measure_theory.measure.with_density_vector_measure

Changes since the initial port

The following section lists changes to this file in mathlib3 and mathlib4 that occured after the initial port. Most recent changes are shown first. Hovering over a commit will show all commits associated with the same mathlib3 commit.

Changes in mathlib3

d1bd9c5d

(last sync)

Changes in mathlib3port

mathlib3

mathlib3port

c2092722

bump to nightly-2024-04-06-08

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

e34029c9

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kexing Ying
 -/
 import MeasureTheory.Measure.VectorMeasure
-import MeasureTheory.Function.AeEqOfIntegral
+import MeasureTheory.Function.AEEqOfIntegral
 
 #align_import measure_theory.measure.with_density_vector_measure from "leanprover-community/mathlib"@"c20927220ef87bb4962ba08bf6da2ce3cf50a6dd"

c2092722

bump to nightly-2024-03-17-08

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

22f01ce4

Diff

@@ -163,7 +163,7 @@ theorem Measure.withDensityᵥ_absolutelyContinuous (μ : Measure α) (f : α 
   by
   by_cases hf : integrable f μ
   · refine' vector_measure.absolutely_continuous.mk fun i hi₁ hi₂ => _
-    rw [to_ennreal_vector_measure_apply_measurable hi₁] at hi₂ 
+    rw [to_ennreal_vector_measure_apply_measurable hi₁] at hi₂
     rw [with_densityᵥ_apply hf hi₁, measure.restrict_zero_set hi₂, integral_zero_measure]
   · rw [with_densityᵥ, dif_neg hf]
     exact vector_measure.absolutely_continuous.zero _
@@ -248,7 +248,7 @@ theorem Integrable.withDensityᵥ_trim_absolutelyContinuous {m m0 : MeasurableSp
     (μ.withDensityᵥ f).trim hm ≪ᵥ (μ.trim hm).toENNRealVectorMeasure :=
   by
   refine' vector_measure.absolutely_continuous.mk fun j hj₁ hj₂ => _
-  rw [measure.to_ennreal_vector_measure_apply_measurable hj₁, trim_measurable_set_eq hm hj₁] at hj₂ 
+  rw [measure.to_ennreal_vector_measure_apply_measurable hj₁, trim_measurable_set_eq hm hj₁] at hj₂
   rw [vector_measure.trim_measurable_set_eq hm hj₁, with_densityᵥ_apply hfi (hm _ hj₁)]
   simp only [measure.restrict_eq_zero.mpr hj₂, integral_zero_measure]
 #align measure_theory.integrable.with_densityᵥ_trim_absolutely_continuous MeasureTheory.Integrable.withDensityᵥ_trim_absolutelyContinuous

c2092722

bump to nightly-2023-09-24-06

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

5655435f

Diff

@@ -3,8 +3,8 @@ Copyright (c) 2021 Kexing Ying. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kexing Ying
 -/
-import Mathbin.MeasureTheory.Measure.VectorMeasure
-import Mathbin.MeasureTheory.Function.AeEqOfIntegral
+import MeasureTheory.Measure.VectorMeasure
+import MeasureTheory.Function.AeEqOfIntegral
 
 #align_import measure_theory.measure.with_density_vector_measure from "leanprover-community/mathlib"@"c20927220ef87bb4962ba08bf6da2ce3cf50a6dd"

c2092722

bump to nightly-2023-07-20-09

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

9c56d0dd

Diff

@@ -2,15 +2,12 @@
 Copyright (c) 2021 Kexing Ying. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kexing Ying
-
-! This file was ported from Lean 3 source module measure_theory.measure.with_density_vector_measure
-! leanprover-community/mathlib commit c20927220ef87bb4962ba08bf6da2ce3cf50a6dd
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.MeasureTheory.Measure.VectorMeasure
 import Mathbin.MeasureTheory.Function.AeEqOfIntegral
 
+#align_import measure_theory.measure.with_density_vector_measure from "leanprover-community/mathlib"@"c20927220ef87bb4962ba08bf6da2ce3cf50a6dd"
+
 /-!
 
 # Vector measure defined by an integral

c2092722

bump to nightly-2023-06-20-01

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

9b351f8c

Diff

@@ -188,7 +188,7 @@ theorem WithDensityᵥEq.congr_ae {f g : α → E} (h : f =ᵐ[μ] g) :
     μ.withDensityᵥ f = μ.withDensityᵥ g :=
   by
   by_cases hf : integrable f μ
-  · ext (i hi)
+  · ext i hi
     rw [with_densityᵥ_apply hf hi, with_densityᵥ_apply (hf.congr h) hi]
     exact integral_congr_ae (ae_restrict_of_ae h)
   · have hg : ¬integrable g μ := by intro hg; exact hf (hg.congr h.symm)
@@ -211,7 +211,7 @@ theorem withDensityᵥ_toReal {f : α → ℝ≥0∞} (hfm : AEMeasurable f μ)
       @toSignedMeasure α _ (μ.withDensity f) (isFiniteMeasure_withDensity hf) :=
   by
   have hfi := integrable_to_real_of_lintegral_ne_top hfm hf
-  ext (i hi)
+  ext i hi
   rw [with_densityᵥ_apply hfi hi, to_signed_measure_apply_measurable hi, with_density_apply _ hi,
     integral_to_real hfm.restrict]
   refine' ae_lt_top' hfm.restrict (ne_top_of_le_ne_top hf _)
@@ -229,7 +229,7 @@ theorem withDensityᵥ_eq_withDensity_pos_part_sub_withDensity_neg_part {f : α
         @toSignedMeasure α _ (μ.withDensity fun x => ENNReal.ofReal <| -f x)
           (isFiniteMeasure_withDensity_ofReal hfi.neg.2) :=
   by
-  ext (i hi)
+  ext i hi
   rw [with_densityᵥ_apply hfi hi,
     integral_eq_lintegral_pos_part_sub_lintegral_neg_part hfi.integrable_on,
     vector_measure.sub_apply, to_signed_measure_apply_measurable hi,

c2092722

bump to nightly-2023-06-13-21

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

829520ac

Diff

@@ -63,8 +63,6 @@ def Measure.withDensityᵥ {m : MeasurableSpace α} (μ : Measure α) (f : α 
 
 open Measure
 
-include m
-
 variable {f g : α → E}
 
 #print MeasureTheory.withDensityᵥ_apply /-
@@ -73,11 +71,14 @@ theorem withDensityᵥ_apply (hf : Integrable f μ) {s : Set α} (hs : Measurabl
 #align measure_theory.with_densityᵥ_apply MeasureTheory.withDensityᵥ_apply
 -/
 
