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[Merged by Bors] - chore(Measure.MeasureSpace): clean up uses of @ #10932

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[Merged by Bors] - chore(Measure.MeasureSpace): clean up uses of @ #10932

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mattrobball Feb 24, 2024
14bffea
fix
mattrobball Feb 24, 2024
1e2a9f0
two instances not one
kbuzzard Feb 24, 2024
1104245
clean up
mattrobball Feb 24, 2024
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mattrobball Feb 25, 2024
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Merge branch 'master' into mrb/clean_up_ats_measure_meas_space
mattrobball Feb 25, 2024
f91de7f
ml4 issue
mattrobball Feb 25, 2024
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mattrobball Feb 25, 2024
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28 changes: 14 additions & 14 deletions Mathlib/MeasureTheory/Measure/MeasureSpace.lean
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Original file line number Diff line number Diff line change
Expand Up @@ -234,7 +234,7 @@ theorem measure_diff_null (h : μ s₂ = 0) : μ (s₁ \ s₂) = μ s₁ :=
#align measure_theory.measure_diff_null MeasureTheory.measure_diff_null

theorem measure_add_diff (hs : MeasurableSet s) (t : Set α) : μ s + μ (t \ s) = μ (s ∪ t) := by
rw [← measure_union' (@disjoint_sdiff_right _ s t) hs, union_diff_self]
rw [← measure_union' disjoint_sdiff_right hs, union_diff_self]
#align measure_theory.measure_add_diff MeasureTheory.measure_add_diff

theorem measure_diff' (s : Set α) (hm : MeasurableSet t) (h_fin : μ t ≠ ∞) :
Expand Down Expand Up @@ -617,9 +617,9 @@ theorem measure_liminf_eq_zero {s : ℕ → Set α} (h : (∑' i, μ (s i)) ≠
exact (μ.mono this).trans (by simp [measure_limsup_eq_zero h])
#align measure_theory.measure_liminf_eq_zero MeasureTheory.measure_liminf_eq_zero

-- Need to specify `α := Set α` below because of diamond; see #19041
theorem limsup_ae_eq_of_forall_ae_eq (s : ℕ → Set α) {t : Set α}
(h : ∀ n, s n =ᵐ[μ] t) : @limsup (Set α) ℕ _ s atTop =ᵐ[μ] t := by
-- Need `@` below because of diamond; see gh issue #16932
(h : ∀ n, s n =ᵐ[μ] t) : limsup (α := Set α) s atTop =ᵐ[μ] t := by
simp_rw [ae_eq_set] at h ⊢
constructor
· rw [atTop.limsup_sdiff s t]
Expand All @@ -630,9 +630,9 @@ theorem limsup_ae_eq_of_forall_ae_eq (s : ℕ → Set α) {t : Set α}
simp [h]
#align measure_theory.limsup_ae_eq_of_forall_ae_eq MeasureTheory.limsup_ae_eq_of_forall_ae_eq

-- Need to specify `α := Set α` above because of diamond; see #19041
theorem liminf_ae_eq_of_forall_ae_eq (s : ℕ → Set α) {t : Set α}
(h : ∀ n, s n =ᵐ[μ] t) : @liminf (Set α) ℕ _ s atTop =ᵐ[μ] t := by
-- Need `@` below because of diamond; see gh issue #16932
(h : ∀ n, s n =ᵐ[μ] t) : liminf (α := Set α) s atTop =ᵐ[μ] t := by
simp_rw [ae_eq_set] at h ⊢
constructor
· rw [atTop.liminf_sdiff s t]
Expand Down Expand Up @@ -813,7 +813,7 @@ variable [SMul R ℝ≥0∞] [IsScalarTower R ℝ≥0∞ ℝ≥0∞]

variable [SMul R' ℝ≥0∞] [IsScalarTower R' ℝ≥0∞ ℝ≥0∞]

-- porting note: TODO: refactor
-- TODO: refactor
instance instSMul [MeasurableSpace α] : SMul R (Measure α) :=
⟨fun c μ =>
{ toOuterMeasure := c • μ.toOuterMeasure
Expand Down Expand Up @@ -869,7 +869,7 @@ end SMul

instance instNoZeroSMulDivisors [Zero R] [SMulWithZero R ℝ≥0∞] [IsScalarTower R ℝ≥0∞ ℝ≥0∞]
[NoZeroSMulDivisors R ℝ≥0∞] : NoZeroSMulDivisors R (Measure α) where
eq_zero_or_eq_zero_of_smul_eq_zero h := by simpa [Ne.def, @ext_iff', forall_or_left] using h
eq_zero_or_eq_zero_of_smul_eq_zero h := by simpa [Ne.def, ext_iff', forall_or_left] using h

instance instMulAction [Monoid R] [MulAction R ℝ≥0∞] [IsScalarTower R ℝ≥0∞ ℝ≥0∞]
[MeasurableSpace α] : MulAction R (Measure α) :=
Expand Down Expand Up @@ -1405,7 +1405,7 @@ theorem NullMeasurableSet.image {β} [MeasurableSpace α] {mβ : MeasurableSpace
swap
· exact hf _ (measurableSet_toMeasurable _ _)
have h : toMeasurable (comap f μ) s =ᵐ[comap f μ] s :=
@NullMeasurableSet.toMeasurable_ae_eq _ _ (μ.comap f : Measure α) s hs
NullMeasurableSet.toMeasurable_ae_eq hs
exact ae_eq_image_of_ae_eq_comap f μ hfi hf h.symm
#align measure_theory.measure.null_measurable_set.image MeasureTheory.Measure.NullMeasurableSet.image

