bcnn_continuous MeasureTheory.ProbabilityMeasure.toWeakDualBCNN_continuous
 
 /- Integration of (nonnegative bounded continuous) test functions against Borel probability
 measures depends continuously on the measure. -/
@@ -262,11 +290,11 @@ theorem toFiniteMeasure_embedding (Ω : Type _) [MeasurableSpace Ω] [Topologica
     inj := fun μ ν h => Subtype.eq (by convert congr_arg coe h) }
 #align measure_theory.probability_measure.to_finite_measure_embedding MeasureTheory.ProbabilityMeasure.toFiniteMeasure_embedding
 
-theorem tendsto_nhds_iff_to_finite_measures_tendsto_nhds {δ : Type _} (F : Filter δ)
+theorem tendsto_nhds_iff_toFiniteMeasure_tendsto_nhds {δ : Type _} (F : Filter δ)
     {μs : δ → ProbabilityMeasure Ω} {μ₀ : ProbabilityMeasure Ω} :
     Tendsto μs F (𝓝 μ₀) ↔ Tendsto (toFiniteMeasure ∘ μs) F (𝓝 μ₀.toFiniteMeasure) :=
   Embedding.tendsto_nhds_iff (toFiniteMeasure_embedding Ω)
-#align measure_theory.probability_measure.tendsto_nhds_iff_to_finite_measures_tendsto_nhds MeasureTheory.ProbabilityMeasure.tendsto_nhds_iff_to_finite_measures_tendsto_nhds
+#align measure_theory.probability_measure.tendsto_nhds_iff_to_finite_measures_tendsto_nhds MeasureTheory.ProbabilityMeasure.tendsto_nhds_iff_toFiniteMeasure_tendsto_nhds
 
 /-- A characterization of weak convergence of probability measures by the condition that the
 integrals of every continuous bounded nonnegative function converge to the integral of the function
@@ -317,6 +345,7 @@ namespace FiniteMeasure
 
 variable {Ω : Type _} [Nonempty Ω] {m0 : MeasurableSpace Ω} (μ : FiniteMeasure Ω)
 
+#print MeasureTheory.FiniteMeasure.normalize /-
 /-- Normalize a finite measure so that it becomes a probability measure, i.e., divide by the
 total mass. -/
 def normalize : ProbabilityMeasure Ω :=
@@ -330,6 +359,7 @@ def normalize : ProbabilityMeasure Ω :=
         norm_cast
         exact inv_mul_cancel zero }
 #align measure_theory.finite_measure.normalize MeasureTheory.FiniteMeasure.normalize
+-/
 
 @[simp]
 theorem self_eq_mass_mul_normalize (s : Set Ω) : μ s = μ.mass * μ.normalize s :=
@@ -343,6 +373,7 @@ theorem self_eq_mass_mul_normalize (s : Set Ω) : μ s = μ.mass * μ.normalize
     finite_measure.coe_fn_eq_to_nnreal_coe_fn_to_measure]
 #align measure_theory.finite_measure.self_eq_mass_mul_normalize MeasureTheory.FiniteMeasure.self_eq_mass_mul_normalize
 
+#print MeasureTheory.FiniteMeasure.self_eq_mass_smul_normalize /-
 theorem self_eq_mass_smul_normalize : μ = μ.mass • μ.normalize.toFiniteMeasure :=
   by
   apply eq_of_forall_apply_eq
@@ -350,12 +381,14 @@ theorem self_eq_mass_smul_normalize : μ = μ.mass • μ.normalize.toFiniteMeas
   rw [μ.self_eq_mass_mul_normalize s, coe_fn_smul_apply, smul_eq_mul,
     probability_measure.coe_fn_comp_to_finite_measure_eq_coe_fn]
 #align measure_theory.finite_measure.self_eq_mass_smul_normalize MeasureTheory.FiniteMeasure.self_eq_mass_smul_normalize
+-/
 
 theorem normalize_eq_of_nonzero (nonzero : μ ≠ 0) (s : Set Ω) : μ.normalize s = μ.mass⁻¹ * μ s := by
   simp only [μ.self_eq_mass_mul_normalize, μ.mass_nonzero_iff.mpr nonzero, inv_mul_cancel_left₀,
     Ne.def, not_false_iff]
 #align measure_theory.finite_measure.normalize_eq_of_nonzero MeasureTheory.FiniteMeasure.normalize_eq_of_nonzero
 
+#print MeasureTheory.FiniteMeasure.normalize_eq_inv_mass_smul_of_nonzero /-
 theorem normalize_eq_inv_mass_smul_of_nonzero (nonzero : μ ≠ 0) :
     μ.normalize.toFiniteMeasure = μ.mass⁻¹ • μ :=
   by
@@ -364,15 +397,18 @@ theorem normalize_eq_inv_mass_smul_of_nonzero (nonzero : μ ≠ 0) :
   simp only [μ.mass_nonzero_iff.mpr nonzero, Algebra.id.smul_eq_mul, inv_mul_cancel, Ne.def,
     not_false_iff, one_smul]
 #align measure_theory.finite_measure.normalize_eq_inv_mass_smul_of_nonzero MeasureTheory.FiniteMeasure.normalize_eq_inv_mass_smul_of_nonzero
+-/
 
-theorem coe_normalize_eq_of_nonzero (nonzero : μ ≠ 0) : (μ.normalize : Measure Ω) = μ.mass⁻¹ • μ :=
+theorem toMeasure_normalize_eq_of_nonzero (nonzero : μ ≠ 0) :
+    (μ.normalize : Measure Ω) = μ.mass⁻¹ • μ :=
   by
   ext1 s s_mble
   simp only [← μ.normalize.ennreal_coe_fn_eq_coe_fn_to_measure s,
     μ.normalize_eq_of_nonzero nonzero s, ENNReal.coe_mul, ennreal_coe_fn_eq_coe_fn_to_measure,
     measure.coe_nnreal_smul_apply]
-#align measure_theory.finite_measure.coe_normalize_eq_of_nonzero MeasureTheory.FiniteMeasure.coe_normalize_eq_of_nonzero
+#align measure_theory.finite_measure.coe_normalize_eq_of_nonzero MeasureTheory.FiniteMeasure.toMeasure_normalize_eq_of_nonzero
 
+#print ProbabilityMeasure.toFiniteMeasure_normalize_eq_self /-
 @[simp]
 theorem ProbabilityMeasure.toFiniteMeasure_normalize_eq_self {m0 : MeasurableSpace Ω}
     (μ : ProbabilityMeasure Ω) : μ.toFiniteMeasure.normalize = μ :=
@@ -383,7 +419,9 @@ theorem ProbabilityMeasure.toFiniteMeasure_normalize_eq_self {m0 : MeasurableSpa
   simp only [probability_measure.mass_to_finite_measure, inv_one, one_mul,
     probability_measure.coe_fn_comp_to_finite_measure_eq_coe_fn]
 #align probability_measure.to_finite_measure_normalize_eq_self ProbabilityMeasure.toFiniteMeasure_normalize_eq_self
+-/
 
+#print MeasureTheory.FiniteMeasure.average_eq_integral_normalize /-
 /-- Averaging with respect to a finite measure is the same as integraing against
 `measure_theory.finite_measure.normalize`. -/
 theorem average_eq_integral_normalize {E : Type _} [NormedAddCommGroup E] [NormedSpace ℝ E]
@@ -395,6 +433,7 @@ theorem average_eq_integral_normalize {E : Type _} [NormedAddCommGroup E] [Norme
   simp only [RingHom.toFun_eq_coe, ENNReal.coe_ofNNRealHom,
     ENNReal.coe_inv (μ.mass_nonzero_iff.mpr nonzero), ennreal_mass]
 #align measure_theory.finite_measure.average_eq_integral_normalize MeasureTheory.FiniteMeasure.average_eq_integral_normalize
+-/
 
 variable [TopologicalSpace Ω]
 
@@ -466,14 +505,14 @@ theorem tendsto_normalize_testAgainstNN_of_tendsto {γ : Type _} {F : Filter γ}
 
 /-- If the normalized versions of finite measures converge weakly and their total masses
 also converge, then the finite measures themselves converge weakly. -/
-theorem tendsto_of_tendsto_normalize_test_against_nn_of_tendsto_mass {γ : Type _} {F : Filter γ}
+theorem tendsto_of_tendsto_normalize_testAgainstNN_of_tendsto_mass {γ : Type _} {F : Filter γ}
     {μs : γ → FiniteMeasure Ω} (μs_lim : Tendsto (fun i => (μs i).normalize) F (𝓝 μ.normalize))
     (mass_lim : Tendsto (fun i => (μs i).mass) F (𝓝 μ.mass)) : Tendsto μs F (𝓝 μ) :=
   by
   rw [tendsto_iff_forall_test_against_nn_tendsto]
   exact fun f =>
     tendsto_test_against_nn_of_tendsto_normalize_test_against_nn_of_tendsto_mass μs_lim mass_lim f
-#align measure_theory.finite_measure.tendsto_of_tendsto_normalize_test_against_nn_of_tendsto_mass MeasureTheory.FiniteMeasure.tendsto_of_tendsto_normalize_test_against_nn_of_tendsto_mass
+#align measure_theory.finite_measure.tendsto_of_tendsto_normalize_test_against_nn_of_tendsto_mass MeasureTheory.FiniteMeasure.tendsto_of_tendsto_normalize_testAgainstNN_of_tendsto_mass
 
 /-- If finite measures themselves converge weakly to a nonzero limit measure, then their
 normalized versions also converge weakly. -/

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

@@ -209,10 +209,10 @@ theorem toFiniteMeasure_nonzero (μ : ProbabilityMeasure Ω) : μ.toFiniteMeasur
 
 variable [TopologicalSpace Ω] [OpensMeasurableSpace Ω]
 
-theorem testAgainstNn_lipschitz (μ : ProbabilityMeasure Ω) :
-    LipschitzWith 1 fun f : Ω →ᵇ ℝ≥0 => μ.toFiniteMeasure.testAgainstNn f :=
-  μ.mass_toFiniteMeasure ▸ μ.toFiniteMeasure.testAgainstNn_lipschitz
-#align measure_theory.probability_measure.test_against_nn_lipschitz MeasureTheory.ProbabilityMeasure.testAgainstNn_lipschitz
+theorem testAgainstNN_lipschitz (μ : ProbabilityMeasure Ω) :
+    LipschitzWith 1 fun f : Ω →ᵇ ℝ≥0 => μ.toFiniteMeasure.testAgainstNN f :=
+  μ.mass_toFiniteMeasure ▸ μ.toFiniteMeasure.testAgainstNN_lipschitz
+#align measure_theory.probability_measure.test_against_nn_lipschitz MeasureTheory.ProbabilityMeasure.testAgainstNN_lipschitz
 
 /-- The topology of weak convergence on `measure_theory.probability_measure Ω`. This is inherited
 (induced) from the topology of weak convergence of finite measures via the inclusion
@@ -228,31 +228,31 @@ theorem toFiniteMeasure_continuous :
 /-- Probability measures yield elements of the `weak_dual` of bounded continuous nonnegative
 functions via `measure_theory.finite_measure.test_against_nn`, i.e., integration. -/
 def toWeakDualBcnn : ProbabilityMeasure Ω → WeakDual ℝ≥0 (Ω →ᵇ ℝ≥0) :=
-  FiniteMeasure.toWeakDualBcnn ∘ toFiniteMeasure
+  FiniteMeasure.toWeakDualBCNN ∘ toFiniteMeasure
 #align measure_theory.probability_measure.to_weak_dual_bcnn MeasureTheory.ProbabilityMeasure.toWeakDualBcnn
 
 @[simp]
 theorem coe_toWeakDualBcnn (μ : ProbabilityMeasure Ω) :
-    ⇑μ.toWeakDualBcnn = μ.toFiniteMeasure.testAgainstNn :=
+    ⇑μ.toWeakDualBCNN = μ.toFiniteMeasure.testAgainstNN :=
   rfl
 #align measure_theory.probability_measure.coe_to_weak_dual_bcnn MeasureTheory.ProbabilityMeasure.coe_toWeakDualBcnn
 
 @[simp]
 theorem toWeakDualBcnn_apply (μ : ProbabilityMeasure Ω) (f : Ω →ᵇ ℝ≥0) :
-    μ.toWeakDualBcnn f = (∫⁻ ω, f ω ∂(μ : Measure Ω)).toNNReal :=
+    μ.toWeakDualBCNN f = (∫⁻ ω, f ω ∂(μ : Measure Ω)).toNNReal :=
   rfl
 #align measure_theory.probability_measure.to_weak_dual_bcnn_apply MeasureTheory.ProbabilityMeasure.toWeakDualBcnn_apply
 
-theorem toWeakDualBcnn_continuous : Continuous fun μ : ProbabilityMeasure Ω => μ.toWeakDualBcnn :=
-  FiniteMeasure.toWeakDualBcnn_continuous.comp toFiniteMeasure_continuous
+theorem toWeakDualBcnn_continuous : Continuous fun μ : ProbabilityMeasure Ω => μ.toWeakDualBCNN :=
+  FiniteMeasure.toWeakDualBCNN_continuous.comp toFiniteMeasure_continuous
 #align measure_theory.probability_measure.to_weak_dual_bcnn_continuous MeasureTheory.ProbabilityMeasure.toWeakDualBcnn_continuous
 
 /- Integration of (nonnegative bounded continuous) test functions against Borel probability
 measures depends continuously on the measure. -/
-theorem continuous_testAgainstNn_eval (f : Ω →ᵇ ℝ≥0) :
-    Continuous fun μ : ProbabilityMeasure Ω => μ.toFiniteMeasure.testAgainstNn f :=
-  (FiniteMeasure.continuous_testAgainstNn_eval f).comp toFiniteMeasure_continuous
-#align measure_theory.probability_measure.continuous_test_against_nn_eval MeasureTheory.ProbabilityMeasure.continuous_testAgainstNn_eval
+theorem continuous_testAgainstNN_eval (f : Ω →ᵇ ℝ≥0) :
+    Continuous fun μ : ProbabilityMeasure Ω => μ.toFiniteMeasure.testAgainstNN f :=
+  (FiniteMeasure.continuous_testAgainstNN_eval f).comp toFiniteMeasure_continuous
+#align measure_theory.probability_measure.continuous_test_against_nn_eval MeasureTheory.ProbabilityMeasure.continuous_testAgainstNN_eval
 
 -- The canonical mapping from probability measures to finite measures is an embedding.
 theorem toFiniteMeasure_embedding (Ω : Type _) [MeasurableSpace Ω] [TopologicalSpace Ω]
@@ -398,46 +398,46 @@ theorem average_eq_integral_normalize {E : Type _} [NormedAddCommGroup E] [Norme
 
 variable [TopologicalSpace Ω]
 
-theorem testAgainstNn_eq_mass_mul (f : Ω →ᵇ ℝ≥0) :
-    μ.testAgainstNn f = μ.mass * μ.normalize.toFiniteMeasure.testAgainstNn f :=
+theorem testAgainstNN_eq_mass_mul (f : Ω →ᵇ ℝ≥0) :
+    μ.testAgainstNN f = μ.mass * μ.normalize.toFiniteMeasure.testAgainstNN f :=
   by
   nth_rw 1 [μ.self_eq_mass_smul_normalize]
   rw [μ.normalize.to_finite_measure.smul_test_against_nn_apply μ.mass f, smul_eq_mul]
-#align measure_theory.finite_measure.test_against_nn_eq_mass_mul MeasureTheory.FiniteMeasure.testAgainstNn_eq_mass_mul
+#align measure_theory.finite_measure.test_against_nn_eq_mass_mul MeasureTheory.FiniteMeasure.testAgainstNN_eq_mass_mul
 
-theorem normalize_testAgainstNn (nonzero : μ ≠ 0) (f : Ω →ᵇ ℝ≥0) :
-    μ.normalize.toFiniteMeasure.testAgainstNn f = μ.mass⁻¹ * μ.testAgainstNn f := by
+theorem normalize_testAgainstNN (nonzero : μ ≠ 0) (f : Ω →ᵇ ℝ≥0) :
+    μ.normalize.toFiniteMeasure.testAgainstNN f = μ.mass⁻¹ * μ.testAgainstNN f := by
   simp [μ.test_against_nn_eq_mass_mul, μ.mass_nonzero_iff.mpr nonzero]
-#align measure_theory.finite_measure.normalize_test_against_nn MeasureTheory.FiniteMeasure.normalize_testAgainstNn
+#align measure_theory.finite_measure.normalize_test_against_nn MeasureTheory.FiniteMeasure.normalize_testAgainstNN
 
 variable [OpensMeasurableSpace Ω]
 
 variable {μ}
 
-theorem tendsto_testAgainstNn_of_tendsto_normalize_testAgainstNn_of_tendsto_mass {γ : Type _}
+theorem tendsto_testAgainstNN_of_tendsto_normalize_testAgainstNN_of_tendsto_mass {γ : Type _}
     {F : Filter γ} {μs : γ → FiniteMeasure Ω}
     (μs_lim : Tendsto (fun i => (μs i).normalize) F (𝓝 μ.normalize))
     (mass_lim : Tendsto (fun i => (μs i).mass) F (𝓝 μ.mass)) (f : Ω →ᵇ ℝ≥0) :
-    Tendsto (fun i => (μs i).testAgainstNn f) F (𝓝 (μ.testAgainstNn f)) :=
+    Tendsto (fun i => (μs i).testAgainstNN f) F (𝓝 (μ.testAgainstNN f)) :=
   by
   by_cases h_mass : μ.mass = 0
   · simp only [μ.mass_zero_iff.mp h_mass, zero.test_against_nn_apply, zero.mass,
       eq_self_iff_true] at *
     exact tendsto_zero_test_against_nn_of_tendsto_zero_mass mass_lim f
-  simp_rw [fun i => (μs i).testAgainstNn_eq_mass_mul f, μ.test_against_nn_eq_mass_mul f]
+  simp_rw [fun i => (μs i).testAgainstNN_eq_mass_mul f, μ.test_against_nn_eq_mass_mul f]
   rw [probability_measure.tendsto_nhds_iff_to_finite_measures_tendsto_nhds] at μs_lim 
   rw [tendsto_iff_forall_test_against_nn_tendsto] at μs_lim 
   have lim_pair :
-    tendsto (fun i => (⟨(μs i).mass, (μs i).normalize.toFiniteMeasure.testAgainstNn f⟩ : ℝ≥0 × ℝ≥0))
+    tendsto (fun i => (⟨(μs i).mass, (μs i).normalize.toFiniteMeasure.testAgainstNN f⟩ : ℝ≥0 × ℝ≥0))
       F (𝓝 ⟨μ.mass, μ.normalize.to_finite_measure.test_against_nn f⟩) :=
     (Prod.tendsto_iff _ _).mpr ⟨mass_lim, μs_lim f⟩
   exact tendsto_mul.comp lim_pair
-#align measure_theory.finite_measure.tendsto_test_against_nn_of_tendsto_normalize_test_against_nn_of_tendsto_mass MeasureTheory.FiniteMeasure.tendsto_testAgainstNn_of_tendsto_normalize_testAgainstNn_of_tendsto_mass
+#align measure_theory.finite_measure.tendsto_test_against_nn_of_tendsto_normalize_test_against_nn_of_tendsto_mass MeasureTheory.FiniteMeasure.tendsto_testAgainstNN_of_tendsto_normalize_testAgainstNN_of_tendsto_mass
 