+#print MeasureTheory.withDensityᵥ_zero /-
 @[simp]
 theorem withDensityᵥ_zero : μ.withDensityᵥ (0 : α → E) = 0 := by ext1 s hs;
   erw [with_densityᵥ_apply (integrable_zero α E μ) hs]; simp
 #align measure_theory.with_densityᵥ_zero MeasureTheory.withDensityᵥ_zero
+-/
 
+#print MeasureTheory.withDensityᵥ_neg /-
 @[simp]
 theorem withDensityᵥ_neg : μ.withDensityᵥ (-f) = -μ.withDensityᵥ f :=
   by
@@ -89,11 +90,15 @@ theorem withDensityᵥ_neg : μ.withDensityᵥ (-f) = -μ.withDensityᵥ f :=
   · rw [with_densityᵥ, with_densityᵥ, dif_neg hf, dif_neg, neg_zero]
     rwa [integrable_neg_iff]
 #align measure_theory.with_densityᵥ_neg MeasureTheory.withDensityᵥ_neg
+-/
 
+#print MeasureTheory.withDensityᵥ_neg' /-
 theorem withDensityᵥ_neg' : (μ.withDensityᵥ fun x => -f x) = -μ.withDensityᵥ f :=
   withDensityᵥ_neg
 #align measure_theory.with_densityᵥ_neg' MeasureTheory.withDensityᵥ_neg'
+-/
 
+#print MeasureTheory.withDensityᵥ_add /-
 @[simp]
 theorem withDensityᵥ_add (hf : Integrable f μ) (hg : Integrable g μ) :
     μ.withDensityᵥ (f + g) = μ.withDensityᵥ f + μ.withDensityᵥ g :=
@@ -106,22 +111,29 @@ theorem withDensityᵥ_add (hf : Integrable f μ) (hg : Integrable g μ) :
   · exact hf.integrable_on.restrict MeasurableSet.univ
   · exact hg.integrable_on.restrict MeasurableSet.univ
 #align measure_theory.with_densityᵥ_add MeasureTheory.withDensityᵥ_add
+-/
 
+#print MeasureTheory.withDensityᵥ_add' /-
 theorem withDensityᵥ_add' (hf : Integrable f μ) (hg : Integrable g μ) :
     (μ.withDensityᵥ fun x => f x + g x) = μ.withDensityᵥ f + μ.withDensityᵥ g :=
   withDensityᵥ_add hf hg
 #align measure_theory.with_densityᵥ_add' MeasureTheory.withDensityᵥ_add'
+-/
 
+#print MeasureTheory.withDensityᵥ_sub /-
 @[simp]
 theorem withDensityᵥ_sub (hf : Integrable f μ) (hg : Integrable g μ) :
     μ.withDensityᵥ (f - g) = μ.withDensityᵥ f - μ.withDensityᵥ g := by
   rw [sub_eq_add_neg, sub_eq_add_neg, with_densityᵥ_add hf hg.neg, with_densityᵥ_neg]
 #align measure_theory.with_densityᵥ_sub MeasureTheory.withDensityᵥ_sub
+-/
 
+#print MeasureTheory.withDensityᵥ_sub' /-
 theorem withDensityᵥ_sub' (hf : Integrable f μ) (hg : Integrable g μ) :
     (μ.withDensityᵥ fun x => f x - g x) = μ.withDensityᵥ f - μ.withDensityᵥ g :=
   withDensityᵥ_sub hf hg
 #align measure_theory.with_densityᵥ_sub' MeasureTheory.withDensityᵥ_sub'
+-/
 
 #print MeasureTheory.withDensityᵥ_smul /-
 @[simp]
@@ -148,6 +160,7 @@ theorem withDensityᵥ_smul' {𝕜 : Type _} [NontriviallyNormedField 𝕜] [Nor
 #align measure_theory.with_densityᵥ_smul' MeasureTheory.withDensityᵥ_smul'
 -/
 
+#print MeasureTheory.Measure.withDensityᵥ_absolutelyContinuous /-
 theorem Measure.withDensityᵥ_absolutelyContinuous (μ : Measure α) (f : α → ℝ) :
     μ.withDensityᵥ f ≪ᵥ μ.toENNRealVectorMeasure :=
   by
@@ -158,6 +171,7 @@ theorem Measure.withDensityᵥ_absolutelyContinuous (μ : Measure α) (f : α 
   · rw [with_densityᵥ, dif_neg hf]
     exact vector_measure.absolutely_continuous.zero _
 #align measure_theory.measure.with_densityᵥ_absolutely_continuous MeasureTheory.Measure.withDensityᵥ_absolutelyContinuous
+-/
 
 #print MeasureTheory.Integrable.ae_eq_of_withDensityᵥ_eq /-
 /-- Having the same density implies the underlying functions are equal almost everywhere. -/
@@ -169,6 +183,7 @@ theorem Integrable.ae_eq_of_withDensityᵥ_eq {f g : α → E} (hf : Integrable
 #align measure_theory.integrable.ae_eq_of_with_densityᵥ_eq MeasureTheory.Integrable.ae_eq_of_withDensityᵥ_eq
 -/
 
+#print MeasureTheory.WithDensityᵥEq.congr_ae /-
 theorem WithDensityᵥEq.congr_ae {f g : α → E} (h : f =ᵐ[μ] g) :
     μ.withDensityᵥ f = μ.withDensityᵥ g :=
   by
@@ -179,6 +194,7 @@ theorem WithDensityᵥEq.congr_ae {f g : α → E} (h : f =ᵐ[μ] g) :
   · have hg : ¬integrable g μ := by intro hg; exact hf (hg.congr h.symm)
     rw [with_densityᵥ, with_densityᵥ, dif_neg hf, dif_neg hg]
 #align measure_theory.with_densityᵥ_eq.congr_ae MeasureTheory.WithDensityᵥEq.congr_ae
+-/
 
 #print MeasureTheory.Integrable.withDensityᵥ_eq_iff /-
 theorem Integrable.withDensityᵥ_eq_iff {f g : α → E} (hf : Integrable f μ) (hg : Integrable g μ) :
@@ -189,6 +205,7 @@ theorem Integrable.withDensityᵥ_eq_iff {f g : α → E} (hf : Integrable f μ)
 
 section SignedMeasure
 
+#print MeasureTheory.withDensityᵥ_toReal /-
 theorem withDensityᵥ_toReal {f : α → ℝ≥0∞} (hfm : AEMeasurable f μ) (hf : ∫⁻ x, f x ∂μ ≠ ∞) :
     (μ.withDensityᵥ fun x => (f x).toReal) =
       @toSignedMeasure α _ (μ.withDensity f) (isFiniteMeasure_withDensity hf) :=
@@ -201,6 +218,7 @@ theorem withDensityᵥ_toReal {f : α → ℝ≥0∞} (hfm : AEMeasurable f μ)
   conv_rhs => rw [← set_lintegral_univ]
   exact lintegral_mono_set (Set.subset_univ _)
 #align measure_theory.with_densityᵥ_to_real MeasureTheory.withDensityᵥ_toReal
+-/
 
