@@ -82,20 +82,22 @@ theorem setIntegral_union₀ (hst : AEDisjoint μ s t) (ht : NullMeasurableSet t
8282 ∫ x in s ∪ t, f x ∂μ = ∫ x in s, f x ∂μ + ∫ x in t, f x ∂μ := by
8383 simp only [Measure.restrict_union₀ hst ht, integral_add_measure hfs hft]
8484
85- @ [deprecated (since := "2025-12-22 " )] alias integral_union_ae := setIntegral_union₀
85+ @ [deprecated (since := "2026-03-04 " )] alias integral_union_ae := setIntegral_union₀
8686
8787theorem setIntegral_union (hst : Disjoint s t) (ht : MeasurableSet t) (hfs : IntegrableOn f s μ)
8888 (hft : IntegrableOn f t μ) : ∫ x in s ∪ t, f x ∂μ = ∫ x in s, f x ∂μ + ∫ x in t, f x ∂μ :=
8989 setIntegral_union₀ hst.aedisjoint ht.nullMeasurableSet hfs hft
9090
91- theorem integral_diff ₀ (ht : NullMeasurableSet t μ) (hfs : IntegrableOn f s μ) (hts : t ⊆ s) :
91+ theorem setIntegral_diff ₀ (ht : NullMeasurableSet t μ) (hfs : IntegrableOn f s μ) (hts : t ⊆ s) :
9292 ∫ x in s \ t, f x ∂μ = ∫ x in s, f x ∂μ - ∫ x in t, f x ∂μ := by
9393 rw [eq_sub_iff_add_eq, ← setIntegral_union₀, diff_union_of_subset hts]
9494 exacts [disjoint_sdiff_self_left.aedisjoint, ht, hfs.mono_set diff_subset, hfs.mono_set hts]
9595
96- theorem integral_diff (ht : MeasurableSet t) (hfs : IntegrableOn f s μ) (hts : t ⊆ s) :
96+ theorem setIntegral_diff (ht : MeasurableSet t) (hfs : IntegrableOn f s μ) (hts : t ⊆ s) :
9797 ∫ x in s \ t, f x ∂μ = ∫ x in s, f x ∂μ - ∫ x in t, f x ∂μ :=
98- integral_diff₀ ht.nullMeasurableSet hfs hts
98+ setIntegral_diff₀ ht.nullMeasurableSet hfs hts
99+
100+ @ [deprecated (since := "2026-03-04" )] alias integral_diff := setIntegral_diff
99101
100102theorem integral_inter_add_diff₀ (ht : NullMeasurableSet t μ) (hfs : IntegrableOn f s μ) :
101103 ∫ 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
270272 have : ∀ᶠ i in atTop, ν (s i) ∈ Icc (ν S - ε) (ν S + ε) :=
271273 tendsto_measure_iUnion_atTop h_mono (ENNReal.Icc_mem_nhds hfi'.ne (ENNReal.coe_pos.2 ε0 ).ne')
272274 filter_upwards [this] with i hi
273- rw [mem_closedBall_iff_norm', ← integral_diff ₀ (hsm i) hfi hsub, ← coe_nnnorm, NNReal.coe_le_coe ,
274- ← ENNReal.coe_le_coe]
275+ rw [mem_closedBall_iff_norm', ← setIntegral_diff ₀ (hsm i) hfi hsub, ← coe_nnnorm,
276+ NNReal.coe_le_coe, ← ENNReal.coe_le_coe]
275277 refine (enorm_integral_le_lintegral_enorm _).trans ?_
276278 have hsm' : NullMeasurableSet (s i) ν := (hsm i).mono_ac (withDensity_absolutelyContinuous ..)
277279 rw [← withDensity_apply₀ _ (hSm.diff (hsm _)), ← hν, measure_diff hsub hsm']
@@ -296,9 +298,9 @@ theorem tendsto_setIntegral_of_antitone
296298 suffices Tendsto (∫ x in s i₀, f x ∂μ - ∫ x in s i₀ \ s ·, f x ∂μ) atTop
297299 (𝓝 (∫ x in s i₀, f x ∂μ - ∫ x in ⋃ i, s i₀ \ s i, f x ∂μ)) by
298300 convert this.congr' <| (eventually_ge_atTop i₀).mono fun i hi ↦ ?_
299- · rw [← diff_iInter, integral_diff _ hi₀ (iInter_subset _ _), sub_sub_cancel]
301+ · rw [← diff_iInter, setIntegral_diff _ hi₀ (iInter_subset _ _), sub_sub_cancel]
300302 exact .iInter_of_antitone h_anti hsm
301- · rw [integral_diff (hsm i) hi₀ (h_anti hi), sub_sub_cancel]
303+ · rw [setIntegral_diff (hsm i) hi₀ (h_anti hi), sub_sub_cancel]
302304 apply tendsto_const_nhds.sub
303305 refine tendsto_setIntegral_of_monotone (by measurability) ?_ ?_
304306 · exact fun i j h ↦ diff_subset_diff_right (h_anti h)
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