-theorem tendsto_normalize_testAgainstNn_of_tendsto {γ : Type _} {F : Filter γ}
+theorem tendsto_normalize_testAgainstNN_of_tendsto {γ : Type _} {F : Filter γ}
     {μs : γ → FiniteMeasure Ω} (μs_lim : Tendsto μs F (𝓝 μ)) (nonzero : μ ≠ 0) (f : Ω →ᵇ ℝ≥0) :
-    Tendsto (fun i => (μs i).normalize.toFiniteMeasure.testAgainstNn f) F
-      (𝓝 (μ.normalize.toFiniteMeasure.testAgainstNn f)) :=
+    Tendsto (fun i => (μs i).normalize.toFiniteMeasure.testAgainstNN f) F
+      (𝓝 (μ.normalize.toFiniteMeasure.testAgainstNN f)) :=
   by
   have lim_mass := μs_lim.mass
   have aux : {(0 : ℝ≥0)}ᶜ ∈ 𝓝 μ.mass :=
@@ -448,21 +448,21 @@ theorem tendsto_normalize_testAgainstNn_of_tendsto {γ : Type _} {F : Filter γ}
     exact lim_mass aux
   have eve :
     ∀ᶠ i in F,
-      (μs i).normalize.toFiniteMeasure.testAgainstNn f = (μs i).mass⁻¹ * (μs i).testAgainstNn f :=
+      (μs i).normalize.toFiniteMeasure.testAgainstNN f = (μs i).mass⁻¹ * (μs i).testAgainstNN f :=
     by
     filter_upwards [eventually_iff.mp eventually_nonzero]
     intro i hi
     apply normalize_test_against_nn _ hi
   simp_rw [tendsto_congr' eve, μ.normalize_test_against_nn nonzero]
   have lim_pair :
-    tendsto (fun i => (⟨(μs i).mass⁻¹, (μs i).testAgainstNn f⟩ : ℝ≥0 × ℝ≥0)) F
+    tendsto (fun i => (⟨(μs i).mass⁻¹, (μs i).testAgainstNN f⟩ : ℝ≥0 × ℝ≥0)) F
       (𝓝 ⟨μ.mass⁻¹, μ.test_against_nn f⟩) :=
     by
     refine' (Prod.tendsto_iff _ _).mpr ⟨_, _⟩
     · exact (continuous_on_inv₀.continuous_at aux).Tendsto.comp lim_mass
     · exact tendsto_iff_forall_test_against_nn_tendsto.mp μs_lim f
   exact tendsto_mul.comp lim_pair
-#align measure_theory.finite_measure.tendsto_normalize_test_against_nn_of_tendsto MeasureTheory.FiniteMeasure.tendsto_normalize_testAgainstNn_of_tendsto
+#align measure_theory.finite_measure.tendsto_normalize_test_against_nn_of_tendsto MeasureTheory.FiniteMeasure.tendsto_normalize_testAgainstNN_of_tendsto
 
 /-- If the normalized versions of finite measures converge weakly and their total masses
 also converge, then the finite measures themselves converge weakly. -/

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

@@ -100,193 +100,192 @@ finite measure, this is implemented as the induced topology from the mapping
 
 /-- Probability measures are defined as the subtype of measures that have the property of being
 probability measures (i.e., their total mass is one). -/
-def ProbabilityMeasureCat (Ω : Type _) [MeasurableSpace Ω] : Type _ :=
-  { μ : Measure Ω // ProbabilityMeasure μ }
-#align measure_theory.probability_measure MeasureTheory.ProbabilityMeasureCat
+def ProbabilityMeasure (Ω : Type _) [MeasurableSpace Ω] : Type _ :=
+  { μ : Measure Ω // IsProbabilityMeasure μ }
+#align measure_theory.probability_measure MeasureTheory.ProbabilityMeasure
 
 namespace ProbabilityMeasure
 
 variable {Ω : Type _} [MeasurableSpace Ω]
 
-instance [Inhabited Ω] : Inhabited (ProbabilityMeasureCat Ω) :=
+instance [Inhabited Ω] : Inhabited (ProbabilityMeasure Ω) :=
   ⟨⟨Measure.dirac default, Measure.dirac.isProbabilityMeasure⟩⟩
 
 /-- A probability measure can be interpreted as a measure. -/
-instance : Coe (ProbabilityMeasureCat Ω) (MeasureTheory.Measure Ω) :=
+instance : Coe (ProbabilityMeasure Ω) (MeasureTheory.Measure Ω) :=
   coeSubtype
 
-instance : CoeFun (ProbabilityMeasureCat Ω) fun _ => Set Ω → ℝ≥0 :=
+instance : CoeFun (ProbabilityMeasure Ω) fun _ => Set Ω → ℝ≥0 :=
   ⟨fun μ s => (μ s).toNNReal⟩
 
-instance (μ : ProbabilityMeasureCat Ω) : ProbabilityMeasure (μ : Measure Ω) :=
+instance (μ : ProbabilityMeasure Ω) : IsProbabilityMeasure (μ : Measure Ω) :=
   μ.Prop
 
-theorem coeFn_eq_toNNReal_coeFn_to_measure (ν : ProbabilityMeasureCat Ω) :
+theorem coeFn_eq_toNNReal_coeFn_to_measure (ν : ProbabilityMeasure Ω) :
     (ν : Set Ω → ℝ≥0) = fun s => ((ν : Measure Ω) s).toNNReal :=
   rfl
-#align measure_theory.probability_measure.coe_fn_eq_to_nnreal_coe_fn_to_measure MeasureTheory.ProbabilityMeasureCat.coeFn_eq_toNNReal_coeFn_to_measure
+#align measure_theory.probability_measure.coe_fn_eq_to_nnreal_coe_fn_to_measure MeasureTheory.ProbabilityMeasure.coeFn_eq_toNNReal_coeFn_to_measure
 
 @[simp]
-theorem val_eq_to_measure (ν : ProbabilityMeasureCat Ω) : ν.val = (ν : Measure Ω) :=
+theorem val_eq_to_measure (ν : ProbabilityMeasure Ω) : ν.val = (ν : Measure Ω) :=
   rfl
-#align measure_theory.probability_measure.val_eq_to_measure MeasureTheory.ProbabilityMeasureCat.val_eq_to_measure
+#align measure_theory.probability_measure.val_eq_to_measure MeasureTheory.ProbabilityMeasure.val_eq_to_measure
 
-theorem coe_injective : Function.Injective (coe : ProbabilityMeasureCat Ω → Measure Ω) :=
+theorem coe_injective : Function.Injective (coe : ProbabilityMeasure Ω → Measure Ω) :=
   Subtype.coe_injective
-#align measure_theory.probability_measure.coe_injective MeasureTheory.ProbabilityMeasureCat.coe_injective
+#align measure_theory.probability_measure.coe_injective MeasureTheory.ProbabilityMeasure.coe_injective
 
 @[simp]
-theorem coeFn_univ (ν : ProbabilityMeasureCat Ω) : ν univ = 1 :=
+theorem coeFn_univ (ν : ProbabilityMeasure Ω) : ν univ = 1 :=
   congr_arg ENNReal.toNNReal ν.Prop.measure_univ
-#align measure_theory.probability_measure.coe_fn_univ MeasureTheory.ProbabilityMeasureCat.coeFn_univ
+#align measure_theory.probability_measure.coe_fn_univ MeasureTheory.ProbabilityMeasure.coeFn_univ
 
-theorem coeFn_univ_ne_zero (ν : ProbabilityMeasureCat Ω) : ν univ ≠ 0 := by
+theorem coeFn_univ_ne_zero (ν : ProbabilityMeasure Ω) : ν univ ≠ 0 := by
   simp only [coe_fn_univ, Ne.def, one_ne_zero, not_false_iff]
-#align measure_theory.probability_measure.coe_fn_univ_ne_zero MeasureTheory.ProbabilityMeasureCat.coeFn_univ_ne_zero
+#align measure_theory.probability_measure.coe_fn_univ_ne_zero MeasureTheory.ProbabilityMeasure.coeFn_univ_ne_zero
 
 /-- A probability measure can be interpreted as a finite measure. -/
-def toFiniteMeasure (μ : ProbabilityMeasureCat Ω) : FiniteMeasureCat Ω :=
+def toFiniteMeasure (μ : ProbabilityMeasure Ω) : FiniteMeasure Ω :=
   ⟨μ, inferInstance⟩
-#align measure_theory.probability_measure.to_finite_measure MeasureTheory.ProbabilityMeasureCat.toFiniteMeasure
+#align measure_theory.probability_measure.to_finite_measure MeasureTheory.ProbabilityMeasure.toFiniteMeasure
 
 @[simp]
-theorem coe_comp_toFiniteMeasure_eq_coe (ν : ProbabilityMeasureCat Ω) :
+theorem coe_comp_toFiniteMeasure_eq_coe (ν : ProbabilityMeasure Ω) :
     (ν.toFiniteMeasure : Measure Ω) = (ν : Measure Ω) :=
   rfl
-#align measure_theory.probability_measure.coe_comp_to_finite_measure_eq_coe MeasureTheory.ProbabilityMeasureCat.coe_comp_toFiniteMeasure_eq_coe
+#align measure_theory.probability_measure.coe_comp_to_finite_measure_eq_coe MeasureTheory.ProbabilityMeasure.coe_comp_toFiniteMeasure_eq_coe
 
 @[simp]
-theorem coeFn_comp_toFiniteMeasure_eq_coeFn (ν : ProbabilityMeasureCat Ω) :
+theorem coeFn_comp_toFiniteMeasure_eq_coeFn (ν : ProbabilityMeasure Ω) :
     (ν.toFiniteMeasure : Set Ω → ℝ≥0) = (ν : Set Ω → ℝ≥0) :=
   rfl
-#align measure_theory.probability_measure.coe_fn_comp_to_finite_measure_eq_coe_fn MeasureTheory.ProbabilityMeasureCat.coeFn_comp_toFiniteMeasure_eq_coeFn
+#align measure_theory.probability_measure.coe_fn_comp_to_finite_measure_eq_coe_fn MeasureTheory.ProbabilityMeasure.coeFn_comp_toFiniteMeasure_eq_coeFn
 
 @[simp]
-theorem eNNReal_coeFn_eq_coeFn_to_measure (ν : ProbabilityMeasureCat Ω) (s : Set Ω) :
+theorem eNNReal_coeFn_eq_coeFn_to_measure (ν : ProbabilityMeasure Ω) (s : Set Ω) :
     (ν s : ℝ≥0∞) = (ν : Measure Ω) s := by
   rw [← coe_fn_comp_to_finite_measure_eq_coe_fn, finite_measure.ennreal_coe_fn_eq_coe_fn_to_measure,
     coe_comp_to_finite_measure_eq_coe]
-#align measure_theory.probability_measure.ennreal_coe_fn_eq_coe_fn_to_measure MeasureTheory.ProbabilityMeasureCat.eNNReal_coeFn_eq_coeFn_to_measure
+#align measure_theory.probability_measure.ennreal_coe_fn_eq_coe_fn_to_measure MeasureTheory.ProbabilityMeasure.eNNReal_coeFn_eq_coeFn_to_measure
 
-theorem apply_mono (μ : ProbabilityMeasureCat Ω) {s₁ s₂ : Set Ω} (h : s₁ ⊆ s₂) : μ s₁ ≤ μ s₂ :=
+theorem apply_mono (μ : ProbabilityMeasure Ω) {s₁ s₂ : Set Ω} (h : s₁ ⊆ s₂) : μ s₁ ≤ μ s₂ :=
   by
   rw [← coe_fn_comp_to_finite_measure_eq_coe_fn]
-  exact MeasureTheory.FiniteMeasureCat.apply_mono _ h
-#align measure_theory.probability_measure.apply_mono MeasureTheory.ProbabilityMeasureCat.apply_mono
+  exact MeasureTheory.FiniteMeasure.apply_mono _ h
+#align measure_theory.probability_measure.apply_mono MeasureTheory.ProbabilityMeasure.apply_mono
 
-theorem nonempty_of_probabilityMeasureCat (μ : ProbabilityMeasureCat Ω) : Nonempty Ω :=
+theorem nonempty_of_probabilityMeasure (μ : ProbabilityMeasure Ω) : Nonempty Ω :=
   by
   by_contra maybe_empty
   have zero : (μ : Measure Ω) univ = 0 := by
     rw [univ_eq_empty_iff.mpr (not_nonempty_iff.mp maybe_empty), measure_empty]
   rw [measure_univ] at zero 
   exact zero_ne_one zero.symm
-#align measure_theory.probability_measure.nonempty_of_probability_measure MeasureTheory.ProbabilityMeasureCat.nonempty_of_probabilityMeasureCat
+#align measure_theory.probability_measure.nonempty_of_probability_measure MeasureTheory.ProbabilityMeasure.nonempty_of_probabilityMeasure
 
 @[ext]
-theorem eq_of_forall_measure_apply_eq (μ ν : ProbabilityMeasureCat Ω)
+theorem eq_of_forall_measure_apply_eq (μ ν : ProbabilityMeasure Ω)
     (h : ∀ s : Set Ω, MeasurableSet s → (μ : Measure Ω) s = (ν : Measure Ω) s) : μ = ν := by ext1;
   ext1 s s_mble; exact h s s_mble
-#align measure_theory.probability_measure.eq_of_forall_measure_apply_eq MeasureTheory.ProbabilityMeasureCat.eq_of_forall_measure_apply_eq
+#align measure_theory.probability_measure.eq_of_forall_measure_apply_eq MeasureTheory.ProbabilityMeasure.eq_of_forall_measure_apply_eq
 
-theorem eq_of_forall_apply_eq (μ ν : ProbabilityMeasureCat Ω)
+theorem eq_of_forall_apply_eq (μ ν : ProbabilityMeasure Ω)
     (h : ∀ s : Set Ω, MeasurableSet s → μ s = ν s) : μ = ν :=
   by
   ext1 s s_mble
   simpa [ennreal_coe_fn_eq_coe_fn_to_measure] using congr_arg (coe : ℝ≥0 → ℝ≥0∞) (h s s_mble)
-#align measure_theory.probability_measure.eq_of_forall_apply_eq MeasureTheory.ProbabilityMeasureCat.eq_of_forall_apply_eq
+#align measure_theory.probability_measure.eq_of_forall_apply_eq MeasureTheory.ProbabilityMeasure.eq_of_forall_apply_eq
 
 @[simp]
-theorem mass_toFiniteMeasure (μ : ProbabilityMeasureCat Ω) : μ.toFiniteMeasure.mass = 1 :=
+theorem mass_toFiniteMeasure (μ : ProbabilityMeasure Ω) : μ.toFiniteMeasure.mass = 1 :=
   μ.coeFn_univ
-#align measure_theory.probability_measure.mass_to_finite_measure MeasureTheory.ProbabilityMeasureCat.mass_toFiniteMeasure
+#align measure_theory.probability_measure.mass_to_finite_measure MeasureTheory.ProbabilityMeasure.mass_toFiniteMeasure
 
-theorem toFiniteMeasure_nonzero (μ : ProbabilityMeasureCat Ω) : μ.toFiniteMeasure ≠ 0 :=
+theorem toFiniteMeasure_nonzero (μ : ProbabilityMeasure Ω) : μ.toFiniteMeasure ≠ 0 :=
   by
   rw [← finite_measure.mass_nonzero_iff, μ.mass_to_finite_measure]
   exact one_ne_zero
-#align measure_theory.probability_measure.to_finite_measure_nonzero MeasureTheory.ProbabilityMeasureCat.toFiniteMeasure_nonzero
+#align measure_theory.probability_measure.to_finite_measure_nonzero MeasureTheory.ProbabilityMeasure.toFiniteMeasure_nonzero
 
 variable [TopologicalSpace Ω] [OpensMeasurableSpace Ω]
 
-theorem testAgainstNn_lipschitz (μ : ProbabilityMeasureCat Ω) :
+theorem testAgainstNn_lipschitz (μ : ProbabilityMeasure Ω) :
     LipschitzWith 1 fun f : Ω →ᵇ ℝ≥0 => μ.toFiniteMeasure.testAgainstNn f :=
   μ.mass_toFiniteMeasure ▸ μ.toFiniteMeasure.testAgainstNn_lipschitz
-#align measure_theory.probability_measure.test_against_nn_lipschitz MeasureTheory.ProbabilityMeasureCat.testAgainstNn_lipschitz
+#align measure_theory.probability_measure.test_against_nn_lipschitz MeasureTheory.ProbabilityMeasure.testAgainstNn_lipschitz
 
 /-- The topology of weak convergence on `measure_theory.probability_measure Ω`. This is inherited
 (induced) from the topology of weak convergence of finite measures via the inclusion
 `measure_theory.probability_measure.to_finite_measure`. -/
-instance : TopologicalSpace (ProbabilityMeasureCat Ω) :=
+instance : TopologicalSpace (ProbabilityMeasure Ω) :=
   TopologicalSpace.induced toFiniteMeasure inferInstance
 
 theorem toFiniteMeasure_continuous :
-    Continuous (toFiniteMeasure : ProbabilityMeasureCat Ω → FiniteMeasureCat Ω) :=
+    Continuous (toFiniteMeasure : ProbabilityMeasure Ω → FiniteMeasure Ω) :=
   continuous_induced_dom
-#align measure_theory.probability_measure.to_finite_measure_continuous MeasureTheory.ProbabilityMeasureCat.toFiniteMeasure_continuous
+#align measure_theory.probability_measure.to_finite_measure_continuous MeasureTheory.ProbabilityMeasure.toFiniteMeasure_continuous
 
 /-- Probability measures yield elements of the `weak_dual` of bounded continuous nonnegative
 functions via `measure_theory.finite_measure.test_against_nn`, i.e., integration. -/
-def toWeakDualBcnn : ProbabilityMeasureCat Ω → WeakDual ℝ≥0 (Ω →ᵇ ℝ≥0) :=
-  FiniteMeasureCat.toWeakDualBcnn ∘ toFiniteMeasure
-#align measure_theory.probability_measure.to_weak_dual_bcnn MeasureTheory.ProbabilityMeasureCat.toWeakDualBcnn
+def toWeakDualBcnn : ProbabilityMeasure Ω → WeakDual ℝ≥0 (Ω →ᵇ ℝ≥0) :=
+  FiniteMeasure.toWeakDualBcnn ∘ toFiniteMeasure
+#align measure_theory.probability_measure.to_weak_dual_bcnn MeasureTheory.ProbabilityMeasure.toWeakDualBcnn
 