 #print MeasureTheory.withDensityᵥ_eq_withDensity_pos_part_sub_withDensity_neg_part /-
 theorem withDensityᵥ_eq_withDensity_pos_part_sub_withDensity_neg_part {f : α → ℝ}
@@ -227,6 +245,7 @@ theorem Integrable.withDensityᵥ_trim_eq_integral {m m0 : MeasurableSpace α} {
 #align measure_theory.integrable.with_densityᵥ_trim_eq_integral MeasureTheory.Integrable.withDensityᵥ_trim_eq_integral
 -/
 
+#print MeasureTheory.Integrable.withDensityᵥ_trim_absolutelyContinuous /-
 theorem Integrable.withDensityᵥ_trim_absolutelyContinuous {m m0 : MeasurableSpace α} {μ : Measure α}
     (hm : m ≤ m0) (hfi : Integrable f μ) :
     (μ.withDensityᵥ f).trim hm ≪ᵥ (μ.trim hm).toENNRealVectorMeasure :=
@@ -236,6 +255,7 @@ theorem Integrable.withDensityᵥ_trim_absolutelyContinuous {m m0 : MeasurableSp
   rw [vector_measure.trim_measurable_set_eq hm hj₁, with_densityᵥ_apply hfi (hm _ hj₁)]
   simp only [measure.restrict_eq_zero.mpr hj₂, integral_zero_measure]
 #align measure_theory.integrable.with_densityᵥ_trim_absolutely_continuous MeasureTheory.Integrable.withDensityᵥ_trim_absolutelyContinuous
+-/
 
 end SignedMeasure

c2092722

bump to nightly-2023-06-10-07

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

3fdc57bc

Diff

@@ -189,7 +189,7 @@ theorem Integrable.withDensityᵥ_eq_iff {f g : α → E} (hf : Integrable f μ)
 
 section SignedMeasure
 
-theorem withDensityᵥ_toReal {f : α → ℝ≥0∞} (hfm : AEMeasurable f μ) (hf : (∫⁻ x, f x ∂μ) ≠ ∞) :
+theorem withDensityᵥ_toReal {f : α → ℝ≥0∞} (hfm : AEMeasurable f μ) (hf : ∫⁻ x, f x ∂μ ≠ ∞) :
     (μ.withDensityᵥ fun x => (f x).toReal) =
       @toSignedMeasure α _ (μ.withDensity f) (isFiniteMeasure_withDensity hf) :=
   by

c2092722

bump to nightly-2023-06-08-03

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

8f04dc2b

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kexing Ying
 
 ! This file was ported from Lean 3 source module measure_theory.measure.with_density_vector_measure
-! leanprover-community/mathlib commit d1bd9c5df2867c1cb463bc6364446d57bdd9f7f1
+! leanprover-community/mathlib commit c20927220ef87bb4962ba08bf6da2ce3cf50a6dd
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -15,6 +15,9 @@ import Mathbin.MeasureTheory.Function.AeEqOfIntegral
 
 # Vector measure defined by an integral
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 Given a measure `μ` and an integrable function `f : α → E`, we can define a vector measure `v` such
 that for all measurable set `s`, `v i = ∫ x in s, f x ∂μ`. This definition is useful for
 the Radon-Nikodym theorem for signed measures.

d1bd9c5d

bump to nightly-2023-06-06-09

mathlib commit https://github.com/leanprover-community/mathlib/commit/a3209ddf94136d36e5e5c624b10b2a347cc9d090

7f33669e

Diff

@@ -41,6 +41,7 @@ variable {μ ν : Measure α}
 
 variable {E : Type _} [NormedAddCommGroup E] [NormedSpace ℝ E] [CompleteSpace E]
 
+#print MeasureTheory.Measure.withDensityᵥ /-
 /-- Given a measure `μ` and an integrable function `f`, `μ.with_densityᵥ f` is
 the vector measure which maps the set `s` to `∫ₛ f ∂μ`. -/
 def Measure.withDensityᵥ {m : MeasurableSpace α} (μ : Measure α) (f : α → E) : VectorMeasure α E :=
@@ -55,6 +56,7 @@ def Measure.withDensityᵥ {m : MeasurableSpace α} (μ : Measure α) (f : α 
         · rw [if_pos (MeasurableSet.iUnion hs₁)] }
   else 0
 #align measure_theory.measure.with_densityᵥ MeasureTheory.Measure.withDensityᵥ
+-/
 
 open Measure
 
@@ -62,9 +64,11 @@ include m
 
 variable {f g : α → E}
 
+#print MeasureTheory.withDensityᵥ_apply /-
 theorem withDensityᵥ_apply (hf : Integrable f μ) {s : Set α} (hs : MeasurableSet s) :
     μ.withDensityᵥ f s = ∫ x in s, f x ∂μ := by rw [with_densityᵥ, dif_pos hf]; exact dif_pos hs
 #align measure_theory.with_densityᵥ_apply MeasureTheory.withDensityᵥ_apply
+-/
 
 @[simp]
 theorem withDensityᵥ_zero : μ.withDensityᵥ (0 : α → E) = 0 := by ext1 s hs;
@@ -116,6 +120,7 @@ theorem withDensityᵥ_sub' (hf : Integrable f μ) (hg : Integrable g μ) :
   withDensityᵥ_sub hf hg
 #align measure_theory.with_densityᵥ_sub' MeasureTheory.withDensityᵥ_sub'
 
+#print MeasureTheory.withDensityᵥ_smul /-
 @[simp]
 theorem withDensityᵥ_smul {𝕜 : Type _} [NontriviallyNormedField 𝕜] [NormedSpace 𝕜 E]
     [SMulCommClass ℝ 𝕜 E] (f : α → E) (r : 𝕜) : μ.withDensityᵥ (r • f) = r • μ.withDensityᵥ f :=
@@ -130,15 +135,18 @@ theorem withDensityᵥ_smul {𝕜 : Type _} [NontriviallyNormedField 𝕜] [Norm
     · rw [with_densityᵥ, with_densityᵥ, dif_neg hf, dif_neg, smul_zero]
       rwa [integrable_smul_iff hr f]
 #align measure_theory.with_densityᵥ_smul MeasureTheory.withDensityᵥ_smul
+-/
 
