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deprecation date, consistent naming
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  • Mathlib/MeasureTheory/Integral/Bochner

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Mathlib/MeasureTheory/Integral/Bochner/Set.lean

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Original file line numberDiff line numberDiff line change
@@ -82,20 +82,22 @@ theorem setIntegral_union₀ (hst : AEDisjoint μ s t) (ht : NullMeasurableSet t
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∫ x in s ∪ t, f x ∂μ = ∫ x in s, f x ∂μ + ∫ x in t, f x ∂μ := by
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simp only [Measure.restrict_union₀ hst ht, integral_add_measure hfs hft]
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@[deprecated (since := "2025-12-22")] alias integral_union_ae := setIntegral_union₀
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@[deprecated (since := "2026-03-04")] alias integral_union_ae := setIntegral_union₀
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theorem setIntegral_union (hst : Disjoint s t) (ht : MeasurableSet t) (hfs : IntegrableOn f s μ)
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(hft : IntegrableOn f t μ) : ∫ x in s ∪ t, f x ∂μ = ∫ x in s, f x ∂μ + ∫ x in t, f x ∂μ :=
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setIntegral_union₀ hst.aedisjoint ht.nullMeasurableSet hfs hft
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theorem integral_diff (ht : NullMeasurableSet t μ) (hfs : IntegrableOn f s μ) (hts : t ⊆ s) :
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theorem setIntegral_diff (ht : NullMeasurableSet t μ) (hfs : IntegrableOn f s μ) (hts : t ⊆ s) :
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∫ x in s \ t, f x ∂μ = ∫ x in s, f x ∂μ - ∫ x in t, f x ∂μ := by
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rw [eq_sub_iff_add_eq, ← setIntegral_union₀, diff_union_of_subset hts]
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exacts [disjoint_sdiff_self_left.aedisjoint, ht, hfs.mono_set diff_subset, hfs.mono_set hts]
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theorem integral_diff (ht : MeasurableSet t) (hfs : IntegrableOn f s μ) (hts : t ⊆ s) :
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theorem setIntegral_diff (ht : MeasurableSet t) (hfs : IntegrableOn f s μ) (hts : t ⊆ s) :
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∫ x in s \ t, f x ∂μ = ∫ x in s, f x ∂μ - ∫ x in t, f x ∂μ :=
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integral_diff₀ ht.nullMeasurableSet hfs hts
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setIntegral_diff₀ ht.nullMeasurableSet hfs hts
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@[deprecated (since := "2026-03-04")] alias integral_diff := setIntegral_diff
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theorem integral_inter_add_diff₀ (ht : NullMeasurableSet t μ) (hfs : IntegrableOn f s μ) :
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∫ x in s ∩ t, f x ∂μ + ∫ x in s \ t, f x ∂μ = ∫ x in s, f x ∂μ := by
@@ -270,8 +272,8 @@ theorem tendsto_setIntegral_of_monotone₀
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have : ∀ᶠ i in atTop, ν (s i) ∈ Icc (ν S - ε) (ν S + ε) :=
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tendsto_measure_iUnion_atTop h_mono (ENNReal.Icc_mem_nhds hfi'.ne (ENNReal.coe_pos.2 ε0).ne')
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filter_upwards [this] with i hi
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rw [mem_closedBall_iff_norm', ← integral_diff₀ (hsm i) hfi hsub, ← coe_nnnorm, NNReal.coe_le_coe,
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← ENNReal.coe_le_coe]
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rw [mem_closedBall_iff_norm', ← setIntegral_diff₀ (hsm i) hfi hsub, ← coe_nnnorm,
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NNReal.coe_le_coe, ← ENNReal.coe_le_coe]
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refine (enorm_integral_le_lintegral_enorm _).trans ?_
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have hsm' : NullMeasurableSet (s i) ν := (hsm i).mono_ac (withDensity_absolutelyContinuous ..)
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rw [← withDensity_apply₀ _ (hSm.diff (hsm _)), ← hν, measure_diff hsub hsm']
@@ -296,9 +298,9 @@ theorem tendsto_setIntegral_of_antitone
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suffices Tendsto (∫ x in s i₀, f x ∂μ - ∫ x in s i₀ \ s ·, f x ∂μ) atTop
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(𝓝 (∫ x in s i₀, f x ∂μ - ∫ x in ⋃ i, s i₀ \ s i, f x ∂μ)) by
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convert this.congr' <| (eventually_ge_atTop i₀).mono fun i hi ↦ ?_
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· rw [← diff_iInter, integral_diff _ hi₀ (iInter_subset _ _), sub_sub_cancel]
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· rw [← diff_iInter, setIntegral_diff _ hi₀ (iInter_subset _ _), sub_sub_cancel]
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exact .iInter_of_antitone h_anti hsm
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· rw [integral_diff (hsm i) hi₀ (h_anti hi), sub_sub_cancel]
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· rw [setIntegral_diff (hsm i) hi₀ (h_anti hi), sub_sub_cancel]
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apply tendsto_const_nhds.sub
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refine tendsto_setIntegral_of_monotone (by measurability) ?_ ?_
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· exact fun i j h ↦ diff_subset_diff_right (h_anti h)

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