 @[simp]
-theorem coe_toWeakDualBcnn (μ : ProbabilityMeasureCat Ω) :
+theorem coe_toWeakDualBcnn (μ : ProbabilityMeasure Ω) :
     ⇑μ.toWeakDualBcnn = μ.toFiniteMeasure.testAgainstNn :=
   rfl
-#align measure_theory.probability_measure.coe_to_weak_dual_bcnn MeasureTheory.ProbabilityMeasureCat.coe_toWeakDualBcnn
+#align measure_theory.probability_measure.coe_to_weak_dual_bcnn MeasureTheory.ProbabilityMeasure.coe_toWeakDualBcnn
 
 @[simp]
-theorem toWeakDualBcnn_apply (μ : ProbabilityMeasureCat Ω) (f : Ω →ᵇ ℝ≥0) :
+theorem toWeakDualBcnn_apply (μ : ProbabilityMeasure Ω) (f : Ω →ᵇ ℝ≥0) :
     μ.toWeakDualBcnn f = (∫⁻ ω, f ω ∂(μ : Measure Ω)).toNNReal :=
   rfl
-#align measure_theory.probability_measure.to_weak_dual_bcnn_apply MeasureTheory.ProbabilityMeasureCat.toWeakDualBcnn_apply
+#align measure_theory.probability_measure.to_weak_dual_bcnn_apply MeasureTheory.ProbabilityMeasure.toWeakDualBcnn_apply
 
-theorem toWeakDualBcnn_continuous :
-    Continuous fun μ : ProbabilityMeasureCat Ω => μ.toWeakDualBcnn :=
-  FiniteMeasureCat.toWeakDualBcnn_continuous.comp toFiniteMeasure_continuous
-#align measure_theory.probability_measure.to_weak_dual_bcnn_continuous MeasureTheory.ProbabilityMeasureCat.toWeakDualBcnn_continuous
+theorem toWeakDualBcnn_continuous : Continuous fun μ : ProbabilityMeasure Ω => μ.toWeakDualBcnn :=
+  FiniteMeasure.toWeakDualBcnn_continuous.comp toFiniteMeasure_continuous
+#align measure_theory.probability_measure.to_weak_dual_bcnn_continuous MeasureTheory.ProbabilityMeasure.toWeakDualBcnn_continuous
 
 /- Integration of (nonnegative bounded continuous) test functions against Borel probability
 measures depends continuously on the measure. -/
 theorem continuous_testAgainstNn_eval (f : Ω →ᵇ ℝ≥0) :
-    Continuous fun μ : ProbabilityMeasureCat Ω => μ.toFiniteMeasure.testAgainstNn f :=
-  (FiniteMeasureCat.continuous_testAgainstNn_eval f).comp toFiniteMeasure_continuous
-#align measure_theory.probability_measure.continuous_test_against_nn_eval MeasureTheory.ProbabilityMeasureCat.continuous_testAgainstNn_eval
+    Continuous fun μ : ProbabilityMeasure Ω => μ.toFiniteMeasure.testAgainstNn f :=
+  (FiniteMeasure.continuous_testAgainstNn_eval f).comp toFiniteMeasure_continuous
+#align measure_theory.probability_measure.continuous_test_against_nn_eval MeasureTheory.ProbabilityMeasure.continuous_testAgainstNn_eval
 
 -- The canonical mapping from probability measures to finite measures is an embedding.
 theorem toFiniteMeasure_embedding (Ω : Type _) [MeasurableSpace Ω] [TopologicalSpace Ω]
     [OpensMeasurableSpace Ω] :
-    Embedding (toFiniteMeasure : ProbabilityMeasureCat Ω → FiniteMeasureCat Ω) :=
+    Embedding (toFiniteMeasure : ProbabilityMeasure Ω → FiniteMeasure Ω) :=
   { induced := rfl
     inj := fun μ ν h => Subtype.eq (by convert congr_arg coe h) }
-#align measure_theory.probability_measure.to_finite_measure_embedding MeasureTheory.ProbabilityMeasureCat.toFiniteMeasure_embedding
+#align measure_theory.probability_measure.to_finite_measure_embedding MeasureTheory.ProbabilityMeasure.toFiniteMeasure_embedding
 
 theorem tendsto_nhds_iff_to_finite_measures_tendsto_nhds {δ : Type _} (F : Filter δ)
-    {μs : δ → ProbabilityMeasureCat Ω} {μ₀ : ProbabilityMeasureCat Ω} :
+    {μs : δ → ProbabilityMeasure Ω} {μ₀ : ProbabilityMeasure Ω} :
     Tendsto μs F (𝓝 μ₀) ↔ Tendsto (toFiniteMeasure ∘ μs) F (𝓝 μ₀.toFiniteMeasure) :=
   Embedding.tendsto_nhds_iff (toFiniteMeasure_embedding Ω)
-#align measure_theory.probability_measure.tendsto_nhds_iff_to_finite_measures_tendsto_nhds MeasureTheory.ProbabilityMeasureCat.tendsto_nhds_iff_to_finite_measures_tendsto_nhds
+#align measure_theory.probability_measure.tendsto_nhds_iff_to_finite_measures_tendsto_nhds MeasureTheory.ProbabilityMeasure.tendsto_nhds_iff_to_finite_measures_tendsto_nhds
 
 /-- A characterization of weak convergence of probability measures by the condition that the
 integrals of every continuous bounded nonnegative function converge to the integral of the function
 against the limit measure. -/
 theorem tendsto_iff_forall_lintegral_tendsto {γ : Type _} {F : Filter γ}
-    {μs : γ → ProbabilityMeasureCat Ω} {μ : ProbabilityMeasureCat Ω} :
+    {μs : γ → ProbabilityMeasure Ω} {μ : ProbabilityMeasure Ω} :
     Tendsto μs F (𝓝 μ) ↔
       ∀ f : Ω →ᵇ ℝ≥0,
         Tendsto (fun i => ∫⁻ ω, f ω ∂(μs i : Measure Ω)) F (𝓝 (∫⁻ ω, f ω ∂(μ : Measure Ω))) :=
   by
   rw [tendsto_nhds_iff_to_finite_measures_tendsto_nhds]
   exact finite_measure.tendsto_iff_forall_lintegral_tendsto
-#align measure_theory.probability_measure.tendsto_iff_forall_lintegral_tendsto MeasureTheory.ProbabilityMeasureCat.tendsto_iff_forall_lintegral_tendsto
+#align measure_theory.probability_measure.tendsto_iff_forall_lintegral_tendsto MeasureTheory.ProbabilityMeasure.tendsto_iff_forall_lintegral_tendsto
 
 /-- The characterization of weak convergence of probability measures by the usual (defining)
 condition that the integrals of every continuous bounded function converge to the integral of the
 function against the limit measure. -/
 theorem tendsto_iff_forall_integral_tendsto {γ : Type _} {F : Filter γ}
-    {μs : γ → ProbabilityMeasureCat Ω} {μ : ProbabilityMeasureCat Ω} :
+    {μs : γ → ProbabilityMeasure Ω} {μ : ProbabilityMeasure Ω} :
     Tendsto μs F (𝓝 μ) ↔
       ∀ f : Ω →ᵇ ℝ,
         Tendsto (fun i => ∫ ω, f ω ∂(μs i : Measure Ω)) F (𝓝 (∫ ω, f ω ∂(μ : Measure Ω))) :=
@@ -294,7 +293,7 @@ theorem tendsto_iff_forall_integral_tendsto {γ : Type _} {F : Filter γ}
   rw [tendsto_nhds_iff_to_finite_measures_tendsto_nhds]
   rw [finite_measure.tendsto_iff_forall_integral_tendsto]
   simp only [coe_comp_to_finite_measure_eq_coe]
-#align measure_theory.probability_measure.tendsto_iff_forall_integral_tendsto MeasureTheory.ProbabilityMeasureCat.tendsto_iff_forall_integral_tendsto
+#align measure_theory.probability_measure.tendsto_iff_forall_integral_tendsto MeasureTheory.ProbabilityMeasure.tendsto_iff_forall_integral_tendsto
 
 end ProbabilityMeasure
 
@@ -316,11 +315,11 @@ measures.
 
 namespace FiniteMeasure
 
-variable {Ω : Type _} [Nonempty Ω] {m0 : MeasurableSpace Ω} (μ : FiniteMeasureCat Ω)
+variable {Ω : Type _} [Nonempty Ω] {m0 : MeasurableSpace Ω} (μ : FiniteMeasure Ω)
 
 /-- Normalize a finite measure so that it becomes a probability measure, i.e., divide by the
 total mass. -/
-def normalize : ProbabilityMeasureCat Ω :=
+def normalize : ProbabilityMeasure Ω :=
   if zero : μ.mass = 0 then ⟨Measure.dirac ‹Nonempty Ω›.some, Measure.dirac.isProbabilityMeasure⟩
   else
     { val := μ.mass⁻¹ • μ
@@ -330,7 +329,7 @@ def normalize : ProbabilityMeasureCat Ω :=
           ennreal_coe_fn_eq_coe_fn_to_measure μ univ]
         norm_cast
         exact inv_mul_cancel zero }
-#align measure_theory.finite_measure.normalize MeasureTheory.FiniteMeasureCat.normalize
+#align measure_theory.finite_measure.normalize MeasureTheory.FiniteMeasure.normalize
 
 @[simp]
 theorem self_eq_mass_mul_normalize (s : Set Ω) : μ s = μ.mass * μ.normalize s :=
@@ -342,7 +341,7 @@ theorem self_eq_mass_mul_normalize (s : Set Ω) : μ s = μ.mass * μ.normalize
     probability_measure.coe_fn_eq_to_nnreal_coe_fn_to_measure, ENNReal.toNNReal_coe,
     MeasureTheory.Measure.coe_nnreal_smul_apply, mul_inv_cancel_left₀ mass_nonzero,
     finite_measure.coe_fn_eq_to_nnreal_coe_fn_to_measure]
-#align measure_theory.finite_measure.self_eq_mass_mul_normalize MeasureTheory.FiniteMeasureCat.self_eq_mass_mul_normalize
+#align measure_theory.finite_measure.self_eq_mass_mul_normalize MeasureTheory.FiniteMeasure.self_eq_mass_mul_normalize
 
 theorem self_eq_mass_smul_normalize : μ = μ.mass • μ.normalize.toFiniteMeasure :=
   by
@@ -350,12 +349,12 @@ theorem self_eq_mass_smul_normalize : μ = μ.mass • μ.normalize.toFiniteMeas
   intro s s_mble
   rw [μ.self_eq_mass_mul_normalize s, coe_fn_smul_apply, smul_eq_mul,
     probability_measure.coe_fn_comp_to_finite_measure_eq_coe_fn]
-#align measure_theory.finite_measure.self_eq_mass_smul_normalize MeasureTheory.FiniteMeasureCat.self_eq_mass_smul_normalize
+#align measure_theory.finite_measure.self_eq_mass_smul_normalize MeasureTheory.FiniteMeasure.self_eq_mass_smul_normalize
 
 theorem normalize_eq_of_nonzero (nonzero : μ ≠ 0) (s : Set Ω) : μ.normalize s = μ.mass⁻¹ * μ s := by
   simp only [μ.self_eq_mass_mul_normalize, μ.mass_nonzero_iff.mpr nonzero, inv_mul_cancel_left₀,
     Ne.def, not_false_iff]
-#align measure_theory.finite_measure.normalize_eq_of_nonzero MeasureTheory.FiniteMeasureCat.normalize_eq_of_nonzero
+#align measure_theory.finite_measure.normalize_eq_of_nonzero MeasureTheory.FiniteMeasure.normalize_eq_of_nonzero
 
 theorem normalize_eq_inv_mass_smul_of_nonzero (nonzero : μ ≠ 0) :
     μ.normalize.toFiniteMeasure = μ.mass⁻¹ • μ :=
@@ -364,7 +363,7 @@ theorem normalize_eq_inv_mass_smul_of_nonzero (nonzero : μ ≠ 0) :
   rw [← smul_assoc]
   simp only [μ.mass_nonzero_iff.mpr nonzero, Algebra.id.smul_eq_mul, inv_mul_cancel, Ne.def,
     not_false_iff, one_smul]
-#align measure_theory.finite_measure.normalize_eq_inv_mass_smul_of_nonzero MeasureTheory.FiniteMeasureCat.normalize_eq_inv_mass_smul_of_nonzero
+#align measure_theory.finite_measure.normalize_eq_inv_mass_smul_of_nonzero MeasureTheory.FiniteMeasure.normalize_eq_inv_mass_smul_of_nonzero
 
 theorem coe_normalize_eq_of_nonzero (nonzero : μ ≠ 0) : (μ.normalize : Measure Ω) = μ.mass⁻¹ • μ :=
   by
@@ -372,11 +371,11 @@ theorem coe_normalize_eq_of_nonzero (nonzero : μ ≠ 0) : (μ.normalize : Measu
   simp only [← μ.normalize.ennreal_coe_fn_eq_coe_fn_to_measure s,
     μ.normalize_eq_of_nonzero nonzero s, ENNReal.coe_mul, ennreal_coe_fn_eq_coe_fn_to_measure,
     measure.coe_nnreal_smul_apply]
-#align measure_theory.finite_measure.coe_normalize_eq_of_nonzero MeasureTheory.FiniteMeasureCat.coe_normalize_eq_of_nonzero
+#align measure_theory.finite_measure.coe_normalize_eq_of_nonzero MeasureTheory.FiniteMeasure.coe_normalize_eq_of_nonzero
 
 @[simp]
 theorem ProbabilityMeasure.toFiniteMeasure_normalize_eq_self {m0 : MeasurableSpace Ω}
-    (μ : ProbabilityMeasureCat Ω) : μ.toFiniteMeasure.normalize = μ :=
+    (μ : ProbabilityMeasure Ω) : μ.toFiniteMeasure.normalize = μ :=
   by
   apply probability_measure.eq_of_forall_apply_eq
   intro s s_mble
@@ -395,7 +394,7 @@ theorem average_eq_integral_normalize {E : Type _} [NormedAddCommGroup E] [Norme
   congr
   simp only [RingHom.toFun_eq_coe, ENNReal.coe_ofNNRealHom,
     ENNReal.coe_inv (μ.mass_nonzero_iff.mpr nonzero), ennreal_mass]
-#align measure_theory.finite_measure.average_eq_integral_normalize MeasureTheory.FiniteMeasureCat.average_eq_integral_normalize
+#align measure_theory.finite_measure.average_eq_integral_normalize MeasureTheory.FiniteMeasure.average_eq_integral_normalize
 
 variable [TopologicalSpace Ω]
 
@@ -404,19 +403,19 @@ theorem testAgainstNn_eq_mass_mul (f : Ω →ᵇ ℝ≥0) :
   by
   nth_rw 1 [μ.self_eq_mass_smul_normalize]
   rw [μ.normalize.to_finite_measure.smul_test_against_nn_apply μ.mass f, smul_eq_mul]
-#align measure_theory.finite_measure.test_against_nn_eq_mass_mul MeasureTheory.FiniteMeasureCat.testAgainstNn_eq_mass_mul
+#align measure_theory.finite_measure.test_against_nn_eq_mass_mul MeasureTheory.FiniteMeasure.testAgainstNn_eq_mass_mul
 
 theorem normalize_testAgainstNn (nonzero : μ ≠ 0) (f : Ω →ᵇ ℝ≥0) :
     μ.normalize.toFiniteMeasure.testAgainstNn f = μ.mass⁻¹ * μ.testAgainstNn f := by
   simp [μ.test_against_nn_eq_mass_mul, μ.mass_nonzero_iff.mpr nonzero]
-#align measure_theory.finite_measure.normalize_test_against_nn MeasureTheory.FiniteMeasureCat.normalize_testAgainstNn
+#align measure_theory.finite_measure.normalize_test_against_nn MeasureTheory.FiniteMeasure.normalize_testAgainstNn
 
 variable [OpensMeasurableSpace Ω]
 
 variable {μ}
 
 theorem tendsto_testAgainstNn_of_tendsto_normalize_testAgainstNn_of_tendsto_mass {γ : Type _}
-    {F : Filter γ} {μs : γ → FiniteMeasureCat Ω}
+    {F : Filter γ} {μs : γ → FiniteMeasure Ω}
     (μs_lim : Tendsto (fun i => (μs i).normalize) F (𝓝 μ.normalize))
     (mass_lim : Tendsto (fun i => (μs i).mass) F (𝓝 μ.mass)) (f : Ω →ᵇ ℝ≥0) :
     Tendsto (fun i => (μs i).testAgainstNn f) F (𝓝 (μ.testAgainstNn f)) :=
@@ -433,10 +432,10 @@ theorem tendsto_testAgainstNn_of_tendsto_normalize_testAgainstNn_of_tendsto_mass
       F (𝓝 ⟨μ.mass, μ.normalize.to_finite_measure.test_against_nn f⟩) :=
     (Prod.tendsto_iff _ _).mpr ⟨mass_lim, μs_lim f⟩
   exact tendsto_mul.comp lim_pair
-#align measure_theory.finite_measure.tendsto_test_against_nn_of_tendsto_normalize_test_against_nn_of_tendsto_mass MeasureTheory.FiniteMeasureCat.tendsto_testAgainstNn_of_tendsto_normalize_testAgainstNn_of_tendsto_mass
+#align measure_theory.finite_measure.tendsto_test_against_nn_of_tendsto_normalize_test_against_nn_of_tendsto_mass MeasureTheory.FiniteMeasure.tendsto_testAgainstNn_of_tendsto_normalize_testAgainstNn_of_tendsto_mass
 
 theorem tendsto_normalize_testAgainstNn_of_tendsto {γ : Type _} {F : Filter γ}
-    {μs : γ → FiniteMeasureCat Ω} (μs_lim : Tendsto μs F (𝓝 μ)) (nonzero : μ ≠ 0) (f : Ω →ᵇ ℝ≥0) :
+    {μs : γ → FiniteMeasure Ω} (μs_lim : Tendsto μs F (𝓝 μ)) (nonzero : μ ≠ 0) (f : Ω →ᵇ ℝ≥0) :
     Tendsto (fun i => (μs i).normalize.toFiniteMeasure.testAgainstNn f) F
       (𝓝 (μ.normalize.toFiniteMeasure.testAgainstNn f)) :=
   by
@@ -463,33 +462,33 @@ theorem tendsto_normalize_testAgainstNn_of_tendsto {γ : Type _} {F : Filter γ}
     · exact (continuous_on_inv₀.continuous_at aux).Tendsto.comp lim_mass
     · exact tendsto_iff_forall_test_against_nn_tendsto.mp μs_lim f
   exact tendsto_mul.comp lim_pair
-#align measure_theory.finite_measure.tendsto_normalize_test_against_nn_of_tendsto MeasureTheory.FiniteMeasureCat.tendsto_normalize_testAgainstNn_of_tendsto
+#align measure_theory.finite_measure.tendsto_normalize_test_against_nn_of_tendsto MeasureTheory.FiniteMeasure.tendsto_normalize_testAgainstNn_of_tendsto
 