+#print MeasureTheory.withDensityᵥ_smul' /-
 theorem withDensityᵥ_smul' {𝕜 : Type _} [NontriviallyNormedField 𝕜] [NormedSpace 𝕜 E]
     [SMulCommClass ℝ 𝕜 E] (f : α → E) (r : 𝕜) :
     (μ.withDensityᵥ fun x => r • f x) = r • μ.withDensityᵥ f :=
   withDensityᵥ_smul f r
 #align measure_theory.with_densityᵥ_smul' MeasureTheory.withDensityᵥ_smul'
+-/
 
 theorem Measure.withDensityᵥ_absolutelyContinuous (μ : Measure α) (f : α → ℝ) :
-    μ.withDensityᵥ f ≪ᵥ μ.toEnnrealVectorMeasure :=
+    μ.withDensityᵥ f ≪ᵥ μ.toENNRealVectorMeasure :=
   by
   by_cases hf : integrable f μ
   · refine' vector_measure.absolutely_continuous.mk fun i hi₁ hi₂ => _
@@ -148,6 +156,7 @@ theorem Measure.withDensityᵥ_absolutelyContinuous (μ : Measure α) (f : α 
     exact vector_measure.absolutely_continuous.zero _
 #align measure_theory.measure.with_densityᵥ_absolutely_continuous MeasureTheory.Measure.withDensityᵥ_absolutelyContinuous
 
+#print MeasureTheory.Integrable.ae_eq_of_withDensityᵥ_eq /-
 /-- Having the same density implies the underlying functions are equal almost everywhere. -/
 theorem Integrable.ae_eq_of_withDensityᵥ_eq {f g : α → E} (hf : Integrable f μ)
     (hg : Integrable g μ) (hfg : μ.withDensityᵥ f = μ.withDensityᵥ g) : f =ᵐ[μ] g :=
@@ -155,6 +164,7 @@ theorem Integrable.ae_eq_of_withDensityᵥ_eq {f g : α → E} (hf : Integrable
   refine' hf.ae_eq_of_forall_set_integral_eq f g hg fun i hi _ => _
   rw [← with_densityᵥ_apply hf hi, hfg, with_densityᵥ_apply hg hi]
 #align measure_theory.integrable.ae_eq_of_with_densityᵥ_eq MeasureTheory.Integrable.ae_eq_of_withDensityᵥ_eq
+-/
 
 theorem WithDensityᵥEq.congr_ae {f g : α → E} (h : f =ᵐ[μ] g) :
     μ.withDensityᵥ f = μ.withDensityᵥ g :=
@@ -167,10 +177,12 @@ theorem WithDensityᵥEq.congr_ae {f g : α → E} (h : f =ᵐ[μ] g) :
     rw [with_densityᵥ, with_densityᵥ, dif_neg hf, dif_neg hg]
 #align measure_theory.with_densityᵥ_eq.congr_ae MeasureTheory.WithDensityᵥEq.congr_ae
 
+#print MeasureTheory.Integrable.withDensityᵥ_eq_iff /-
 theorem Integrable.withDensityᵥ_eq_iff {f g : α → E} (hf : Integrable f μ) (hg : Integrable g μ) :
     μ.withDensityᵥ f = μ.withDensityᵥ g ↔ f =ᵐ[μ] g :=
   ⟨fun hfg => hf.ae_eq_of_withDensityᵥ_eq hg hfg, fun h => WithDensityᵥEq.congr_ae h⟩
 #align measure_theory.integrable.with_densityᵥ_eq_iff MeasureTheory.Integrable.withDensityᵥ_eq_iff
+-/
 
 section SignedMeasure
 
@@ -187,6 +199,7 @@ theorem withDensityᵥ_toReal {f : α → ℝ≥0∞} (hfm : AEMeasurable f μ)
   exact lintegral_mono_set (Set.subset_univ _)
 #align measure_theory.with_densityᵥ_to_real MeasureTheory.withDensityᵥ_toReal
 
+#print MeasureTheory.withDensityᵥ_eq_withDensity_pos_part_sub_withDensity_neg_part /-
 theorem withDensityᵥ_eq_withDensity_pos_part_sub_withDensity_neg_part {f : α → ℝ}
     (hfi : Integrable f μ) :
     μ.withDensityᵥ f =
@@ -201,16 +214,19 @@ theorem withDensityᵥ_eq_withDensity_pos_part_sub_withDensity_neg_part {f : α
     vector_measure.sub_apply, to_signed_measure_apply_measurable hi,
     to_signed_measure_apply_measurable hi, with_density_apply _ hi, with_density_apply _ hi]
 #align measure_theory.with_densityᵥ_eq_with_density_pos_part_sub_with_density_neg_part MeasureTheory.withDensityᵥ_eq_withDensity_pos_part_sub_withDensity_neg_part
+-/
 
+#print MeasureTheory.Integrable.withDensityᵥ_trim_eq_integral /-
 theorem Integrable.withDensityᵥ_trim_eq_integral {m m0 : MeasurableSpace α} {μ : Measure α}
     (hm : m ≤ m0) {f : α → ℝ} (hf : Integrable f μ) {i : Set α} (hi : measurable_set[m] i) :
     (μ.withDensityᵥ f).trim hm i = ∫ x in i, f x ∂μ := by
   rw [vector_measure.trim_measurable_set_eq hm hi, with_densityᵥ_apply hf (hm _ hi)]
 #align measure_theory.integrable.with_densityᵥ_trim_eq_integral MeasureTheory.Integrable.withDensityᵥ_trim_eq_integral
+-/
 
 theorem Integrable.withDensityᵥ_trim_absolutelyContinuous {m m0 : MeasurableSpace α} {μ : Measure α}
     (hm : m ≤ m0) (hfi : Integrable f μ) :
-    (μ.withDensityᵥ f).trim hm ≪ᵥ (μ.trim hm).toEnnrealVectorMeasure :=
+    (μ.withDensityᵥ f).trim hm ≪ᵥ (μ.trim hm).toENNRealVectorMeasure :=
   by
   refine' vector_measure.absolutely_continuous.mk fun j hj₁ hj₂ => _
   rw [measure.to_ennreal_vector_measure_apply_measurable hj₁, trim_measurable_set_eq hm hj₁] at hj₂

d1bd9c5d

bump to nightly-2023-06-04-18

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

3fb4268b

Diff

@@ -176,7 +176,7 @@ section SignedMeasure
 
 theorem withDensityᵥ_toReal {f : α → ℝ≥0∞} (hfm : AEMeasurable f μ) (hf : (∫⁻ x, f x ∂μ) ≠ ∞) :
     (μ.withDensityᵥ fun x => (f x).toReal) =
-      @toSignedMeasure α _ (μ.withDensity f) (finiteMeasure_withDensity hf) :=
+      @toSignedMeasure α _ (μ.withDensity f) (isFiniteMeasure_withDensity hf) :=
   by
   have hfi := integrable_to_real_of_lintegral_ne_top hfm hf
   ext (i hi)
@@ -191,9 +191,9 @@ theorem withDensityᵥ_eq_withDensity_pos_part_sub_withDensity_neg_part {f : α
     (hfi : Integrable f μ) :
     μ.withDensityᵥ f =
       @toSignedMeasure α _ (μ.withDensity fun x => ENNReal.ofReal <| f x)
-          (finiteMeasure_withDensity_ofReal hfi.2) -
+          (isFiniteMeasure_withDensity_ofReal hfi.2) -
         @toSignedMeasure α _ (μ.withDensity fun x => ENNReal.ofReal <| -f x)
-          (finiteMeasure_withDensity_ofReal hfi.neg.2) :=
+          (isFiniteMeasure_withDensity_ofReal hfi.neg.2) :=
   by
   ext (i hi)
   rw [with_densityᵥ_apply hfi hi,