Expand Down Expand Up @@ -1797,9 +1797,9 @@ theorem image_zpow_ae_eq {s : Set α} {e : α ≃ α} (he : QuasiMeasurePreservi
rwa [Equiv.Perm.iterate_eq_pow e k] at he
#align measure_theory.measure.quasi_measure_preserving.image_zpow_ae_eq MeasureTheory.Measure.QuasiMeasurePreserving.image_zpow_ae_eq

-- Need to specify `α := Set α` below because of diamond; see #19041
theorem limsup_preimage_iterate_ae_eq {f : α → α} (hf : QuasiMeasurePreserving f μ μ)
(hs : f ⁻¹' s =ᵐ[μ] s) : @limsup (Set α) ℕ _ (fun n => (preimage f)^[n] s) atTop =ᵐ[μ] s :=
-- Need `@` below because of diamond; see gh issue #16932
(hs : f ⁻¹' s =ᵐ[μ] s) : limsup (α := Set α) (fun n => (preimage f)^[n] s) atTop =ᵐ[μ] s :=
haveI : ∀ n, (preimage f)^[n] s =ᵐ[μ] s := by
intro n
induction' n with n ih
Expand All @@ -1808,9 +1808,9 @@ theorem limsup_preimage_iterate_ae_eq {f : α → α} (hf : QuasiMeasurePreservi
(limsup_ae_eq_of_forall_ae_eq (fun n => (preimage f)^[n] s) this).trans (ae_eq_refl _)
#align measure_theory.measure.quasi_measure_preserving.limsup_preimage_iterate_ae_eq MeasureTheory.Measure.QuasiMeasurePreserving.limsup_preimage_iterate_ae_eq

-- Need to specify `α := Set α` below because of diamond; see #19041
theorem liminf_preimage_iterate_ae_eq {f : α → α} (hf : QuasiMeasurePreserving f μ μ)
(hs : f ⁻¹' s =ᵐ[μ] s) : @liminf (Set α) ℕ _ (fun n => (preimage f)^[n] s) atTop =ᵐ[μ] s := by
-- Need `@` below because of diamond; see gh issue #16932
(hs : f ⁻¹' s =ᵐ[μ] s) : liminf (α := Set α) (fun n => (preimage f)^[n] s) atTop =ᵐ[μ] s := by
rw [← ae_eq_set_compl_compl, @Filter.liminf_compl (Set α)]
rw [← ae_eq_set_compl_compl, ← preimage_compl] at hs
convert hf.limsup_preimage_iterate_ae_eq hs
Expand All @@ -1827,7 +1827,7 @@ theorem exists_preimage_eq_of_preimage_ae {f : α → α} (h : QuasiMeasurePrese
∃ t : Set α, MeasurableSet t ∧ t =ᵐ[μ] s ∧ f ⁻¹' t = t :=
⟨limsup (fun n => (preimage f)^[n] s) atTop,
MeasurableSet.measurableSet_limsup fun n =>
@preimage_iterate_eq α f n ▸ h.measurable.iterate n hs,
preimage_iterate_eq ▸ h.measurable.iterate n hs,
h.limsup_preimage_iterate_ae_eq hs',
Filter.CompleteLatticeHom.apply_limsup_iterate (CompleteLatticeHom.setPreimage f) s⟩
#align measure_theory.measure.quasi_measure_preserving.exists_preimage_eq_of_preimage_ae MeasureTheory.Measure.QuasiMeasurePreserving.exists_preimage_eq_of_preimage_ae
Expand Down Expand Up @@ -2061,7 +2061,7 @@ theorem Iio_ae_eq_Iic' (ha : μ {a} = 0) : Iio a =ᵐ[μ] Iic a := by
#align measure_theory.Iio_ae_eq_Iic' MeasureTheory.Iio_ae_eq_Iic'

theorem Ioi_ae_eq_Ici' (ha : μ {a} = 0) : Ioi a =ᵐ[μ] Ici a :=
@Iio_ae_eq_Iic' αᵒᵈ _ μ _ _ ha
Iio_ae_eq_Iic' (α := αᵒᵈ) ha
#align measure_theory.Ioi_ae_eq_Ici' MeasureTheory.Ioi_ae_eq_Ici'

theorem Ioo_ae_eq_Ioc' (hb : μ {b} = 0) : Ioo a b =ᵐ[μ] Ioc a b :=
Expand Down
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