 /-- If the normalized versions of finite measures converge weakly and their total masses
 also converge, then the finite measures themselves converge weakly. -/
 theorem tendsto_of_tendsto_normalize_test_against_nn_of_tendsto_mass {γ : Type _} {F : Filter γ}
-    {μs : γ → FiniteMeasureCat Ω} (μs_lim : Tendsto (fun i => (μs i).normalize) F (𝓝 μ.normalize))
+    {μs : γ → FiniteMeasure Ω} (μs_lim : Tendsto (fun i => (μs i).normalize) F (𝓝 μ.normalize))
     (mass_lim : Tendsto (fun i => (μs i).mass) F (𝓝 μ.mass)) : Tendsto μs F (𝓝 μ) :=
   by
   rw [tendsto_iff_forall_test_against_nn_tendsto]
   exact fun f =>
     tendsto_test_against_nn_of_tendsto_normalize_test_against_nn_of_tendsto_mass μs_lim mass_lim f
-#align measure_theory.finite_measure.tendsto_of_tendsto_normalize_test_against_nn_of_tendsto_mass MeasureTheory.FiniteMeasureCat.tendsto_of_tendsto_normalize_test_against_nn_of_tendsto_mass
+#align measure_theory.finite_measure.tendsto_of_tendsto_normalize_test_against_nn_of_tendsto_mass MeasureTheory.FiniteMeasure.tendsto_of_tendsto_normalize_test_against_nn_of_tendsto_mass
 
 /-- If finite measures themselves converge weakly to a nonzero limit measure, then their
 normalized versions also converge weakly. -/
-theorem tendsto_normalize_of_tendsto {γ : Type _} {F : Filter γ} {μs : γ → FiniteMeasureCat Ω}
+theorem tendsto_normalize_of_tendsto {γ : Type _} {F : Filter γ} {μs : γ → FiniteMeasure Ω}
     (μs_lim : Tendsto μs F (𝓝 μ)) (nonzero : μ ≠ 0) :
     Tendsto (fun i => (μs i).normalize) F (𝓝 μ.normalize) :=
   by
   rw [probability_measure.tendsto_nhds_iff_to_finite_measures_tendsto_nhds,
     tendsto_iff_forall_test_against_nn_tendsto]
   exact fun f => tendsto_normalize_test_against_nn_of_tendsto μs_lim nonzero f
-#align measure_theory.finite_measure.tendsto_normalize_of_tendsto MeasureTheory.FiniteMeasureCat.tendsto_normalize_of_tendsto
+#align measure_theory.finite_measure.tendsto_normalize_of_tendsto MeasureTheory.FiniteMeasure.tendsto_normalize_of_tendsto
 
 /-- The weak convergence of finite measures to a nonzero limit can be characterized by the weak
 convergence of both their normalized versions (probability measures) and their total masses. -/
-theorem tendsto_normalize_iff_tendsto {γ : Type _} {F : Filter γ} {μs : γ → FiniteMeasureCat Ω}
+theorem tendsto_normalize_iff_tendsto {γ : Type _} {F : Filter γ} {μs : γ → FiniteMeasure Ω}
     (nonzero : μ ≠ 0) :
     Tendsto (fun i => (μs i).normalize) F (𝓝 μ.normalize) ∧
         Tendsto (fun i => (μs i).mass) F (𝓝 μ.mass) ↔
@@ -500,7 +499,7 @@ theorem tendsto_normalize_iff_tendsto {γ : Type _} {F : Filter γ} {μs : γ 
     exact tendsto_of_tendsto_normalize_test_against_nn_of_tendsto_mass normalized_lim mass_lim
   · intro μs_lim
     refine' ⟨tendsto_normalize_of_tendsto μs_lim nonzero, μs_lim.mass⟩
-#align measure_theory.finite_measure.tendsto_normalize_iff_tendsto MeasureTheory.FiniteMeasureCat.tendsto_normalize_iff_tendsto
+#align measure_theory.finite_measure.tendsto_normalize_iff_tendsto MeasureTheory.FiniteMeasure.tendsto_normalize_iff_tendsto
 
 end FiniteMeasure
 

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

@@ -179,7 +179,7 @@ theorem nonempty_of_probabilityMeasureCat (μ : ProbabilityMeasureCat Ω) : None
   by_contra maybe_empty
   have zero : (μ : Measure Ω) univ = 0 := by
     rw [univ_eq_empty_iff.mpr (not_nonempty_iff.mp maybe_empty), measure_empty]
-  rw [measure_univ] at zero
+  rw [measure_univ] at zero 
   exact zero_ne_one zero.symm
 #align measure_theory.probability_measure.nonempty_of_probability_measure MeasureTheory.ProbabilityMeasureCat.nonempty_of_probabilityMeasureCat
 
@@ -426,8 +426,8 @@ theorem tendsto_testAgainstNn_of_tendsto_normalize_testAgainstNn_of_tendsto_mass
       eq_self_iff_true] at *
     exact tendsto_zero_test_against_nn_of_tendsto_zero_mass mass_lim f
   simp_rw [fun i => (μs i).testAgainstNn_eq_mass_mul f, μ.test_against_nn_eq_mass_mul f]
-  rw [probability_measure.tendsto_nhds_iff_to_finite_measures_tendsto_nhds] at μs_lim
-  rw [tendsto_iff_forall_test_against_nn_tendsto] at μs_lim
+  rw [probability_measure.tendsto_nhds_iff_to_finite_measures_tendsto_nhds] at μs_lim 
+  rw [tendsto_iff_forall_test_against_nn_tendsto] at μs_lim 
   have lim_pair :
     tendsto (fun i => (⟨(μs i).mass, (μs i).normalize.toFiniteMeasure.testAgainstNn f⟩ : ℝ≥0 × ℝ≥0))
       F (𝓝 ⟨μ.mass, μ.normalize.to_finite_measure.test_against_nn f⟩) :=

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

@@ -79,7 +79,7 @@ open Filter
 
 open BoundedContinuousFunction
 
-open Topology ENNReal NNReal BoundedContinuousFunction
+open scoped Topology ENNReal NNReal BoundedContinuousFunction
 
 namespace MeasureTheory
 

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

@@ -185,11 +185,8 @@ theorem nonempty_of_probabilityMeasureCat (μ : ProbabilityMeasureCat Ω) : None
 
 @[ext]
 theorem eq_of_forall_measure_apply_eq (μ ν : ProbabilityMeasureCat Ω)
-    (h : ∀ s : Set Ω, MeasurableSet s → (μ : Measure Ω) s = (ν : Measure Ω) s) : μ = ν :=
-  by
-  ext1
-  ext1 s s_mble
-  exact h s s_mble
+    (h : ∀ s : Set Ω, MeasurableSet s → (μ : Measure Ω) s = (ν : Measure Ω) s) : μ = ν := by ext1;
+  ext1 s s_mble; exact h s s_mble
 #align measure_theory.probability_measure.eq_of_forall_measure_apply_eq MeasureTheory.ProbabilityMeasureCat.eq_of_forall_measure_apply_eq
 
 theorem eq_of_forall_apply_eq (μ ν : ProbabilityMeasureCat Ω)

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

@@ -100,195 +100,196 @@ finite measure, this is implemented as the induced topology from the mapping
 
 /-- Probability measures are defined as the subtype of measures that have the property of being
 probability measures (i.e., their total mass is one). -/
-def ProbabilityMeasure (Ω : Type _) [MeasurableSpace Ω] : Type _ :=
-  { μ : Measure Ω // IsProbabilityMeasure μ }
-#align measure_theory.probability_measure MeasureTheory.ProbabilityMeasure
+def ProbabilityMeasureCat (Ω : Type _) [MeasurableSpace Ω] : Type _ :=
+  { μ : Measure Ω // ProbabilityMeasure μ }
+#align measure_theory.probability_measure MeasureTheory.ProbabilityMeasureCat
 
 namespace ProbabilityMeasure
 
 variable {Ω : Type _} [MeasurableSpace Ω]
 
-instance [Inhabited Ω] : Inhabited (ProbabilityMeasure Ω) :=
+instance [Inhabited Ω] : Inhabited (ProbabilityMeasureCat Ω) :=
   ⟨⟨Measure.dirac default, Measure.dirac.isProbabilityMeasure⟩⟩
 
 /-- A probability measure can be interpreted as a measure. -/
-instance : Coe (ProbabilityMeasure Ω) (MeasureTheory.Measure Ω) :=
+instance : Coe (ProbabilityMeasureCat Ω) (MeasureTheory.Measure Ω) :=
   coeSubtype
 
-instance : CoeFun (ProbabilityMeasure Ω) fun _ => Set Ω → ℝ≥0 :=
+instance : CoeFun (ProbabilityMeasureCat Ω) fun _ => Set Ω → ℝ≥0 :=
   ⟨fun μ s => (μ s).toNNReal⟩
 
-instance (μ : ProbabilityMeasure Ω) : IsProbabilityMeasure (μ : Measure Ω) :=
+instance (μ : ProbabilityMeasureCat Ω) : ProbabilityMeasure (μ : Measure Ω) :=
   μ.Prop
 
-theorem coeFn_eq_toNNReal_coeFn_to_measure (ν : ProbabilityMeasure Ω) :
+theorem coeFn_eq_toNNReal_coeFn_to_measure (ν : ProbabilityMeasureCat Ω) :
     (ν : Set Ω → ℝ≥0) = fun s => ((ν : Measure Ω) s).toNNReal :=
   rfl
-#align measure_theory.probability_measure.coe_fn_eq_to_nnreal_coe_fn_to_measure MeasureTheory.ProbabilityMeasure.coeFn_eq_toNNReal_coeFn_to_measure
+#align measure_theory.probability_measure.coe_fn_eq_to_nnreal_coe_fn_to_measure MeasureTheory.ProbabilityMeasureCat.coeFn_eq_toNNReal_coeFn_to_measure
 
 @[simp]
-theorem val_eq_to_measure (ν : ProbabilityMeasure Ω) : ν.val = (ν : Measure Ω) :=
+theorem val_eq_to_measure (ν : ProbabilityMeasureCat Ω) : ν.val = (ν : Measure Ω) :=
   rfl
-#align measure_theory.probability_measure.val_eq_to_measure MeasureTheory.ProbabilityMeasure.val_eq_to_measure
+#align measure_theory.probability_measure.val_eq_to_measure MeasureTheory.ProbabilityMeasureCat.val_eq_to_measure
 
-theorem coe_injective : Function.Injective (coe : ProbabilityMeasure Ω → Measure Ω) :=
+theorem coe_injective : Function.Injective (coe : ProbabilityMeasureCat Ω → Measure Ω) :=
   Subtype.coe_injective
-#align measure_theory.probability_measure.coe_injective MeasureTheory.ProbabilityMeasure.coe_injective
+#align measure_theory.probability_measure.coe_injective MeasureTheory.ProbabilityMeasureCat.coe_injective
 
 @[simp]
-theorem coeFn_univ (ν : ProbabilityMeasure Ω) : ν univ = 1 :=
+theorem coeFn_univ (ν : ProbabilityMeasureCat Ω) : ν univ = 1 :=
   congr_arg ENNReal.toNNReal ν.Prop.measure_univ
-#align measure_theory.probability_measure.coe_fn_univ MeasureTheory.ProbabilityMeasure.coeFn_univ
+#align measure_theory.probability_measure.coe_fn_univ MeasureTheory.ProbabilityMeasureCat.coeFn_univ
 
-theorem coeFn_univ_ne_zero (ν : ProbabilityMeasure Ω) : ν univ ≠ 0 := by
+theorem coeFn_univ_ne_zero (ν : ProbabilityMeasureCat Ω) : ν univ ≠ 0 := by
   simp only [coe_fn_univ, Ne.def, one_ne_zero, not_false_iff]
-#align measure_theory.probability_measure.coe_fn_univ_ne_zero MeasureTheory.ProbabilityMeasure.coeFn_univ_ne_zero
+#align measure_theory.probability_measure.coe_fn_univ_ne_zero MeasureTheory.ProbabilityMeasureCat.coeFn_univ_ne_zero
 
 /-- A probability measure can be interpreted as a finite measure. -/
-def toFiniteMeasure (μ : ProbabilityMeasure Ω) : FiniteMeasure Ω :=
+def toFiniteMeasure (μ : ProbabilityMeasureCat Ω) : FiniteMeasureCat Ω :=
   ⟨μ, inferInstance⟩
-#align measure_theory.probability_measure.to_finite_measure MeasureTheory.ProbabilityMeasure.toFiniteMeasure
+#align measure_theory.probability_measure.to_finite_measure MeasureTheory.ProbabilityMeasureCat.toFiniteMeasure
 
 @[simp]
-theorem coe_comp_toFiniteMeasure_eq_coe (ν : ProbabilityMeasure Ω) :
+theorem coe_comp_toFiniteMeasure_eq_coe (ν : ProbabilityMeasureCat Ω) :
     (ν.toFiniteMeasure : Measure Ω) = (ν : Measure Ω) :=
   rfl
-#align measure_theory.probability_measure.coe_comp_to_finite_measure_eq_coe MeasureTheory.ProbabilityMeasure.coe_comp_toFiniteMeasure_eq_coe
+#align measure_theory.probability_measure.coe_comp_to_finite_measure_eq_coe MeasureTheory.ProbabilityMeasureCat.coe_comp_toFiniteMeasure_eq_coe
 
 @[simp]
-theorem coeFn_comp_toFiniteMeasure_eq_coeFn (ν : ProbabilityMeasure Ω) :
+theorem coeFn_comp_toFiniteMeasure_eq_coeFn (ν : ProbabilityMeasureCat Ω) :
     (ν.toFiniteMeasure : Set Ω → ℝ≥0) = (ν : Set Ω → ℝ≥0) :=
   rfl
-#align measure_theory.probability_measure.coe_fn_comp_to_finite_measure_eq_coe_fn MeasureTheory.ProbabilityMeasure.coeFn_comp_toFiniteMeasure_eq_coeFn
+#align measure_theory.probability_measure.coe_fn_comp_to_finite_measure_eq_coe_fn MeasureTheory.ProbabilityMeasureCat.coeFn_comp_toFiniteMeasure_eq_coeFn
 
 @[simp]
-theorem eNNReal_coeFn_eq_coeFn_to_measure (ν : ProbabilityMeasure Ω) (s : Set Ω) :
+theorem eNNReal_coeFn_eq_coeFn_to_measure (ν : ProbabilityMeasureCat Ω) (s : Set Ω) :
     (ν s : ℝ≥0∞) = (ν : Measure Ω) s := by
   rw [← coe_fn_comp_to_finite_measure_eq_coe_fn, finite_measure.ennreal_coe_fn_eq_coe_fn_to_measure,
     coe_comp_to_finite_measure_eq_coe]
-#align measure_theory.probability_measure.ennreal_coe_fn_eq_coe_fn_to_measure MeasureTheory.ProbabilityMeasure.eNNReal_coeFn_eq_coeFn_to_measure
+#align measure_theory.probability_measure.ennreal_coe_fn_eq_coe_fn_to_measure MeasureTheory.ProbabilityMeasureCat.eNNReal_coeFn_eq_coeFn_to_measure
 
-theorem apply_mono (μ : ProbabilityMeasure Ω) {s₁ s₂ : Set Ω} (h : s₁ ⊆ s₂) : μ s₁ ≤ μ s₂ :=
+theorem apply_mono (μ : ProbabilityMeasureCat Ω) {s₁ s₂ : Set Ω} (h : s₁ ⊆ s₂) : μ s₁ ≤ μ s₂ :=
   by
   rw [← coe_fn_comp_to_finite_measure_eq_coe_fn]
-  exact MeasureTheory.FiniteMeasure.apply_mono _ h
-#align measure_theory.probability_measure.apply_mono MeasureTheory.ProbabilityMeasure.apply_mono
+  exact MeasureTheory.FiniteMeasureCat.apply_mono _ h
+#align measure_theory.probability_measure.apply_mono MeasureTheory.ProbabilityMeasureCat.apply_mono
 
-theorem nonempty_of_probabilityMeasure (μ : ProbabilityMeasure Ω) : Nonempty Ω :=
+theorem nonempty_of_probabilityMeasureCat (μ : ProbabilityMeasureCat Ω) : Nonempty Ω :=
   by
   by_contra maybe_empty
   have zero : (μ : Measure Ω) univ = 0 := by
     rw [univ_eq_empty_iff.mpr (not_nonempty_iff.mp maybe_empty), measure_empty]
   rw [measure_univ] at zero
   exact zero_ne_one zero.symm
-#align measure_theory.probability_measure.nonempty_of_probability_measure MeasureTheory.ProbabilityMeasure.nonempty_of_probabilityMeasure
+#align measure_theory.probability_measure.nonempty_of_probability_measure MeasureTheory.ProbabilityMeasureCat.nonempty_of_probabilityMeasureCat
 
 @[ext]
-theorem eq_of_forall_measure_apply_eq (μ ν : ProbabilityMeasure Ω)
+theorem eq_of_forall_measure_apply_eq (μ ν : ProbabilityMeasureCat Ω)
     (h : ∀ s : Set Ω, MeasurableSet s → (μ : Measure Ω) s = (ν : Measure Ω) s) : μ = ν :=
   by
   ext1
   ext1 s s_mble
   exact h s s_mble
-#align measure_theory.probability_measure.eq_of_forall_measure_apply_eq MeasureTheory.ProbabilityMeasure.eq_of_forall_measure_apply_eq
+#align measure_theory.probability_measure.eq_of_forall_measure_apply_eq MeasureTheory.ProbabilityMeasureCat.eq_of_forall_measure_apply_eq
 
-theorem eq_of_forall_apply_eq (μ ν : ProbabilityMeasure Ω)
+theorem eq_of_forall_apply_eq (μ ν : ProbabilityMeasureCat Ω)
     (h : ∀ s : Set Ω, MeasurableSet s → μ s = ν s) : μ = ν :=
   by
   ext1 s s_mble
   simpa [ennreal_coe_fn_eq_coe_fn_to_measure] using congr_arg (coe : ℝ≥0 → ℝ≥0∞) (h s s_mble)
-#align measure_theory.probability_measure.eq_of_forall_apply_eq MeasureTheory.ProbabilityMeasure.eq_of_forall_apply_eq
+#align measure_theory.probability_measure.eq_of_forall_apply_eq MeasureTheory.ProbabilityMeasureCat.eq_of_forall_apply_eq
 