d1bd9c5d

bump to nightly-2023-06-01-16

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

b9c87c70

Diff

@@ -142,7 +142,7 @@ theorem Measure.withDensityᵥ_absolutelyContinuous (μ : Measure α) (f : α 
   by
   by_cases hf : integrable f μ
   · refine' vector_measure.absolutely_continuous.mk fun i hi₁ hi₂ => _
-    rw [to_ennreal_vector_measure_apply_measurable hi₁] at hi₂
+    rw [to_ennreal_vector_measure_apply_measurable hi₁] at hi₂ 
     rw [with_densityᵥ_apply hf hi₁, measure.restrict_zero_set hi₂, integral_zero_measure]
   · rw [with_densityᵥ, dif_neg hf]
     exact vector_measure.absolutely_continuous.zero _
@@ -213,7 +213,7 @@ theorem Integrable.withDensityᵥ_trim_absolutelyContinuous {m m0 : MeasurableSp
     (μ.withDensityᵥ f).trim hm ≪ᵥ (μ.trim hm).toEnnrealVectorMeasure :=
   by
   refine' vector_measure.absolutely_continuous.mk fun j hj₁ hj₂ => _
-  rw [measure.to_ennreal_vector_measure_apply_measurable hj₁, trim_measurable_set_eq hm hj₁] at hj₂
+  rw [measure.to_ennreal_vector_measure_apply_measurable hj₁, trim_measurable_set_eq hm hj₁] at hj₂ 
   rw [vector_measure.trim_measurable_set_eq hm hj₁, with_densityᵥ_apply hfi (hm _ hj₁)]
   simp only [measure.restrict_eq_zero.mpr hj₂, integral_zero_measure]
 #align measure_theory.integrable.with_densityᵥ_trim_absolutely_continuous MeasureTheory.Integrable.withDensityᵥ_trim_absolutelyContinuous

d1bd9c5d

bump to nightly-2023-06-01-04

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

4d9eaa85

Diff

@@ -48,7 +48,7 @@ def Measure.withDensityᵥ {m : MeasurableSpace α} (μ : Measure α) (f : α 
     { measureOf' := fun s => if MeasurableSet s then ∫ x in s, f x ∂μ else 0
       empty' := by simp
       not_measurable' := fun s hs => if_neg hs
-      m_Union' := fun s hs₁ hs₂ =>
+      m_iUnion' := fun s hs₁ hs₂ =>
         by
         convert has_sum_integral_Union hs₁ hs₂ hf.integrable_on
         · ext n; rw [if_pos (hs₁ n)]
@@ -137,7 +137,7 @@ theorem withDensityᵥ_smul' {𝕜 : Type _} [NontriviallyNormedField 𝕜] [Nor
   withDensityᵥ_smul f r
 #align measure_theory.with_densityᵥ_smul' MeasureTheory.withDensityᵥ_smul'
 
-theorem Measure.withDensityᵥAbsolutelyContinuous (μ : Measure α) (f : α → ℝ) :
+theorem Measure.withDensityᵥ_absolutelyContinuous (μ : Measure α) (f : α → ℝ) :
     μ.withDensityᵥ f ≪ᵥ μ.toEnnrealVectorMeasure :=
   by
   by_cases hf : integrable f μ
@@ -146,7 +146,7 @@ theorem Measure.withDensityᵥAbsolutelyContinuous (μ : Measure α) (f : α →
     rw [with_densityᵥ_apply hf hi₁, measure.restrict_zero_set hi₂, integral_zero_measure]
   · rw [with_densityᵥ, dif_neg hf]
     exact vector_measure.absolutely_continuous.zero _
-#align measure_theory.measure.with_densityᵥ_absolutely_continuous MeasureTheory.Measure.withDensityᵥAbsolutelyContinuous
+#align measure_theory.measure.with_densityᵥ_absolutely_continuous MeasureTheory.Measure.withDensityᵥ_absolutelyContinuous
 
 /-- Having the same density implies the underlying functions are equal almost everywhere. -/
 theorem Integrable.ae_eq_of_withDensityᵥ_eq {f g : α → E} (hf : Integrable f μ)
@@ -208,7 +208,7 @@ theorem Integrable.withDensityᵥ_trim_eq_integral {m m0 : MeasurableSpace α} {
   rw [vector_measure.trim_measurable_set_eq hm hi, with_densityᵥ_apply hf (hm _ hi)]
 #align measure_theory.integrable.with_densityᵥ_trim_eq_integral MeasureTheory.Integrable.withDensityᵥ_trim_eq_integral
 
-theorem Integrable.withDensityᵥTrimAbsolutelyContinuous {m m0 : MeasurableSpace α} {μ : Measure α}
+theorem Integrable.withDensityᵥ_trim_absolutelyContinuous {m m0 : MeasurableSpace α} {μ : Measure α}
     (hm : m ≤ m0) (hfi : Integrable f μ) :
     (μ.withDensityᵥ f).trim hm ≪ᵥ (μ.trim hm).toEnnrealVectorMeasure :=
   by
@@ -216,7 +216,7 @@ theorem Integrable.withDensityᵥTrimAbsolutelyContinuous {m m0 : MeasurableSpac
   rw [measure.to_ennreal_vector_measure_apply_measurable hj₁, trim_measurable_set_eq hm hj₁] at hj₂
   rw [vector_measure.trim_measurable_set_eq hm hj₁, with_densityᵥ_apply hfi (hm _ hj₁)]
   simp only [measure.restrict_eq_zero.mpr hj₂, integral_zero_measure]
-#align measure_theory.integrable.with_densityᵥ_trim_absolutely_continuous MeasureTheory.Integrable.withDensityᵥTrimAbsolutelyContinuous
+#align measure_theory.integrable.with_densityᵥ_trim_absolutely_continuous MeasureTheory.Integrable.withDensityᵥ_trim_absolutelyContinuous
 
 end SignedMeasure

d1bd9c5d

bump to nightly-2023-05-28-18

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

8d353152

Diff

@@ -29,7 +29,7 @@ the Radon-Nikodym theorem for signed measures.
 
 noncomputable section
 
-open Classical MeasureTheory NNReal ENNReal
+open scoped Classical MeasureTheory NNReal ENNReal
 
 variable {α β : Type _} {m : MeasurableSpace α}

d1bd9c5d

bump to nightly-2023-05-28-04

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

6797a637

Diff

@@ -51,8 +51,7 @@ def Measure.withDensityᵥ {m : MeasurableSpace α} (μ : Measure α) (f : α 
       m_Union' := fun s hs₁ hs₂ =>
         by
         convert has_sum_integral_Union hs₁ hs₂ hf.integrable_on
-        · ext n
-          rw [if_pos (hs₁ n)]
+        · ext n; rw [if_pos (hs₁ n)]
         · rw [if_pos (MeasurableSet.iUnion hs₁)] }
   else 0
 #align measure_theory.measure.with_densityᵥ MeasureTheory.Measure.withDensityᵥ
@@ -64,18 +63,12 @@ include m
 variable {f g : α → E}
 
 theorem withDensityᵥ_apply (hf : Integrable f μ) {s : Set α} (hs : MeasurableSet s) :
-    μ.withDensityᵥ f s = ∫ x in s, f x ∂μ :=
-  by
-  rw [with_densityᵥ, dif_pos hf]
-  exact dif_pos hs
+    μ.withDensityᵥ f s = ∫ x in s, f x ∂μ := by rw [with_densityᵥ, dif_pos hf]; exact dif_pos hs
 #align measure_theory.with_densityᵥ_apply MeasureTheory.withDensityᵥ_apply
 
 @[simp]
-theorem withDensityᵥ_zero : μ.withDensityᵥ (0 : α → E) = 0 :=
-  by
-  ext1 s hs
-  erw [with_densityᵥ_apply (integrable_zero α E μ) hs]
-  simp
+theorem withDensityᵥ_zero : μ.withDensityᵥ (0 : α → E) = 0 := by ext1 s hs;
+  erw [with_densityᵥ_apply (integrable_zero α E μ) hs]; simp
 #align measure_theory.with_densityᵥ_zero MeasureTheory.withDensityᵥ_zero
 
 @[simp]
@@ -170,9 +163,7 @@ theorem WithDensityᵥEq.congr_ae {f g : α → E} (h : f =ᵐ[μ] g) :
   · ext (i hi)
     rw [with_densityᵥ_apply hf hi, with_densityᵥ_apply (hf.congr h) hi]
     exact integral_congr_ae (ae_restrict_of_ae h)
-  · have hg : ¬integrable g μ := by
-      intro hg
-      exact hf (hg.congr h.symm)
+  · have hg : ¬integrable g μ := by intro hg; exact hf (hg.congr h.symm)
     rw [with_densityᵥ, with_densityᵥ, dif_neg hf, dif_neg hg]
 #align measure_theory.with_densityᵥ_eq.congr_ae MeasureTheory.WithDensityᵥEq.congr_ae

d1bd9c5d

bump to nightly-2023-05-14-08

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

d31da313

Diff

@@ -53,7 +53,7 @@ def Measure.withDensityᵥ {m : MeasurableSpace α} (μ : Measure α) (f : α 
         convert has_sum_integral_Union hs₁ hs₂ hf.integrable_on
         · ext n
           rw [if_pos (hs₁ n)]
-        · rw [if_pos (MeasurableSet.unionᵢ hs₁)] }
+        · rw [if_pos (MeasurableSet.iUnion hs₁)] }
   else 0
 #align measure_theory.measure.with_densityᵥ MeasureTheory.Measure.withDensityᵥ

d1bd9c5d

bump to nightly-2023-05-09-08

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

244524af

Diff

@@ -185,7 +185,7 @@ section SignedMeasure
 
 theorem withDensityᵥ_toReal {f : α → ℝ≥0∞} (hfm : AEMeasurable f μ) (hf : (∫⁻ x, f x ∂μ) ≠ ∞) :
     (μ.withDensityᵥ fun x => (f x).toReal) =
-      @toSignedMeasure α _ (μ.withDensity f) (isFiniteMeasure_withDensity hf) :=
+      @toSignedMeasure α _ (μ.withDensity f) (finiteMeasure_withDensity hf) :=
   by
   have hfi := integrable_to_real_of_lintegral_ne_top hfm hf
   ext (i hi)
@@ -200,9 +200,9 @@ theorem withDensityᵥ_eq_withDensity_pos_part_sub_withDensity_neg_part {f : α
     (hfi : Integrable f μ) :
     μ.withDensityᵥ f =
       @toSignedMeasure α _ (μ.withDensity fun x => ENNReal.ofReal <| f x)
-          (isFiniteMeasure_withDensity_ofReal hfi.2) -
+          (finiteMeasure_withDensity_ofReal hfi.2) -
         @toSignedMeasure α _ (μ.withDensity fun x => ENNReal.ofReal <| -f x)
-          (isFiniteMeasure_withDensity_ofReal hfi.neg.2) :=
+          (finiteMeasure_withDensity_ofReal hfi.neg.2) :=
   by
   ext (i hi)
   rw [with_densityᵥ_apply hfi hi,

d1bd9c5d

bump to nightly-2023-05-04-10

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

3d8894bd

Diff

@@ -183,9 +183,9 @@ theorem Integrable.withDensityᵥ_eq_iff {f g : α → E} (hf : Integrable f μ)
 
 section SignedMeasure
 
-theorem withDensityᵥ_toReal {f : α → ℝ≥0∞} (hfm : AeMeasurable f μ) (hf : (∫⁻ x, f x ∂μ) ≠ ∞) :
+theorem withDensityᵥ_toReal {f : α → ℝ≥0∞} (hfm : AEMeasurable f μ) (hf : (∫⁻ x, f x ∂μ) ≠ ∞) :
     (μ.withDensityᵥ fun x => (f x).toReal) =
-      @toSignedMeasure α _ (μ.withDensity f) (isFiniteMeasureWithDensity hf) :=
+      @toSignedMeasure α _ (μ.withDensity f) (isFiniteMeasure_withDensity hf) :=
   by
   have hfi := integrable_to_real_of_lintegral_ne_top hfm hf
   ext (i hi)
@@ -200,9 +200,9 @@ theorem withDensityᵥ_eq_withDensity_pos_part_sub_withDensity_neg_part {f : α
     (hfi : Integrable f μ) :
     μ.withDensityᵥ f =
       @toSignedMeasure α _ (μ.withDensity fun x => ENNReal.ofReal <| f x)
-          (isFiniteMeasureWithDensityOfReal hfi.2) -
+          (isFiniteMeasure_withDensity_ofReal hfi.2) -
         @toSignedMeasure α _ (μ.withDensity fun x => ENNReal.ofReal <| -f x)
-          (isFiniteMeasureWithDensityOfReal hfi.neg.2) :=
+          (isFiniteMeasure_withDensity_ofReal hfi.neg.2) :=
   by
   ext (i hi)
   rw [with_densityᵥ_apply hfi hi,

d1bd9c5d

bump to nightly-2023-02-27-10

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

49ff026a

Diff

@@ -29,7 +29,7 @@ the Radon-Nikodym theorem for signed measures.
 