 @[simp]
-theorem mass_toFiniteMeasure (μ : ProbabilityMeasure Ω) : μ.toFiniteMeasure.mass = 1 :=
+theorem mass_toFiniteMeasure (μ : ProbabilityMeasureCat Ω) : μ.toFiniteMeasure.mass = 1 :=
   μ.coeFn_univ
-#align measure_theory.probability_measure.mass_to_finite_measure MeasureTheory.ProbabilityMeasure.mass_toFiniteMeasure
+#align measure_theory.probability_measure.mass_to_finite_measure MeasureTheory.ProbabilityMeasureCat.mass_toFiniteMeasure
 
-theorem toFiniteMeasure_nonzero (μ : ProbabilityMeasure Ω) : μ.toFiniteMeasure ≠ 0 :=
+theorem toFiniteMeasure_nonzero (μ : ProbabilityMeasureCat Ω) : μ.toFiniteMeasure ≠ 0 :=
   by
   rw [← finite_measure.mass_nonzero_iff, μ.mass_to_finite_measure]
   exact one_ne_zero
-#align measure_theory.probability_measure.to_finite_measure_nonzero MeasureTheory.ProbabilityMeasure.toFiniteMeasure_nonzero
+#align measure_theory.probability_measure.to_finite_measure_nonzero MeasureTheory.ProbabilityMeasureCat.toFiniteMeasure_nonzero
 
 variable [TopologicalSpace Ω] [OpensMeasurableSpace Ω]
 
-theorem testAgainstNn_lipschitz (μ : ProbabilityMeasure Ω) :
+theorem testAgainstNn_lipschitz (μ : ProbabilityMeasureCat Ω) :
     LipschitzWith 1 fun f : Ω →ᵇ ℝ≥0 => μ.toFiniteMeasure.testAgainstNn f :=
   μ.mass_toFiniteMeasure ▸ μ.toFiniteMeasure.testAgainstNn_lipschitz
-#align measure_theory.probability_measure.test_against_nn_lipschitz MeasureTheory.ProbabilityMeasure.testAgainstNn_lipschitz
+#align measure_theory.probability_measure.test_against_nn_lipschitz MeasureTheory.ProbabilityMeasureCat.testAgainstNn_lipschitz
 
 /-- The topology of weak convergence on `measure_theory.probability_measure Ω`. This is inherited
 (induced) from the topology of weak convergence of finite measures via the inclusion
 `measure_theory.probability_measure.to_finite_measure`. -/
-instance : TopologicalSpace (ProbabilityMeasure Ω) :=
+instance : TopologicalSpace (ProbabilityMeasureCat Ω) :=
   TopologicalSpace.induced toFiniteMeasure inferInstance
 
 theorem toFiniteMeasure_continuous :
-    Continuous (toFiniteMeasure : ProbabilityMeasure Ω → FiniteMeasure Ω) :=
+    Continuous (toFiniteMeasure : ProbabilityMeasureCat Ω → FiniteMeasureCat Ω) :=
   continuous_induced_dom
-#align measure_theory.probability_measure.to_finite_measure_continuous MeasureTheory.ProbabilityMeasure.toFiniteMeasure_continuous
+#align measure_theory.probability_measure.to_finite_measure_continuous MeasureTheory.ProbabilityMeasureCat.toFiniteMeasure_continuous
 
 /-- Probability measures yield elements of the `weak_dual` of bounded continuous nonnegative
 functions via `measure_theory.finite_measure.test_against_nn`, i.e., integration. -/
-def toWeakDualBcnn : ProbabilityMeasure Ω → WeakDual ℝ≥0 (Ω →ᵇ ℝ≥0) :=
-  FiniteMeasure.toWeakDualBcnn ∘ toFiniteMeasure
-#align measure_theory.probability_measure.to_weak_dual_bcnn MeasureTheory.ProbabilityMeasure.toWeakDualBcnn
+def toWeakDualBcnn : ProbabilityMeasureCat Ω → WeakDual ℝ≥0 (Ω →ᵇ ℝ≥0) :=
+  FiniteMeasureCat.toWeakDualBcnn ∘ toFiniteMeasure
+#align measure_theory.probability_measure.to_weak_dual_bcnn MeasureTheory.ProbabilityMeasureCat.toWeakDualBcnn
 
 @[simp]
-theorem coe_toWeakDualBcnn (μ : ProbabilityMeasure Ω) :
+theorem coe_toWeakDualBcnn (μ : ProbabilityMeasureCat Ω) :
     ⇑μ.toWeakDualBcnn = μ.toFiniteMeasure.testAgainstNn :=
   rfl
-#align measure_theory.probability_measure.coe_to_weak_dual_bcnn MeasureTheory.ProbabilityMeasure.coe_toWeakDualBcnn
+#align measure_theory.probability_measure.coe_to_weak_dual_bcnn MeasureTheory.ProbabilityMeasureCat.coe_toWeakDualBcnn
 
 @[simp]
-theorem toWeakDualBcnn_apply (μ : ProbabilityMeasure Ω) (f : Ω →ᵇ ℝ≥0) :
+theorem toWeakDualBcnn_apply (μ : ProbabilityMeasureCat Ω) (f : Ω →ᵇ ℝ≥0) :
     μ.toWeakDualBcnn f = (∫⁻ ω, f ω ∂(μ : Measure Ω)).toNNReal :=
   rfl
-#align measure_theory.probability_measure.to_weak_dual_bcnn_apply MeasureTheory.ProbabilityMeasure.toWeakDualBcnn_apply
+#align measure_theory.probability_measure.to_weak_dual_bcnn_apply MeasureTheory.ProbabilityMeasureCat.toWeakDualBcnn_apply
 
-theorem toWeakDualBcnn_continuous : Continuous fun μ : ProbabilityMeasure Ω => μ.toWeakDualBcnn :=
-  FiniteMeasure.toWeakDualBcnn_continuous.comp toFiniteMeasure_continuous
-#align measure_theory.probability_measure.to_weak_dual_bcnn_continuous MeasureTheory.ProbabilityMeasure.toWeakDualBcnn_continuous
+theorem toWeakDualBcnn_continuous :
+    Continuous fun μ : ProbabilityMeasureCat Ω => μ.toWeakDualBcnn :=
+  FiniteMeasureCat.toWeakDualBcnn_continuous.comp toFiniteMeasure_continuous
+#align measure_theory.probability_measure.to_weak_dual_bcnn_continuous MeasureTheory.ProbabilityMeasureCat.toWeakDualBcnn_continuous
 
 /- Integration of (nonnegative bounded continuous) test functions against Borel probability
 measures depends continuously on the measure. -/
 theorem continuous_testAgainstNn_eval (f : Ω →ᵇ ℝ≥0) :
-    Continuous fun μ : ProbabilityMeasure Ω => μ.toFiniteMeasure.testAgainstNn f :=
-  (FiniteMeasure.continuous_testAgainstNn_eval f).comp toFiniteMeasure_continuous
-#align measure_theory.probability_measure.continuous_test_against_nn_eval MeasureTheory.ProbabilityMeasure.continuous_testAgainstNn_eval
+    Continuous fun μ : ProbabilityMeasureCat Ω => μ.toFiniteMeasure.testAgainstNn f :=
+  (FiniteMeasureCat.continuous_testAgainstNn_eval f).comp toFiniteMeasure_continuous
+#align measure_theory.probability_measure.continuous_test_against_nn_eval MeasureTheory.ProbabilityMeasureCat.continuous_testAgainstNn_eval
 
 -- The canonical mapping from probability measures to finite measures is an embedding.
 theorem toFiniteMeasure_embedding (Ω : Type _) [MeasurableSpace Ω] [TopologicalSpace Ω]
     [OpensMeasurableSpace Ω] :
-    Embedding (toFiniteMeasure : ProbabilityMeasure Ω → FiniteMeasure Ω) :=
+    Embedding (toFiniteMeasure : ProbabilityMeasureCat Ω → FiniteMeasureCat Ω) :=
   { induced := rfl
     inj := fun μ ν h => Subtype.eq (by convert congr_arg coe h) }
-#align measure_theory.probability_measure.to_finite_measure_embedding MeasureTheory.ProbabilityMeasure.toFiniteMeasure_embedding
+#align measure_theory.probability_measure.to_finite_measure_embedding MeasureTheory.ProbabilityMeasureCat.toFiniteMeasure_embedding
 
 theorem tendsto_nhds_iff_to_finite_measures_tendsto_nhds {δ : Type _} (F : Filter δ)
-    {μs : δ → ProbabilityMeasure Ω} {μ₀ : ProbabilityMeasure Ω} :
+    {μs : δ → ProbabilityMeasureCat Ω} {μ₀ : ProbabilityMeasureCat Ω} :
     Tendsto μs F (𝓝 μ₀) ↔ Tendsto (toFiniteMeasure ∘ μs) F (𝓝 μ₀.toFiniteMeasure) :=
   Embedding.tendsto_nhds_iff (toFiniteMeasure_embedding Ω)
-#align measure_theory.probability_measure.tendsto_nhds_iff_to_finite_measures_tendsto_nhds MeasureTheory.ProbabilityMeasure.tendsto_nhds_iff_to_finite_measures_tendsto_nhds
+#align measure_theory.probability_measure.tendsto_nhds_iff_to_finite_measures_tendsto_nhds MeasureTheory.ProbabilityMeasureCat.tendsto_nhds_iff_to_finite_measures_tendsto_nhds
 
 /-- A characterization of weak convergence of probability measures by the condition that the
 integrals of every continuous bounded nonnegative function converge to the integral of the function
 against the limit measure. -/
 theorem tendsto_iff_forall_lintegral_tendsto {γ : Type _} {F : Filter γ}
-    {μs : γ → ProbabilityMeasure Ω} {μ : ProbabilityMeasure Ω} :
+    {μs : γ → ProbabilityMeasureCat Ω} {μ : ProbabilityMeasureCat Ω} :
     Tendsto μs F (𝓝 μ) ↔
       ∀ f : Ω →ᵇ ℝ≥0,
         Tendsto (fun i => ∫⁻ ω, f ω ∂(μs i : Measure Ω)) F (𝓝 (∫⁻ ω, f ω ∂(μ : Measure Ω))) :=
   by
   rw [tendsto_nhds_iff_to_finite_measures_tendsto_nhds]
   exact finite_measure.tendsto_iff_forall_lintegral_tendsto
-#align measure_theory.probability_measure.tendsto_iff_forall_lintegral_tendsto MeasureTheory.ProbabilityMeasure.tendsto_iff_forall_lintegral_tendsto
+#align measure_theory.probability_measure.tendsto_iff_forall_lintegral_tendsto MeasureTheory.ProbabilityMeasureCat.tendsto_iff_forall_lintegral_tendsto
 
 /-- The characterization of weak convergence of probability measures by the usual (defining)
 condition that the integrals of every continuous bounded function converge to the integral of the
 function against the limit measure. -/
 theorem tendsto_iff_forall_integral_tendsto {γ : Type _} {F : Filter γ}
-    {μs : γ → ProbabilityMeasure Ω} {μ : ProbabilityMeasure Ω} :
+    {μs : γ → ProbabilityMeasureCat Ω} {μ : ProbabilityMeasureCat Ω} :
     Tendsto μs F (𝓝 μ) ↔
       ∀ f : Ω →ᵇ ℝ,
         Tendsto (fun i => ∫ ω, f ω ∂(μs i : Measure Ω)) F (𝓝 (∫ ω, f ω ∂(μ : Measure Ω))) :=
@@ -296,7 +297,7 @@ theorem tendsto_iff_forall_integral_tendsto {γ : Type _} {F : Filter γ}
   rw [tendsto_nhds_iff_to_finite_measures_tendsto_nhds]
   rw [finite_measure.tendsto_iff_forall_integral_tendsto]
   simp only [coe_comp_to_finite_measure_eq_coe]
-#align measure_theory.probability_measure.tendsto_iff_forall_integral_tendsto MeasureTheory.ProbabilityMeasure.tendsto_iff_forall_integral_tendsto
+#align measure_theory.probability_measure.tendsto_iff_forall_integral_tendsto MeasureTheory.ProbabilityMeasureCat.tendsto_iff_forall_integral_tendsto
 
 end ProbabilityMeasure
 
@@ -318,11 +319,11 @@ measures.
 
 namespace FiniteMeasure
 
-variable {Ω : Type _} [Nonempty Ω] {m0 : MeasurableSpace Ω} (μ : FiniteMeasure Ω)
+variable {Ω : Type _} [Nonempty Ω] {m0 : MeasurableSpace Ω} (μ : FiniteMeasureCat Ω)
 
 /-- Normalize a finite measure so that it becomes a probability measure, i.e., divide by the
 total mass. -/
-def normalize : ProbabilityMeasure Ω :=
+def normalize : ProbabilityMeasureCat Ω :=
   if zero : μ.mass = 0 then ⟨Measure.dirac ‹Nonempty Ω›.some, Measure.dirac.isProbabilityMeasure⟩
   else
     { val := μ.mass⁻¹ • μ
@@ -332,7 +333,7 @@ def normalize : ProbabilityMeasure Ω :=
           ennreal_coe_fn_eq_coe_fn_to_measure μ univ]
         norm_cast
         exact inv_mul_cancel zero }
-#align measure_theory.finite_measure.normalize MeasureTheory.FiniteMeasure.normalize
+#align measure_theory.finite_measure.normalize MeasureTheory.FiniteMeasureCat.normalize
 
 @[simp]
 theorem self_eq_mass_mul_normalize (s : Set Ω) : μ s = μ.mass * μ.normalize s :=
@@ -342,9 +343,9 @@ theorem self_eq_mass_mul_normalize (s : Set Ω) : μ s = μ.mass * μ.normalize
   have mass_nonzero : μ.mass ≠ 0 := by rwa [μ.mass_nonzero_iff]
   simp only [normalize, dif_neg mass_nonzero, ENNReal.toNNReal_mul, Subtype.coe_mk,
     probability_measure.coe_fn_eq_to_nnreal_coe_fn_to_measure, ENNReal.toNNReal_coe,
-    MeasureTheory.Measure.coe_nNReal_smul_apply, mul_inv_cancel_left₀ mass_nonzero,
+    MeasureTheory.Measure.coe_nnreal_smul_apply, mul_inv_cancel_left₀ mass_nonzero,
     finite_measure.coe_fn_eq_to_nnreal_coe_fn_to_measure]
-#align measure_theory.finite_measure.self_eq_mass_mul_normalize MeasureTheory.FiniteMeasure.self_eq_mass_mul_normalize
+#align measure_theory.finite_measure.self_eq_mass_mul_normalize MeasureTheory.FiniteMeasureCat.self_eq_mass_mul_normalize
 
 theorem self_eq_mass_smul_normalize : μ = μ.mass • μ.normalize.toFiniteMeasure :=
   by
@@ -352,12 +353,12 @@ theorem self_eq_mass_smul_normalize : μ = μ.mass • μ.normalize.toFiniteMeas
   intro s s_mble
   rw [μ.self_eq_mass_mul_normalize s, coe_fn_smul_apply, smul_eq_mul,
     probability_measure.coe_fn_comp_to_finite_measure_eq_coe_fn]
-#align measure_theory.finite_measure.self_eq_mass_smul_normalize MeasureTheory.FiniteMeasure.self_eq_mass_smul_normalize
+#align measure_theory.finite_measure.self_eq_mass_smul_normalize MeasureTheory.FiniteMeasureCat.self_eq_mass_smul_normalize
 
 theorem normalize_eq_of_nonzero (nonzero : μ ≠ 0) (s : Set Ω) : μ.normalize s = μ.mass⁻¹ * μ s := by
   simp only [μ.self_eq_mass_mul_normalize, μ.mass_nonzero_iff.mpr nonzero, inv_mul_cancel_left₀,
     Ne.def, not_false_iff]
-#align measure_theory.finite_measure.normalize_eq_of_nonzero MeasureTheory.FiniteMeasure.normalize_eq_of_nonzero
+#align measure_theory.finite_measure.normalize_eq_of_nonzero MeasureTheory.FiniteMeasureCat.normalize_eq_of_nonzero
 
 theorem normalize_eq_inv_mass_smul_of_nonzero (nonzero : μ ≠ 0) :
     μ.normalize.toFiniteMeasure = μ.mass⁻¹ • μ :=
@@ -366,7 +367,7 @@ theorem normalize_eq_inv_mass_smul_of_nonzero (nonzero : μ ≠ 0) :
   rw [← smul_assoc]
   simp only [μ.mass_nonzero_iff.mpr nonzero, Algebra.id.smul_eq_mul, inv_mul_cancel, Ne.def,
     not_false_iff, one_smul]
-#align measure_theory.finite_measure.normalize_eq_inv_mass_smul_of_nonzero MeasureTheory.FiniteMeasure.normalize_eq_inv_mass_smul_of_nonzero
+#align measure_theory.finite_measure.normalize_eq_inv_mass_smul_of_nonzero MeasureTheory.FiniteMeasureCat.normalize_eq_inv_mass_smul_of_nonzero
 
 theorem coe_normalize_eq_of_nonzero (nonzero : μ ≠ 0) : (μ.normalize : Measure Ω) = μ.mass⁻¹ • μ :=
   by
@@ -374,11 +375,11 @@ theorem coe_normalize_eq_of_nonzero (nonzero : μ ≠ 0) : (μ.normalize : Measu
   simp only [← μ.normalize.ennreal_coe_fn_eq_coe_fn_to_measure s,
     μ.normalize_eq_of_nonzero nonzero s, ENNReal.coe_mul, ennreal_coe_fn_eq_coe_fn_to_measure,
     measure.coe_nnreal_smul_apply]
-#align measure_theory.finite_measure.coe_normalize_eq_of_nonzero MeasureTheory.FiniteMeasure.coe_normalize_eq_of_nonzero
+#align measure_theory.finite_measure.coe_normalize_eq_of_nonzero MeasureTheory.FiniteMeasureCat.coe_normalize_eq_of_nonzero
 