 noncomputable section
 
-open Classical MeasureTheory NNReal Ennreal
+open Classical MeasureTheory NNReal ENNReal
 
 variable {α β : Type _} {m : MeasurableSpace α}
 
@@ -199,9 +199,9 @@ theorem withDensityᵥ_toReal {f : α → ℝ≥0∞} (hfm : AeMeasurable f μ)
 theorem withDensityᵥ_eq_withDensity_pos_part_sub_withDensity_neg_part {f : α → ℝ}
     (hfi : Integrable f μ) :
     μ.withDensityᵥ f =
-      @toSignedMeasure α _ (μ.withDensity fun x => Ennreal.ofReal <| f x)
+      @toSignedMeasure α _ (μ.withDensity fun x => ENNReal.ofReal <| f x)
           (isFiniteMeasureWithDensityOfReal hfi.2) -
-        @toSignedMeasure α _ (μ.withDensity fun x => Ennreal.ofReal <| -f x)
+        @toSignedMeasure α _ (μ.withDensity fun x => ENNReal.ofReal <| -f x)
           (isFiniteMeasureWithDensityOfReal hfi.neg.2) :=
   by
   ext (i hi)

d1bd9c5d

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

d1bd9c5d

chore: replace set_integral with setIntegral (#12215)

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

f4b4298b

Diff

@@ -134,7 +134,7 @@ theorem withDensityᵥ_smul_eq_withDensityᵥ_withDensity {f : α → ℝ≥0} {
   ext s hs
   rw [withDensityᵥ_apply hfg hs,
     withDensityᵥ_apply ((integrable_withDensity_iff_integrable_smul₀ hf).mpr hfg) hs,
-    set_integral_withDensity_eq_set_integral_smul₀ hf.restrict _ hs]
+    setIntegral_withDensity_eq_setIntegral_smul₀ hf.restrict _ hs]
   rfl
 
 theorem withDensityᵥ_smul_eq_withDensityᵥ_withDensity' {f : α → ℝ≥0∞} {g : α → E}
@@ -158,7 +158,7 @@ theorem Measure.withDensityᵥ_absolutelyContinuous (μ : Measure α) (f : α 
 /-- Having the same density implies the underlying functions are equal almost everywhere. -/
 theorem Integrable.ae_eq_of_withDensityᵥ_eq {f g : α → E} (hf : Integrable f μ)
     (hg : Integrable g μ) (hfg : μ.withDensityᵥ f = μ.withDensityᵥ g) : f =ᵐ[μ] g := by
-  refine' hf.ae_eq_of_forall_set_integral_eq f g hg fun i hi _ => _
+  refine' hf.ae_eq_of_forall_setIntegral_eq f g hg fun i hi _ => _
   rw [← withDensityᵥ_apply hf hi, hfg, withDensityᵥ_apply hg hi]
 #align measure_theory.integrable.ae_eq_of_with_densityᵥ_eq MeasureTheory.Integrable.ae_eq_of_withDensityᵥ_eq

d1bd9c5d

chore(*): remove empty lines between variable statements (#11418)

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)

75c86f04

Diff

@@ -35,7 +35,6 @@ namespace MeasureTheory
 open TopologicalSpace
 
 variable {μ ν : Measure α}
-
 variable {E : Type*} [NormedAddCommGroup E] [NormedSpace ℝ E] [CompleteSpace E]
 
 /-- Given a measure `μ` and an integrable function `f`, `μ.withDensityᵥ f` is

d1bd9c5d

refactor(Probability/Density): define pdf using rnDeriv (#8544)

Defines pdf in terms of rnDeriv.

Main definition change:

/-- A random variable `X : Ω → E` is said to `HasPDF` with respect to the measure `ℙ` on `Ω` and
`μ` on `E` if the push-forward measure of `ℙ` along `X` is absolutely continuous with respect to
`μ` and they `HaveLebesgueDecomposition`. -/
class HasPDF {m : MeasurableSpace Ω} (X : Ω → E) (ℙ : Measure Ω)
    (μ : Measure E := by volume_tac) : Prop where
  pdf' : Measurable X ∧ HaveLebesgueDecomposition (map X ℙ) μ ∧ map X ℙ ≪ μ

/-- If `X` is a random variable that `HasPDF X ℙ μ`, then `pdf X` is the Radon–Nikodym
derivative of the push-forward measure of `ℙ` along `X` with respect to `μ`. -/
def pdf {_ : MeasurableSpace Ω} (X : Ω → E) (ℙ : Measure Ω) (μ : Measure E := by volume_tac) :
    E → ℝ≥0∞ :=
  if HasPDF X ℙ μ then (map X ℙ).rnDeriv μ else 0

The law of the unconscious statistician is first generalized to rnDeriv on a general Banach space (∫ x, (μ.rnDeriv ν x).toReal • f x ∂ν = ∫ x, f x ∂μ), and then proven for PDFs.

Zulip thread

3f88a472

Diff

@@ -129,6 +129,23 @@ theorem withDensityᵥ_smul' {𝕜 : Type*} [NontriviallyNormedField 𝕜] [Norm
   withDensityᵥ_smul f r
 #align measure_theory.with_densityᵥ_smul' MeasureTheory.withDensityᵥ_smul'
 
+theorem withDensityᵥ_smul_eq_withDensityᵥ_withDensity {f : α → ℝ≥0} {g : α → E}
+    (hf : AEMeasurable f μ) (hfg : Integrable (f • g) μ) :
+    μ.withDensityᵥ (f • g) = (μ.withDensity (fun x ↦ f x)).withDensityᵥ g := by
+  ext s hs
+  rw [withDensityᵥ_apply hfg hs,
+    withDensityᵥ_apply ((integrable_withDensity_iff_integrable_smul₀ hf).mpr hfg) hs,
+    set_integral_withDensity_eq_set_integral_smul₀ hf.restrict _ hs]
+  rfl
+
+theorem withDensityᵥ_smul_eq_withDensityᵥ_withDensity' {f : α → ℝ≥0∞} {g : α → E}
+    (hf : AEMeasurable f μ) (hflt : ∀ᵐ x ∂μ, f x < ∞)
+    (hfg : Integrable (fun x ↦ (f x).toReal • g x) μ) :
+    μ.withDensityᵥ (fun x ↦ (f x).toReal • g x) = (μ.withDensity f).withDensityᵥ g := by
+  rw [← withDensity_congr_ae (coe_toNNReal_ae_eq hflt),
+    ← withDensityᵥ_smul_eq_withDensityᵥ_withDensity hf.ennreal_toNNReal hfg]
+  rfl
+
 theorem Measure.withDensityᵥ_absolutelyContinuous (μ : Measure α) (f : α → ℝ) :
     μ.withDensityᵥ f ≪ᵥ μ.toENNRealVectorMeasure := by
   by_cases hf : Integrable f μ

d1bd9c5d

chore: banish Type _ and Sort _ (#6499)

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

This has nice performance benefits.