 @[simp]
 theorem ProbabilityMeasure.toFiniteMeasure_normalize_eq_self {m0 : MeasurableSpace Ω}
-    (μ : ProbabilityMeasure Ω) : μ.toFiniteMeasure.normalize = μ :=
+    (μ : ProbabilityMeasureCat Ω) : μ.toFiniteMeasure.normalize = μ :=
   by
   apply probability_measure.eq_of_forall_apply_eq
   intro s s_mble
@@ -397,7 +398,7 @@ theorem average_eq_integral_normalize {E : Type _} [NormedAddCommGroup E] [Norme
   congr
   simp only [RingHom.toFun_eq_coe, ENNReal.coe_ofNNRealHom,
     ENNReal.coe_inv (μ.mass_nonzero_iff.mpr nonzero), ennreal_mass]
-#align measure_theory.finite_measure.average_eq_integral_normalize MeasureTheory.FiniteMeasure.average_eq_integral_normalize
+#align measure_theory.finite_measure.average_eq_integral_normalize MeasureTheory.FiniteMeasureCat.average_eq_integral_normalize
 
 variable [TopologicalSpace Ω]
 
@@ -406,19 +407,19 @@ theorem testAgainstNn_eq_mass_mul (f : Ω →ᵇ ℝ≥0) :
   by
   nth_rw 1 [μ.self_eq_mass_smul_normalize]
   rw [μ.normalize.to_finite_measure.smul_test_against_nn_apply μ.mass f, smul_eq_mul]
-#align measure_theory.finite_measure.test_against_nn_eq_mass_mul MeasureTheory.FiniteMeasure.testAgainstNn_eq_mass_mul
+#align measure_theory.finite_measure.test_against_nn_eq_mass_mul MeasureTheory.FiniteMeasureCat.testAgainstNn_eq_mass_mul
 
 theorem normalize_testAgainstNn (nonzero : μ ≠ 0) (f : Ω →ᵇ ℝ≥0) :
     μ.normalize.toFiniteMeasure.testAgainstNn f = μ.mass⁻¹ * μ.testAgainstNn f := by
   simp [μ.test_against_nn_eq_mass_mul, μ.mass_nonzero_iff.mpr nonzero]
-#align measure_theory.finite_measure.normalize_test_against_nn MeasureTheory.FiniteMeasure.normalize_testAgainstNn
+#align measure_theory.finite_measure.normalize_test_against_nn MeasureTheory.FiniteMeasureCat.normalize_testAgainstNn
 
 variable [OpensMeasurableSpace Ω]
 
 variable {μ}
 
 theorem tendsto_testAgainstNn_of_tendsto_normalize_testAgainstNn_of_tendsto_mass {γ : Type _}
-    {F : Filter γ} {μs : γ → FiniteMeasure Ω}
+    {F : Filter γ} {μs : γ → FiniteMeasureCat Ω}
     (μs_lim : Tendsto (fun i => (μs i).normalize) F (𝓝 μ.normalize))
     (mass_lim : Tendsto (fun i => (μs i).mass) F (𝓝 μ.mass)) (f : Ω →ᵇ ℝ≥0) :
     Tendsto (fun i => (μs i).testAgainstNn f) F (𝓝 (μ.testAgainstNn f)) :=
@@ -435,10 +436,10 @@ theorem tendsto_testAgainstNn_of_tendsto_normalize_testAgainstNn_of_tendsto_mass
       F (𝓝 ⟨μ.mass, μ.normalize.to_finite_measure.test_against_nn f⟩) :=
     (Prod.tendsto_iff _ _).mpr ⟨mass_lim, μs_lim f⟩
   exact tendsto_mul.comp lim_pair
-#align measure_theory.finite_measure.tendsto_test_against_nn_of_tendsto_normalize_test_against_nn_of_tendsto_mass MeasureTheory.FiniteMeasure.tendsto_testAgainstNn_of_tendsto_normalize_testAgainstNn_of_tendsto_mass
+#align measure_theory.finite_measure.tendsto_test_against_nn_of_tendsto_normalize_test_against_nn_of_tendsto_mass MeasureTheory.FiniteMeasureCat.tendsto_testAgainstNn_of_tendsto_normalize_testAgainstNn_of_tendsto_mass
 
 theorem tendsto_normalize_testAgainstNn_of_tendsto {γ : Type _} {F : Filter γ}
-    {μs : γ → FiniteMeasure Ω} (μs_lim : Tendsto μs F (𝓝 μ)) (nonzero : μ ≠ 0) (f : Ω →ᵇ ℝ≥0) :
+    {μs : γ → FiniteMeasureCat Ω} (μs_lim : Tendsto μs F (𝓝 μ)) (nonzero : μ ≠ 0) (f : Ω →ᵇ ℝ≥0) :
     Tendsto (fun i => (μs i).normalize.toFiniteMeasure.testAgainstNn f) F
       (𝓝 (μ.normalize.toFiniteMeasure.testAgainstNn f)) :=
   by
@@ -465,33 +466,33 @@ theorem tendsto_normalize_testAgainstNn_of_tendsto {γ : Type _} {F : Filter γ}
     · exact (continuous_on_inv₀.continuous_at aux).Tendsto.comp lim_mass
     · exact tendsto_iff_forall_test_against_nn_tendsto.mp μs_lim f
   exact tendsto_mul.comp lim_pair
-#align measure_theory.finite_measure.tendsto_normalize_test_against_nn_of_tendsto MeasureTheory.FiniteMeasure.tendsto_normalize_testAgainstNn_of_tendsto
+#align measure_theory.finite_measure.tendsto_normalize_test_against_nn_of_tendsto MeasureTheory.FiniteMeasureCat.tendsto_normalize_testAgainstNn_of_tendsto
 
 /-- If the normalized versions of finite measures converge weakly and their total masses
 also converge, then the finite measures themselves converge weakly. -/
 theorem tendsto_of_tendsto_normalize_test_against_nn_of_tendsto_mass {γ : Type _} {F : Filter γ}
-    {μs : γ → FiniteMeasure Ω} (μs_lim : Tendsto (fun i => (μs i).normalize) F (𝓝 μ.normalize))
+    {μs : γ → FiniteMeasureCat Ω} (μs_lim : Tendsto (fun i => (μs i).normalize) F (𝓝 μ.normalize))
     (mass_lim : Tendsto (fun i => (μs i).mass) F (𝓝 μ.mass)) : Tendsto μs F (𝓝 μ) :=
   by
   rw [tendsto_iff_forall_test_against_nn_tendsto]
   exact fun f =>
     tendsto_test_against_nn_of_tendsto_normalize_test_against_nn_of_tendsto_mass μs_lim mass_lim f
-#align measure_theory.finite_measure.tendsto_of_tendsto_normalize_test_against_nn_of_tendsto_mass MeasureTheory.FiniteMeasure.tendsto_of_tendsto_normalize_test_against_nn_of_tendsto_mass
+#align measure_theory.finite_measure.tendsto_of_tendsto_normalize_test_against_nn_of_tendsto_mass MeasureTheory.FiniteMeasureCat.tendsto_of_tendsto_normalize_test_against_nn_of_tendsto_mass
 
 /-- If finite measures themselves converge weakly to a nonzero limit measure, then their
 normalized versions also converge weakly. -/
-theorem tendsto_normalize_of_tendsto {γ : Type _} {F : Filter γ} {μs : γ → FiniteMeasure Ω}
+theorem tendsto_normalize_of_tendsto {γ : Type _} {F : Filter γ} {μs : γ → FiniteMeasureCat Ω}
     (μs_lim : Tendsto μs F (𝓝 μ)) (nonzero : μ ≠ 0) :
     Tendsto (fun i => (μs i).normalize) F (𝓝 μ.normalize) :=
   by
   rw [probability_measure.tendsto_nhds_iff_to_finite_measures_tendsto_nhds,
     tendsto_iff_forall_test_against_nn_tendsto]
   exact fun f => tendsto_normalize_test_against_nn_of_tendsto μs_lim nonzero f
-#align measure_theory.finite_measure.tendsto_normalize_of_tendsto MeasureTheory.FiniteMeasure.tendsto_normalize_of_tendsto
+#align measure_theory.finite_measure.tendsto_normalize_of_tendsto MeasureTheory.FiniteMeasureCat.tendsto_normalize_of_tendsto
 
 /-- The weak convergence of finite measures to a nonzero limit can be characterized by the weak
 convergence of both their normalized versions (probability measures) and their total masses. -/
-theorem tendsto_normalize_iff_tendsto {γ : Type _} {F : Filter γ} {μs : γ → FiniteMeasure Ω}
+theorem tendsto_normalize_iff_tendsto {γ : Type _} {F : Filter γ} {μs : γ → FiniteMeasureCat Ω}
     (nonzero : μ ≠ 0) :
     Tendsto (fun i => (μs i).normalize) F (𝓝 μ.normalize) ∧
         Tendsto (fun i => (μs i).mass) F (𝓝 μ.mass) ↔
@@ -502,7 +503,7 @@ theorem tendsto_normalize_iff_tendsto {γ : Type _} {F : Filter γ} {μs : γ 
     exact tendsto_of_tendsto_normalize_test_against_nn_of_tendsto_mass normalized_lim mass_lim
   · intro μs_lim
     refine' ⟨tendsto_normalize_of_tendsto μs_lim nonzero, μs_lim.mass⟩
-#align measure_theory.finite_measure.tendsto_normalize_iff_tendsto MeasureTheory.FiniteMeasure.tendsto_normalize_iff_tendsto
+#align measure_theory.finite_measure.tendsto_normalize_iff_tendsto MeasureTheory.FiniteMeasureCat.tendsto_normalize_iff_tendsto
 
 end FiniteMeasure
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/738054fa93d43512da144ec45ce799d18fd44248

@@ -4,13 +4,12 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kalle Kytölä
 
 ! This file was ported from Lean 3 source module measure_theory.measure.probability_measure
-! leanprover-community/mathlib commit f2ce6086713c78a7f880485f7917ea547a215982
+! leanprover-community/mathlib commit f0c8bf9245297a541f468be517f1bde6195105e9
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
 import Mathbin.MeasureTheory.Measure.FiniteMeasure
 import Mathbin.MeasureTheory.Integral.Average
-import Mathbin.Probability.ConditionalProbability
 
 /-!
 # Probability measures

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

@@ -339,7 +339,7 @@ def normalize : ProbabilityMeasure Ω :=
 theorem self_eq_mass_mul_normalize (s : Set Ω) : μ s = μ.mass * μ.normalize s :=
   by
   obtain rfl | h := eq_or_ne μ 0
-  · simp only [zero.mass, coe_fn_zero, Pi.zero_apply, zero_mul]
+  · simp only [zero.mass, coe_fn_zero, Pi.zero_apply, MulZeroClass.zero_mul]
   have mass_nonzero : μ.mass ≠ 0 := by rwa [μ.mass_nonzero_iff]
   simp only [normalize, dif_neg mass_nonzero, ENNReal.toNNReal_mul, Subtype.coe_mk,
     probability_measure.coe_fn_eq_to_nnreal_coe_fn_to_measure, ENNReal.toNNReal_coe,

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

@@ -80,7 +80,7 @@ open Filter
 
 open BoundedContinuousFunction
 
-open Topology Ennreal NNReal BoundedContinuousFunction
+open Topology ENNReal NNReal BoundedContinuousFunction
 
 namespace MeasureTheory
 
@@ -122,10 +122,10 @@ instance : CoeFun (ProbabilityMeasure Ω) fun _ => Set Ω → ℝ≥0 :=
 instance (μ : ProbabilityMeasure Ω) : IsProbabilityMeasure (μ : Measure Ω) :=
   μ.Prop
 
-theorem coeFn_eq_toNnreal_coeFn_to_measure (ν : ProbabilityMeasure Ω) :
+theorem coeFn_eq_toNNReal_coeFn_to_measure (ν : ProbabilityMeasure Ω) :
     (ν : Set Ω → ℝ≥0) = fun s => ((ν : Measure Ω) s).toNNReal :=
   rfl
-#align measure_theory.probability_measure.coe_fn_eq_to_nnreal_coe_fn_to_measure MeasureTheory.ProbabilityMeasure.coeFn_eq_toNnreal_coeFn_to_measure
+#align measure_theory.probability_measure.coe_fn_eq_to_nnreal_coe_fn_to_measure MeasureTheory.ProbabilityMeasure.coeFn_eq_toNNReal_coeFn_to_measure
 
 @[simp]
 theorem val_eq_to_measure (ν : ProbabilityMeasure Ω) : ν.val = (ν : Measure Ω) :=
@@ -138,7 +138,7 @@ theorem coe_injective : Function.Injective (coe : ProbabilityMeasure Ω → Meas
 
 @[simp]
 theorem coeFn_univ (ν : ProbabilityMeasure Ω) : ν univ = 1 :=
-  congr_arg Ennreal.toNnreal ν.Prop.measure_univ
+  congr_arg ENNReal.toNNReal ν.Prop.measure_univ
 #align measure_theory.probability_measure.coe_fn_univ MeasureTheory.ProbabilityMeasure.coeFn_univ
 
 theorem coeFn_univ_ne_zero (ν : ProbabilityMeasure Ω) : ν univ ≠ 0 := by
@@ -163,11 +163,11 @@ theorem coeFn_comp_toFiniteMeasure_eq_coeFn (ν : ProbabilityMeasure Ω) :
 #align measure_theory.probability_measure.coe_fn_comp_to_finite_measure_eq_coe_fn MeasureTheory.ProbabilityMeasure.coeFn_comp_toFiniteMeasure_eq_coeFn
 
 @[simp]
-theorem ennreal_coeFn_eq_coeFn_to_measure (ν : ProbabilityMeasure Ω) (s : Set Ω) :
+theorem eNNReal_coeFn_eq_coeFn_to_measure (ν : ProbabilityMeasure Ω) (s : Set Ω) :
     (ν s : ℝ≥0∞) = (ν : Measure Ω) s := by
   rw [← coe_fn_comp_to_finite_measure_eq_coe_fn, finite_measure.ennreal_coe_fn_eq_coe_fn_to_measure,
     coe_comp_to_finite_measure_eq_coe]
-#align measure_theory.probability_measure.ennreal_coe_fn_eq_coe_fn_to_measure MeasureTheory.ProbabilityMeasure.ennreal_coeFn_eq_coeFn_to_measure
+#align measure_theory.probability_measure.ennreal_coe_fn_eq_coe_fn_to_measure MeasureTheory.ProbabilityMeasure.eNNReal_coeFn_eq_coeFn_to_measure
 
 theorem apply_mono (μ : ProbabilityMeasure Ω) {s₁ s₂ : Set Ω} (h : s₁ ⊆ s₂) : μ s₁ ≤ μ s₂ :=
   by
@@ -341,8 +341,8 @@ theorem self_eq_mass_mul_normalize (s : Set Ω) : μ s = μ.mass * μ.normalize
   obtain rfl | h := eq_or_ne μ 0
   · simp only [zero.mass, coe_fn_zero, Pi.zero_apply, zero_mul]
   have mass_nonzero : μ.mass ≠ 0 := by rwa [μ.mass_nonzero_iff]
-  simp only [normalize, dif_neg mass_nonzero, Ennreal.toNnreal_mul, Subtype.coe_mk,
-    probability_measure.coe_fn_eq_to_nnreal_coe_fn_to_measure, Ennreal.toNnreal_coe,
+  simp only [normalize, dif_neg mass_nonzero, ENNReal.toNNReal_mul, Subtype.coe_mk,
+    probability_measure.coe_fn_eq_to_nnreal_coe_fn_to_measure, ENNReal.toNNReal_coe,
     MeasureTheory.Measure.coe_nNReal_smul_apply, mul_inv_cancel_left₀ mass_nonzero,
     finite_measure.coe_fn_eq_to_nnreal_coe_fn_to_measure]
 #align measure_theory.finite_measure.self_eq_mass_mul_normalize MeasureTheory.FiniteMeasure.self_eq_mass_mul_normalize
@@ -373,7 +373,7 @@ theorem coe_normalize_eq_of_nonzero (nonzero : μ ≠ 0) : (μ.normalize : Measu
   by
   ext1 s s_mble
   simp only [← μ.normalize.ennreal_coe_fn_eq_coe_fn_to_measure s,
-    μ.normalize_eq_of_nonzero nonzero s, Ennreal.coe_mul, ennreal_coe_fn_eq_coe_fn_to_measure,
+    μ.normalize_eq_of_nonzero nonzero s, ENNReal.coe_mul, ennreal_coe_fn_eq_coe_fn_to_measure,
     measure.coe_nnreal_smul_apply]
 #align measure_theory.finite_measure.coe_normalize_eq_of_nonzero MeasureTheory.FiniteMeasure.coe_normalize_eq_of_nonzero
 
@@ -396,8 +396,8 @@ theorem average_eq_integral_normalize {E : Type _} [NormedAddCommGroup E] [Norme
   by
   rw [μ.coe_normalize_eq_of_nonzero nonzero, average]
   congr
-  simp only [RingHom.toFun_eq_coe, Ennreal.coe_ofNnrealHom,
-    Ennreal.coe_inv (μ.mass_nonzero_iff.mpr nonzero), ennreal_mass]
+  simp only [RingHom.toFun_eq_coe, ENNReal.coe_ofNNRealHom,
+    ENNReal.coe_inv (μ.mass_nonzero_iff.mpr nonzero), ennreal_mass]
 #align measure_theory.finite_measure.average_eq_integral_normalize MeasureTheory.FiniteMeasure.average_eq_integral_normalize
 
 variable [TopologicalSpace Ω]

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

These are changes from #11997, the latest adaptation PR for nightly-2024-04-07, which can be made directly on master.

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

@@ -355,7 +355,7 @@ def normalize : ProbabilityMeasure Ω :=
         rw [FiniteMeasure.toMeasure_smul]
         simp only [Measure.smul_toOuterMeasure, OuterMeasure.coe_smul, Pi.smul_apply,
           Measure.nnreal_smul_coe_apply, ne_eq, mass_zero_iff, ENNReal.coe_inv zero, ennreal_mass]
-        rw [← Ne.def, ← ENNReal.coe_ne_zero, ennreal_mass] at zero
+        rw [← Ne, ← ENNReal.coe_ne_zero, ennreal_mass] at zero
         exact ENNReal.inv_mul_cancel zero μ.prop.measure_univ_lt_top.ne }
 #align measure_theory.finite_measure.normalize MeasureTheory.FiniteMeasure.normalize
 

@@ -152,7 +152,7 @@ theorem coeFn_univ (ν : ProbabilityMeasure Ω) : ν univ = 1 :=
 #align measure_theory.probability_measure.coe_fn_univ MeasureTheory.ProbabilityMeasure.coeFn_univ
 
 theorem coeFn_univ_ne_zero (ν : ProbabilityMeasure Ω) : ν univ ≠ 0 := by
-  simp only [coeFn_univ, Ne.def, one_ne_zero, not_false_iff]
+  simp only [coeFn_univ, Ne, one_ne_zero, not_false_iff]
 #align measure_theory.probability_measure.coe_fn_univ_ne_zero MeasureTheory.ProbabilityMeasure.coeFn_univ_ne_zero
 
 /-- A probability measure can be interpreted as a finite measure. -/
@@ -382,14 +382,14 @@ theorem self_eq_mass_smul_normalize : μ = μ.mass • μ.normalize.toFiniteMeas
 
 theorem normalize_eq_of_nonzero (nonzero : μ ≠ 0) (s : Set Ω) : μ.normalize s = μ.mass⁻¹ * μ s := by
   simp only [μ.self_eq_mass_mul_normalize, μ.mass_nonzero_iff.mpr nonzero, inv_mul_cancel_left₀,
-    Ne.def, not_false_iff]
+    Ne, not_false_iff]
 #align measure_theory.finite_measure.normalize_eq_of_nonzero MeasureTheory.FiniteMeasure.normalize_eq_of_nonzero
 
 theorem normalize_eq_inv_mass_smul_of_nonzero (nonzero : μ ≠ 0) :
     μ.normalize.toFiniteMeasure = μ.mass⁻¹ • μ := by
   nth_rw 3 [μ.self_eq_mass_smul_normalize]
   rw [← smul_assoc]
-  simp only [μ.mass_nonzero_iff.mpr nonzero, Algebra.id.smul_eq_mul, inv_mul_cancel, Ne.def,
+  simp only [μ.mass_nonzero_iff.mpr nonzero, Algebra.id.smul_eq_mul, inv_mul_cancel, Ne,
     not_false_iff, one_smul]
 #align measure_theory.finite_measure.normalize_eq_inv_mass_smul_of_nonzero MeasureTheory.FiniteMeasure.normalize_eq_inv_mass_smul_of_nonzero
 

Classifies by adding issue number #10618 to porting notes claiming "simp can prove it".

@@ -146,7 +146,7 @@ theorem toMeasure_injective : Function.Injective ((↑) : ProbabilityMeasure Ω
   Subtype.coe_injective
 #align measure_theory.probability_measure.coe_injective MeasureTheory.ProbabilityMeasure.toMeasure_injective
 
--- Porting note: removed `@[simp]` because `simp` can prove it
+-- Porting note (#10618): removed `@[simp]` because `simp` can prove it
 theorem coeFn_univ (ν : ProbabilityMeasure Ω) : ν univ = 1 :=
   congr_arg ENNReal.toNNReal ν.prop.measure_univ
 #align measure_theory.probability_measure.coe_fn_univ MeasureTheory.ProbabilityMeasure.coeFn_univ

Empty lines were removed by executing the following Python script twice

import os
import re


# Loop through each file in the repository
for dir_path, dirs, files in os.walk('.'):
  for filename in files:
    if filename.endswith('.lean'):
      file_path = os.path.join(dir_path, filename)

      # Open the file and read its contents
      with open(file_path, 'r') as file:
        content = file.read()

      # Use a regular expression to replace sequences of "variable" lines separated by empty lines
      # with sequences without empty lines
      modified_content = re.sub(r'(variable.*\n)\n(variable(?! .* in))', r'\1\2', content)

      # Write the modified content back to the file
      with open(file_path, 'w') as file:
        file.write(modified_content)

@@ -312,7 +312,6 @@ end convergence_in_distribution -- section
 section Hausdorff
 
 variable [TopologicalSpace Ω] [HasOuterApproxClosed Ω] [BorelSpace Ω]
-
 variable (Ω)
 
 /-- On topological spaces where indicators of closed sets have decreasing approximating sequences of
@@ -436,7 +435,6 @@ theorem normalize_testAgainstNN (nonzero : μ ≠ 0) (f : Ω →ᵇ ℝ≥0) :
 #align measure_theory.finite_measure.normalize_test_against_nn MeasureTheory.FiniteMeasure.normalize_testAgainstNN
 
 variable [OpensMeasurableSpace Ω]
-
 variable {μ}
 
 theorem tendsto_testAgainstNN_of_tendsto_normalize_testAgainstNN_of_tendsto_mass {γ : Type*}

Homogenises porting notes via capitalisation and addition of whitespace.

It makes the following changes:

• converts "--porting note" into "-- Porting note";
• converts "porting note" into "Porting note".

@@ -116,7 +116,7 @@ variable {Ω : Type*} [MeasurableSpace Ω]
 instance [Inhabited Ω] : Inhabited (ProbabilityMeasure Ω) :=
   ⟨⟨Measure.dirac default, Measure.dirac.isProbabilityMeasure⟩⟩
 
--- porting note: as with other subtype synonyms (e.g., `ℝ≥0`), we need a new function for the
+-- Porting note: as with other subtype synonyms (e.g., `ℝ≥0`), we need a new function for the
 -- coercion instead of relying on `Subtype.val`.
 /-- Coercion from `MeasureTheory.ProbabilityMeasure Ω` to `MeasureTheory.Measure Ω`. -/
 @[coe]
@@ -132,7 +132,7 @@ instance : CoeFun (ProbabilityMeasure Ω) fun _ => Set Ω → ℝ≥0 :=
 instance (μ : ProbabilityMeasure Ω) : IsProbabilityMeasure (μ : Measure Ω) :=
   μ.prop
 
--- porting note: syntactic tautology because of the way coercions work in Lean 4
+-- Porting note: syntactic tautology because of the way coercions work in Lean 4
 #noalign measure_theory.probability_measure.coe_fn_eq_to_nnreal_coe_fn_to_measure
 
 @[simp, norm_cast] lemma coe_mk (μ : Measure Ω) (hμ) : toMeasure ⟨μ, hμ⟩ = μ := rfl
@@ -146,7 +146,7 @@ theorem toMeasure_injective : Function.Injective ((↑) : ProbabilityMeasure Ω
   Subtype.coe_injective
 #align measure_theory.probability_measure.coe_injective MeasureTheory.ProbabilityMeasure.toMeasure_injective
 
--- porting note: removed `@[simp]` because `simp` can prove it
+-- Porting note: removed `@[simp]` because `simp` can prove it
 theorem coeFn_univ (ν : ProbabilityMeasure Ω) : ν univ = 1 :=
   congr_arg ENNReal.toNNReal ν.prop.measure_univ
 #align measure_theory.probability_measure.coe_fn_univ MeasureTheory.ProbabilityMeasure.coeFn_univ
@@ -352,7 +352,7 @@ def normalize : ProbabilityMeasure Ω :=
     { val := ↑(μ.mass⁻¹ • μ)
       property := by
         refine' ⟨_⟩
-        -- porting note: paying the price that this isn't `simp` lemma now.
+        -- Porting note: paying the price that this isn't `simp` lemma now.
         rw [FiniteMeasure.toMeasure_smul]
         simp only [Measure.smul_toOuterMeasure, OuterMeasure.coe_smul, Pi.smul_apply,
           Measure.nnreal_smul_coe_apply, ne_eq, mass_zero_iff, ENNReal.coe_inv zero, ennreal_mass]
@@ -368,7 +368,7 @@ theorem self_eq_mass_mul_normalize (s : Set Ω) : μ s = μ.mass * μ.normalize
   have mass_nonzero : μ.mass ≠ 0 := by rwa [μ.mass_nonzero_iff]
   simp only [normalize, dif_neg mass_nonzero]
   change μ s = mass μ * ((mass μ)⁻¹ • μ) s
-  -- porting note: this `change` is a hack, but I had trouble coming up with something better
+  -- Porting note: this `change` is a hack, but I had trouble coming up with something better
   simp only [toMeasure_smul, Measure.smul_toOuterMeasure, OuterMeasure.coe_smul, Pi.smul_apply,
     Measure.nnreal_smul_coe_apply, ne_eq, mass_zero_iff, ENNReal.toNNReal_mul, ENNReal.toNNReal_coe,
     mul_inv_cancel_left₀ mass_nonzero]

I replaced a few "terminal" refine/refine's with exact.

The strategy was very simple-minded: essentially any refine whose following line had smaller indentation got replaced by exact and then I cleaned up the mess.

This PR certainly leaves some further terminal refines, but maybe the current change is beneficial.

@@ -515,7 +515,7 @@ theorem tendsto_normalize_iff_tendsto {γ : Type*} {F : Filter γ} {μs : γ →
   · rintro ⟨normalized_lim, mass_lim⟩
     exact tendsto_of_tendsto_normalize_testAgainstNN_of_tendsto_mass normalized_lim mass_lim
   · intro μs_lim
-    refine' ⟨tendsto_normalize_of_tendsto μs_lim nonzero, μs_lim.mass⟩
+    exact ⟨tendsto_normalize_of_tendsto μs_lim nonzero, μs_lim.mass⟩
 #align measure_theory.finite_measure.tendsto_normalize_iff_tendsto MeasureTheory.FiniteMeasure.tendsto_normalize_iff_tendsto
 
 end FiniteMeasure --namespace

From PFR

@@ -135,6 +135,8 @@ instance (μ : ProbabilityMeasure Ω) : IsProbabilityMeasure (μ : Measure Ω) :
 -- porting note: syntactic tautology because of the way coercions work in Lean 4
 #noalign measure_theory.probability_measure.coe_fn_eq_to_nnreal_coe_fn_to_measure
 
+@[simp, norm_cast] lemma coe_mk (μ : Measure Ω) (hμ) : toMeasure ⟨μ, hμ⟩ = μ := rfl
+
 @[simp]
 theorem val_eq_to_measure (ν : ProbabilityMeasure Ω) : ν.val = (ν : Measure Ω) :=
   rfl

Upstreaming from PFR project

This PR defines binary products of finite measures and probability measures.

Co-authored-by: kkytola <“kalle.kytola@aalto.fi”> Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: kkytola <39528102+kkytola@users.noreply.github.com>

@@ -533,6 +533,9 @@ noncomputable def map (ν : ProbabilityMeasure Ω) {f : Ω → Ω'} (f_aemble :
    ⟨by simp only [Measure.map_apply_of_aemeasurable f_aemble MeasurableSet.univ,
                   preimage_univ, measure_univ]⟩⟩
 
+@[simp] lemma toMeasure_map (ν : ProbabilityMeasure Ω) {f : Ω → Ω'} (hf : AEMeasurable f ν) :
+    (ν.map hf).toMeasure = ν.toMeasure.map f := rfl
+
 /-- Note that this is an equality of elements of `ℝ≥0∞`. See also
 `MeasureTheory.ProbabilityMeasure.map_apply` for the corresponding equality as elements of `ℝ≥0`. -/
 lemma map_apply' (ν : ProbabilityMeasure Ω) {f : Ω → Ω'} (f_aemble : AEMeasurable f ν)
@@ -546,7 +549,7 @@ lemma map_apply_of_aemeasurable (ν : ProbabilityMeasure Ω) {f : Ω → Ω'}
   have := ν.map_apply' f_aemble A_mble
   exact (ENNReal.toNNReal_eq_toNNReal_iff' (measure_ne_top _ _) (measure_ne_top _ _)).mpr this
 
-@[simp] lemma map_apply (ν : ProbabilityMeasure Ω) {f : Ω → Ω'} (f_aemble : AEMeasurable f ν)
+lemma map_apply (ν : ProbabilityMeasure Ω) {f : Ω → Ω'} (f_aemble : AEMeasurable f ν)
     {A : Set Ω'} (A_mble : MeasurableSet A) :
     (ν.map f_aemble) A = ν (f ⁻¹' A) :=
   map_apply_of_aemeasurable ν f_aemble A_mble

This PR adds a type class HasOuterApproxClosed for topological spaces in which indicator functions of closed sets can be approximated from above by sequences of bounded continuous functions. All pseudo-(e)metrizable spaces satisfy this.

In spaces with this property, finite Borel measures are characterized by the integrals of bounded continuous functions. Also weak limits of finite Borel measures are unique. More precisely, the topologies of weak convergence of finite Borel measures and of Borel probability measures are Hausdorff.

Co-authored-by: Peter Pfaffelhuber <p.p@stochastik.uni-freiburg.de>

Co-authored-by: kkytola <39528102+kkytola@users.noreply.github.com> Co-authored-by: kkytola <“kalle.kytola@aalto.fi”>

@@ -46,6 +46,9 @@ The main definitions are
  * `MeasureTheory.ProbabilityMeasure.continuous_map`: For a continuous function `f : Ω → Ω'`, the
    push-forward of probability measures `f* : ProbabilityMeasure Ω → ProbabilityMeasure Ω'` is
    continuous.
+ * `MeasureTheory.ProbabilityMeasure.t2Space`: The topology of convergence in distribution is
+   Hausdorff on Borel spaces where indicators of closed sets have continuous decreasing
+   approximating sequences (in particular on any pseudo-metrizable spaces).
 
 TODO:
  * Probability measures form a convex space.
@@ -214,6 +217,8 @@ theorem toFiniteMeasure_nonzero (μ : ProbabilityMeasure Ω) : μ.toFiniteMeasur
   exact one_ne_zero
 #align measure_theory.probability_measure.to_finite_measure_nonzero MeasureTheory.ProbabilityMeasure.toFiniteMeasure_nonzero
 
+section convergence_in_distribution
+
 variable [TopologicalSpace Ω] [OpensMeasurableSpace Ω]
 
 theorem testAgainstNN_lipschitz (μ : ProbabilityMeasure Ω) :
@@ -300,6 +305,22 @@ theorem tendsto_iff_forall_integral_tendsto {γ : Type*} {F : Filter γ}
   rfl
 #align measure_theory.probability_measure.tendsto_iff_forall_integral_tendsto MeasureTheory.ProbabilityMeasure.tendsto_iff_forall_integral_tendsto
 
+end convergence_in_distribution -- section
+
+section Hausdorff
+
+variable [TopologicalSpace Ω] [HasOuterApproxClosed Ω] [BorelSpace Ω]
+
+variable (Ω)
+
+/-- On topological spaces where indicators of closed sets have decreasing approximating sequences of
+continuous functions (`HasOuterApproxClosed`), the topology of convergence in distribution of Borel
+probability measures is Hausdorff (`T2Space`). -/
+instance t2Space : T2Space (ProbabilityMeasure Ω) :=
+  Embedding.t2Space (toFiniteMeasure_embedding Ω)
+
+end Hausdorff -- section
+
 end ProbabilityMeasure
 
 -- namespace

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

@@ -333,7 +333,7 @@ def normalize : ProbabilityMeasure Ω :=
         rw [FiniteMeasure.toMeasure_smul]
         simp only [Measure.smul_toOuterMeasure, OuterMeasure.coe_smul, Pi.smul_apply,
           Measure.nnreal_smul_coe_apply, ne_eq, mass_zero_iff, ENNReal.coe_inv zero, ennreal_mass]
-        rw [←Ne.def, ←ENNReal.coe_ne_zero, ennreal_mass] at zero
+        rw [← Ne.def, ← ENNReal.coe_ne_zero, ennreal_mass] at zero
         exact ENNReal.inv_mul_cancel zero μ.prop.measure_univ_lt_top.ne }
 #align measure_theory.finite_measure.normalize MeasureTheory.FiniteMeasure.normalize
 

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>

@@ -326,7 +326,7 @@ total mass. -/
 def normalize : ProbabilityMeasure Ω :=
   if zero : μ.mass = 0 then ⟨Measure.dirac ‹Nonempty Ω›.some, Measure.dirac.isProbabilityMeasure⟩
   else
-    { val := μ.mass⁻¹ • μ
+    { val := ↑(μ.mass⁻¹ • μ)
       property := by
         refine' ⟨_⟩
         -- porting note: paying the price that this isn't `simp` lemma now.

We have turned to Type* instead of Type _, but many of them remained in mathlib because the straight replacement did not work. In general, having Type _ before the colon is a code smell, though, as it hides which types should be in the same universe and which shouldn't, and is not very robust.

This PR replaces most of the remaining Type _ before the colon (except those in category theory) by Type* or Type u. This has uncovered a few bugs (where declarations were not as polymorphic as they should be).

I had to increase heartbeats at two places when replacing Type _ by Type*, but I think it's worth it as it's really more robust.

@@ -501,7 +501,7 @@ end NormalizeFiniteMeasure -- section
 
 section map
 
-variable {Ω Ω' : Type _} [MeasurableSpace Ω] [MeasurableSpace Ω']
+variable {Ω Ω' : Type*} [MeasurableSpace Ω] [MeasurableSpace Ω']
 
 namespace ProbabilityMeasure
 

This removes redundant field values of the form add := add for smaller terms and less unfolding during unification.

A list of all files containing a structure instance of the form { a1, ... with x1 := val, ... } where some xi is a field of some aj was generated by modifying the structure instance elaboration algorithm to print such overlaps to stdout in a custom toolchain.

Using that toolchain, I went through each file on the list and attempted to remove algebraic fields that overlapped and were redundant, eg add := add and not toFun (though some other ones did creep in). If things broke (which was the case in a couple of cases), I did not push further and reverted.

It is possible that pushing harder and trying to remove all redundant overlaps will yield further improvements.

@@ -396,8 +396,7 @@ theorem average_eq_integral_normalize {E : Type*} [NormedAddCommGroup E] [Normed
     average (μ : Measure Ω) f = ∫ ω, f ω ∂(μ.normalize : Measure Ω) := by
   rw [μ.toMeasure_normalize_eq_of_nonzero nonzero, average]
   congr
-  simp only [RingHom.toFun_eq_coe, ENNReal.coe_ofNNRealHom,
-    ENNReal.coe_inv (μ.mass_nonzero_iff.mpr nonzero), ennreal_mass]
+  simp [ENNReal.coe_inv (μ.mass_nonzero_iff.mpr nonzero), ennreal_mass]
 #align measure_theory.finite_measure.average_eq_integral_normalize MeasureTheory.FiniteMeasure.average_eq_integral_normalize
 
 variable [TopologicalSpace Ω]

Add push-forwards of finite measures and probability measures, and prove that push-forwards under continuous functions are continuous (w.r.t. the topologies of weak convergence of measures).

Besides being a natural addition to the API, this should enable simple proofs of, for example, continuity of some parametric distributions (multi-dimensional gaussians, exponential distribution, ...) with respect to their parameters.

Co-authored-by: kkytola <39528102+kkytola@users.noreply.github.com>

@@ -28,6 +28,8 @@ The main definitions are
    a finite measure;
  * `MeasureTheory.FiniteMeasure.normalize`: Normalize a finite measure to a probability measure
    (returns junk for the zero measure).
+ * `MeasureTheory.ProbabilityMeasure.map`: The push-forward `f* μ` of a probability measure
+   `μ` on `Ω` along a measurable function `f : Ω → Ω'`.
 
 ## Main results
 
@@ -41,6 +43,9 @@ The main definitions are
  * `MeasureTheory.FiniteMeasure.tendsto_normalize_iff_tendsto`: The convergence of finite
    measures to a nonzero limit is characterized by the convergence of the probability-normalized
    versions and of the total masses.
+ * `MeasureTheory.ProbabilityMeasure.continuous_map`: For a continuous function `f : Ω → Ω'`, the
+   push-forward of probability measures `f* : ProbabilityMeasure Ω → ProbabilityMeasure Ω'` is
+   continuous.
 