32de3f67

Diff

@@ -28,7 +28,7 @@ noncomputable section
 
 open scoped Classical MeasureTheory NNReal ENNReal
 
-variable {α β : Type _} {m : MeasurableSpace α}
+variable {α β : Type*} {m : MeasurableSpace α}
 
 namespace MeasureTheory
 
@@ -36,7 +36,7 @@ open TopologicalSpace
 
 variable {μ ν : Measure α}
 
-variable {E : Type _} [NormedAddCommGroup E] [NormedSpace ℝ E] [CompleteSpace E]
+variable {E : Type*} [NormedAddCommGroup E] [NormedSpace ℝ E] [CompleteSpace E]
 
 /-- Given a measure `μ` and an integrable function `f`, `μ.withDensityᵥ f` is
 the vector measure which maps the set `s` to `∫ₛ f ∂μ`. -/
@@ -110,7 +110,7 @@ theorem withDensityᵥ_sub' (hf : Integrable f μ) (hg : Integrable g μ) :
 #align measure_theory.with_densityᵥ_sub' MeasureTheory.withDensityᵥ_sub'
 
 @[simp]
-theorem withDensityᵥ_smul {𝕜 : Type _} [NontriviallyNormedField 𝕜] [NormedSpace 𝕜 E]
+theorem withDensityᵥ_smul {𝕜 : Type*} [NontriviallyNormedField 𝕜] [NormedSpace 𝕜 E]
     [SMulCommClass ℝ 𝕜 E] (f : α → E) (r : 𝕜) : μ.withDensityᵥ (r • f) = r • μ.withDensityᵥ f := by
   by_cases hf : Integrable f μ
   · ext1 i hi
@@ -123,7 +123,7 @@ theorem withDensityᵥ_smul {𝕜 : Type _} [NontriviallyNormedField 𝕜] [Norm
       rwa [integrable_smul_iff hr f]
 #align measure_theory.with_densityᵥ_smul MeasureTheory.withDensityᵥ_smul
 
-theorem withDensityᵥ_smul' {𝕜 : Type _} [NontriviallyNormedField 𝕜] [NormedSpace 𝕜 E]
+theorem withDensityᵥ_smul' {𝕜 : Type*} [NontriviallyNormedField 𝕜] [NormedSpace 𝕜 E]
     [SMulCommClass ℝ 𝕜 E] (f : α → E) (r : 𝕜) :
     (μ.withDensityᵥ fun x => r • f x) = r • μ.withDensityᵥ f :=
   withDensityᵥ_smul f r

d1bd9c5d

chore: script to replace headers with #align_import statements (#5979)

depends on: #5966

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

89aa3a3b

Diff

@@ -2,15 +2,12 @@
 Copyright (c) 2021 Kexing Ying. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kexing Ying
-
-! This file was ported from Lean 3 source module measure_theory.measure.with_density_vector_measure
-! leanprover-community/mathlib commit d1bd9c5df2867c1cb463bc6364446d57bdd9f7f1
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.MeasureTheory.Measure.VectorMeasure
 import Mathlib.MeasureTheory.Function.AEEqOfIntegral
 
+#align_import measure_theory.measure.with_density_vector_measure from "leanprover-community/mathlib"@"d1bd9c5df2867c1cb463bc6364446d57bdd9f7f1"
+
 /-!
 
 # Vector measure defined by an integral

d1bd9c5d

chore: bump Std4 (#5219)

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

59c36da5

Diff

@@ -152,7 +152,7 @@ theorem Integrable.ae_eq_of_withDensityᵥ_eq {f g : α → E} (hf : Integrable
 theorem WithDensityᵥEq.congr_ae {f g : α → E} (h : f =ᵐ[μ] g) :
     μ.withDensityᵥ f = μ.withDensityᵥ g := by
   by_cases hf : Integrable f μ
-  · ext i; intro hi
+  · ext i hi
     rw [withDensityᵥ_apply hf hi, withDensityᵥ_apply (hf.congr h) hi]
     exact integral_congr_ae (ae_restrict_of_ae h)
   · have hg : ¬Integrable g μ := by intro hg; exact hf (hg.congr h.symm)
@@ -171,7 +171,7 @@ theorem withDensityᵥ_toReal {f : α → ℝ≥0∞} (hfm : AEMeasurable f μ)
       @toSignedMeasure α _ (μ.withDensity f) (isFiniteMeasure_withDensity hf) := by
   have hfi := integrable_toReal_of_lintegral_ne_top hfm hf
   haveI := isFiniteMeasure_withDensity hf
-  ext i; intro hi
+  ext i hi
   rw [withDensityᵥ_apply hfi hi, toSignedMeasure_apply_measurable hi, withDensity_apply _ hi,
     integral_toReal hfm.restrict]
   refine' ae_lt_top' hfm.restrict (ne_top_of_le_ne_top hf _)
@@ -188,7 +188,7 @@ theorem withDensityᵥ_eq_withDensity_pos_part_sub_withDensity_neg_part {f : α
           (isFiniteMeasure_withDensity_ofReal hfi.neg.2) := by
   haveI := isFiniteMeasure_withDensity_ofReal hfi.2
   haveI := isFiniteMeasure_withDensity_ofReal hfi.neg.2
-  ext i; intro hi
+  ext i hi
   rw [withDensityᵥ_apply hfi hi,
     integral_eq_lintegral_pos_part_sub_lintegral_neg_part hfi.integrableOn,
     VectorMeasure.sub_apply, toSignedMeasure_apply_measurable hi,

d1bd9c5d

feat: port MeasureTheory.Measure.WithDensityVectorMeasure (#4715)

c340d963

`measure_theory.measure.with_density_vector_measure` ⟷ `Mathlib.MeasureTheory.Measure.WithDensityVectorMeasure`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 12 + 973

measure_theory.measure.with_density_vector_measure ⟷ Mathlib.MeasureTheory.Measure.WithDensityVectorMeasure

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 12 + 973

`measure_theory.measure.with_density_vector_measure` ⟷ `Mathlib.MeasureTheory.Measure.WithDensityVectorMeasure`