 TODO:
  * Probability measures form a convex space.
@@ -491,10 +496,69 @@ theorem tendsto_normalize_iff_tendsto {γ : Type*} {F : Filter γ} {μs : γ →
     refine' ⟨tendsto_normalize_of_tendsto μs_lim nonzero, μs_lim.mass⟩
 #align measure_theory.finite_measure.tendsto_normalize_iff_tendsto MeasureTheory.FiniteMeasure.tendsto_normalize_iff_tendsto
 
-end FiniteMeasure
+end FiniteMeasure --namespace
 
---namespace
-end NormalizeFiniteMeasure
+end NormalizeFiniteMeasure -- section
 
--- section
-end MeasureTheory
+section map
+
+variable {Ω Ω' : Type _} [MeasurableSpace Ω] [MeasurableSpace Ω']
+
+namespace ProbabilityMeasure
+
+/-- The push-forward of a probability measure by a measurable function. -/
+noncomputable def map (ν : ProbabilityMeasure Ω) {f : Ω → Ω'} (f_aemble : AEMeasurable f ν) :
+    ProbabilityMeasure Ω' :=
+  ⟨(ν : Measure Ω).map f,
+   ⟨by simp only [Measure.map_apply_of_aemeasurable f_aemble MeasurableSet.univ,
+                  preimage_univ, measure_univ]⟩⟩
+
+/-- Note that this is an equality of elements of `ℝ≥0∞`. See also
+`MeasureTheory.ProbabilityMeasure.map_apply` for the corresponding equality as elements of `ℝ≥0`. -/
+lemma map_apply' (ν : ProbabilityMeasure Ω) {f : Ω → Ω'} (f_aemble : AEMeasurable f ν)
+    {A : Set Ω'} (A_mble : MeasurableSet A) :
+    (ν.map f_aemble : Measure Ω') A = (ν : Measure Ω) (f ⁻¹' A) :=
+  Measure.map_apply_of_aemeasurable f_aemble A_mble
+
+lemma map_apply_of_aemeasurable (ν : ProbabilityMeasure Ω) {f : Ω → Ω'}
+    (f_aemble : AEMeasurable f ν) {A : Set Ω'} (A_mble : MeasurableSet A) :
+    (ν.map f_aemble) A = ν (f ⁻¹' A) := by
+  have := ν.map_apply' f_aemble A_mble
+  exact (ENNReal.toNNReal_eq_toNNReal_iff' (measure_ne_top _ _) (measure_ne_top _ _)).mpr this
+
+@[simp] lemma map_apply (ν : ProbabilityMeasure Ω) {f : Ω → Ω'} (f_aemble : AEMeasurable f ν)
+    {A : Set Ω'} (A_mble : MeasurableSet A) :
+    (ν.map f_aemble) A = ν (f ⁻¹' A) :=
+  map_apply_of_aemeasurable ν f_aemble A_mble
+
+variable [TopologicalSpace Ω] [OpensMeasurableSpace Ω]
+variable [TopologicalSpace Ω'] [BorelSpace Ω']
+
+/-- If `f : X → Y` is continuous and `Y` is equipped with the Borel sigma algebra, then
+convergence (in distribution) of `ProbabilityMeasure`s on `X` implies convergence (in
+distribution) of the push-forwards of these measures by `f`. -/
+lemma tendsto_map_of_tendsto_of_continuous {ι : Type*} {L : Filter ι}
+    (νs : ι → ProbabilityMeasure Ω) (ν : ProbabilityMeasure Ω) (lim : Tendsto νs L (𝓝 ν))
+    {f : Ω → Ω'} (f_cont : Continuous f) :
+    Tendsto (fun i ↦ (νs i).map f_cont.measurable.aemeasurable) L
+      (𝓝 (ν.map f_cont.measurable.aemeasurable)) := by
+  rw [ProbabilityMeasure.tendsto_iff_forall_lintegral_tendsto] at lim ⊢
+  intro g
+  convert lim (g.compContinuous ⟨f, f_cont⟩) <;>
+  · simp only [map, compContinuous_apply, ContinuousMap.coe_mk]
+    refine lintegral_map ?_ f_cont.measurable
+    exact (ENNReal.continuous_coe.comp g.continuous).measurable
+
+/-- If `f : X → Y` is continuous and `Y` is equipped with the Borel sigma algebra, then
+the push-forward of probability measures `f* : ProbabilityMeasure X → ProbabilityMeasure Y`
+is continuous (in the topologies of convergence in distribution). -/
+lemma continuous_map {f : Ω → Ω'} (f_cont : Continuous f) :
+    Continuous (fun ν ↦ ProbabilityMeasure.map ν f_cont.measurable.aemeasurable) := by
+  rw [continuous_iff_continuousAt]
+  exact fun _ ↦ tendsto_map_of_tendsto_of_continuous _ _ continuous_id.continuousAt f_cont
+
+end ProbabilityMeasure -- namespace
+
+end map -- section
+
+end MeasureTheory -- namespace

Add one implication of portmanteau theorem: a Borel set limit condition implies a closed set limsup condition.

Co-authored-by: kkytola <“kalle.kytola@aalto.fi”> Co-authored-by: kkytola <39528102+kkytola@users.noreply.github.com>

@@ -174,6 +174,9 @@ theorem apply_mono (μ : ProbabilityMeasure Ω) {s₁ s₂ : Set Ω} (h : s₁ 
   exact MeasureTheory.FiniteMeasure.apply_mono _ h
 #align measure_theory.probability_measure.apply_mono MeasureTheory.ProbabilityMeasure.apply_mono
 
+@[simp] theorem apply_le_one (μ : ProbabilityMeasure Ω) (s : Set Ω) : μ s ≤ 1 := by
+  simpa using apply_mono μ (subset_univ s)
+
 theorem nonempty (μ : ProbabilityMeasure Ω) : Nonempty Ω := by
   by_contra maybe_empty
   have zero : (μ : Measure Ω) univ = 0 := by

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).

@@ -332,7 +332,7 @@ def normalize : ProbabilityMeasure Ω :=
 @[simp]
 theorem self_eq_mass_mul_normalize (s : Set Ω) : μ s = μ.mass * μ.normalize s := by
   obtain rfl | h := eq_or_ne μ 0
-  · simp only [zero_mass, coeFn_zero, Pi.zero_apply, MulZeroClass.zero_mul]
+  · simp only [zero_mass, coeFn_zero, Pi.zero_apply, zero_mul]
     rfl
   have mass_nonzero : μ.mass ≠ 0 := by rwa [μ.mass_nonzero_iff]
   simp only [normalize, dif_neg mass_nonzero]

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

This has nice performance benefits.

@@ -97,13 +97,13 @@ finite measure, this is implemented as the induced topology from the mapping
 
 /-- Probability measures are defined as the subtype of measures that have the property of being
 probability measures (i.e., their total mass is one). -/
-def ProbabilityMeasure (Ω : Type _) [MeasurableSpace Ω] : Type _ :=
+def ProbabilityMeasure (Ω : Type*) [MeasurableSpace Ω] : Type _ :=
   { μ : Measure Ω // IsProbabilityMeasure μ }
 #align measure_theory.probability_measure MeasureTheory.ProbabilityMeasure
 
 namespace ProbabilityMeasure
 
-variable {Ω : Type _} [MeasurableSpace Ω]
+variable {Ω : Type*} [MeasurableSpace Ω]
 
 instance [Inhabited Ω] : Inhabited (ProbabilityMeasure Ω) :=
   ⟨⟨Measure.dirac default, Measure.dirac.isProbabilityMeasure⟩⟩
@@ -254,14 +254,14 @@ theorem continuous_testAgainstNN_eval (f : Ω →ᵇ ℝ≥0) :
 #align measure_theory.probability_measure.continuous_test_against_nn_eval MeasureTheory.ProbabilityMeasure.continuous_testAgainstNN_eval
 
 -- The canonical mapping from probability measures to finite measures is an embedding.
-theorem toFiniteMeasure_embedding (Ω : Type _) [MeasurableSpace Ω] [TopologicalSpace Ω]
+theorem toFiniteMeasure_embedding (Ω : Type*) [MeasurableSpace Ω] [TopologicalSpace Ω]
     [OpensMeasurableSpace Ω] :
     Embedding (toFiniteMeasure : ProbabilityMeasure Ω → FiniteMeasure Ω) :=
   { induced := rfl
     inj := fun _μ _ν h => Subtype.eq <| congr_arg FiniteMeasure.toMeasure h }
 #align measure_theory.probability_measure.to_finite_measure_embedding MeasureTheory.ProbabilityMeasure.toFiniteMeasure_embedding
 
-theorem tendsto_nhds_iff_toFiniteMeasure_tendsto_nhds {δ : Type _} (F : Filter δ)
+theorem tendsto_nhds_iff_toFiniteMeasure_tendsto_nhds {δ : Type*} (F : Filter δ)
     {μs : δ → ProbabilityMeasure Ω} {μ₀ : ProbabilityMeasure Ω} :
     Tendsto μs F (𝓝 μ₀) ↔ Tendsto (toFiniteMeasure ∘ μs) F (𝓝 μ₀.toFiniteMeasure) :=
   Embedding.tendsto_nhds_iff (toFiniteMeasure_embedding Ω)
@@ -270,7 +270,7 @@ theorem tendsto_nhds_iff_toFiniteMeasure_tendsto_nhds {δ : Type _} (F : Filter
 /-- A characterization of weak convergence of probability measures by the condition that the
 integrals of every continuous bounded nonnegative function converge to the integral of the function
 against the limit measure. -/
-theorem tendsto_iff_forall_lintegral_tendsto {γ : Type _} {F : Filter γ}
+theorem tendsto_iff_forall_lintegral_tendsto {γ : Type*} {F : Filter γ}
     {μs : γ → ProbabilityMeasure Ω} {μ : ProbabilityMeasure Ω} :
     Tendsto μs F (𝓝 μ) ↔
       ∀ f : Ω →ᵇ ℝ≥0,
@@ -282,7 +282,7 @@ theorem tendsto_iff_forall_lintegral_tendsto {γ : Type _} {F : Filter γ}
 /-- The characterization of weak convergence of probability measures by the usual (defining)
 condition that the integrals of every continuous bounded function converge to the integral of the
 function against the limit measure. -/
-theorem tendsto_iff_forall_integral_tendsto {γ : Type _} {F : Filter γ}
+theorem tendsto_iff_forall_integral_tendsto {γ : Type*} {F : Filter γ}
     {μs : γ → ProbabilityMeasure Ω} {μ : ProbabilityMeasure Ω} :
     Tendsto μs F (𝓝 μ) ↔
       ∀ f : Ω →ᵇ ℝ,
@@ -311,7 +311,7 @@ measures.
 
 namespace FiniteMeasure
 
-variable {Ω : Type _} [Nonempty Ω] {m0 : MeasurableSpace Ω} (μ : FiniteMeasure Ω)
+variable {Ω : Type*} [Nonempty Ω] {m0 : MeasurableSpace Ω} (μ : FiniteMeasure Ω)
 
 /-- Normalize a finite measure so that it becomes a probability measure, i.e., divide by the
 total mass. -/
@@ -383,7 +383,7 @@ theorem _root_.ProbabilityMeasure.toFiniteMeasure_normalize_eq_self {m0 : Measur
 
 /-- Averaging with respect to a finite measure is the same as integrating against
 `MeasureTheory.FiniteMeasure.normalize`. -/
-theorem average_eq_integral_normalize {E : Type _} [NormedAddCommGroup E] [NormedSpace ℝ E]
+theorem average_eq_integral_normalize {E : Type*} [NormedAddCommGroup E] [NormedSpace ℝ E]
     (nonzero : μ ≠ 0) (f : Ω → E) :
     average (μ : Measure Ω) f = ∫ ω, f ω ∂(μ.normalize : Measure Ω) := by
   rw [μ.toMeasure_normalize_eq_of_nonzero nonzero, average]
@@ -409,7 +409,7 @@ variable [OpensMeasurableSpace Ω]
 
 variable {μ}
 
-theorem tendsto_testAgainstNN_of_tendsto_normalize_testAgainstNN_of_tendsto_mass {γ : Type _}
+theorem tendsto_testAgainstNN_of_tendsto_normalize_testAgainstNN_of_tendsto_mass {γ : Type*}
     {F : Filter γ} {μs : γ → FiniteMeasure Ω}
     (μs_lim : Tendsto (fun i => (μs i).normalize) F (𝓝 μ.normalize))
     (mass_lim : Tendsto (fun i => (μs i).mass) F (𝓝 μ.mass)) (f : Ω →ᵇ ℝ≥0) :
@@ -428,7 +428,7 @@ theorem tendsto_testAgainstNN_of_tendsto_normalize_testAgainstNN_of_tendsto_mass
   exact tendsto_mul.comp lim_pair
 #align measure_theory.finite_measure.tendsto_test_against_nn_of_tendsto_normalize_test_against_nn_of_tendsto_mass MeasureTheory.FiniteMeasure.tendsto_testAgainstNN_of_tendsto_normalize_testAgainstNN_of_tendsto_mass
 
-theorem tendsto_normalize_testAgainstNN_of_tendsto {γ : Type _} {F : Filter γ}
+theorem tendsto_normalize_testAgainstNN_of_tendsto {γ : Type*} {F : Filter γ}
     {μs : γ → FiniteMeasure Ω} (μs_lim : Tendsto μs F (𝓝 μ)) (nonzero : μ ≠ 0) (f : Ω →ᵇ ℝ≥0) :
     Tendsto (fun i => (μs i).normalize.toFiniteMeasure.testAgainstNN f) F
       (𝓝 (μ.normalize.toFiniteMeasure.testAgainstNN f)) := by
@@ -456,7 +456,7 @@ theorem tendsto_normalize_testAgainstNN_of_tendsto {γ : Type _} {F : Filter γ}
 
 /-- If the normalized versions of finite measures converge weakly and their total masses
 also converge, then the finite measures themselves converge weakly. -/
-theorem tendsto_of_tendsto_normalize_testAgainstNN_of_tendsto_mass {γ : Type _} {F : Filter γ}
+theorem tendsto_of_tendsto_normalize_testAgainstNN_of_tendsto_mass {γ : Type*} {F : Filter γ}
     {μs : γ → FiniteMeasure Ω} (μs_lim : Tendsto (fun i => (μs i).normalize) F (𝓝 μ.normalize))
     (mass_lim : Tendsto (fun i => (μs i).mass) F (𝓝 μ.mass)) : Tendsto μs F (𝓝 μ) := by
   rw [tendsto_iff_forall_testAgainstNN_tendsto]
@@ -466,7 +466,7 @@ theorem tendsto_of_tendsto_normalize_testAgainstNN_of_tendsto_mass {γ : Type _}
 
 /-- If finite measures themselves converge weakly to a nonzero limit measure, then their
 normalized versions also converge weakly. -/
-theorem tendsto_normalize_of_tendsto {γ : Type _} {F : Filter γ} {μs : γ → FiniteMeasure Ω}
+theorem tendsto_normalize_of_tendsto {γ : Type*} {F : Filter γ} {μs : γ → FiniteMeasure Ω}
     (μs_lim : Tendsto μs F (𝓝 μ)) (nonzero : μ ≠ 0) :
     Tendsto (fun i => (μs i).normalize) F (𝓝 μ.normalize) := by
   rw [ProbabilityMeasure.tendsto_nhds_iff_toFiniteMeasure_tendsto_nhds,
@@ -476,7 +476,7 @@ theorem tendsto_normalize_of_tendsto {γ : Type _} {F : Filter γ} {μs : γ →
 
 /-- The weak convergence of finite measures to a nonzero limit can be characterized by the weak
 convergence of both their normalized versions (probability measures) and their total masses. -/
-theorem tendsto_normalize_iff_tendsto {γ : Type _} {F : Filter γ} {μs : γ → FiniteMeasure Ω}
+theorem tendsto_normalize_iff_tendsto {γ : Type*} {F : Filter γ} {μs : γ → FiniteMeasure Ω}
     (nonzero : μ ≠ 0) :
     Tendsto (fun i => (μs i).normalize) F (𝓝 μ.normalize) ∧
         Tendsto (fun i => (μs i).mass) F (𝓝 μ.mass) ↔

• 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 Kalle Kytölä. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kalle Kytölä
-
-! This file was ported from Lean 3 source module measure_theory.measure.probability_measure
-! leanprover-community/mathlib commit f0c8bf9245297a541f468be517f1bde6195105e9
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.MeasureTheory.Measure.FiniteMeasure
 import Mathlib.MeasureTheory.Integral.Average
 
+#align_import measure_theory.measure.probability_measure from "leanprover-community/mathlib"@"f0c8bf9245297a541f468be517f1bde6195105e9"
+
 /-!
 # Probability measures
 

The notion of Bochner integral of a function taking values in a normed space E requires that E is complete. This means that whenever we write down an integral, the term contains the assertion that E is complete.

In this PR, we remove the completeness requirement from the definition, using the junk value 0 when the space is not complete. Mathematically this does not make any difference, as all reasonable applications will be with a complete E. But it means that terms involving integrals become a little bit simpler and that completeness will not have to be checked by the system when applying a bunch of basic lemmas on integrals.

@@ -387,7 +387,7 @@ theorem _root_.ProbabilityMeasure.toFiniteMeasure_normalize_eq_self {m0 : Measur
 /-- Averaging with respect to a finite measure is the same as integrating against
 `MeasureTheory.FiniteMeasure.normalize`. -/
 theorem average_eq_integral_normalize {E : Type _} [NormedAddCommGroup E] [NormedSpace ℝ E]
-    [CompleteSpace E] (nonzero : μ ≠ 0) (f : Ω → E) :
+    (nonzero : μ ≠ 0) (f : Ω → E) :
     average (μ : Measure Ω) f = ∫ ω, f ω ∂(μ.normalize : Measure Ω) := by
   rw [μ.toMeasure_normalize_eq_of_nonzero nonzero, average]
   congr

These are all doc fixes

@@ -384,7 +384,7 @@ theorem _root_.ProbabilityMeasure.toFiniteMeasure_normalize_eq_self {m0 : Measur
   congr
 #align probability_measure.to_finite_measure_normalize_eq_self ProbabilityMeasure.toFiniteMeasure_normalize_eq_self
 
-/-- Averaging with respect to a finite measure is the same as integraing against
+/-- Averaging with respect to a finite measure is the same as integrating against
 `MeasureTheory.FiniteMeasure.normalize`. -/
 theorem average_eq_integral_normalize {E : Type _} [NormedAddCommGroup E] [NormedSpace ℝ E]
     [CompleteSpace E] (nonzero : μ ≠ 0) (f : Ω → E) :