Skip to content

Commit 948086a

Browse files
authored
chore: drop the aestronglyMeasurable field in BoundedFiniteSupport (#272)
as it's already contained in the `MemLp` assumption. Also, I ran the linter on the project, and fixed a few of the things it mentioned.
1 parent 9f034d7 commit 948086a

File tree

13 files changed

+63
-64
lines changed

13 files changed

+63
-64
lines changed

Carleson/Antichain/AntichainTileCount.lean

Lines changed: 0 additions & 1 deletion
Original file line numberDiff line numberDiff line change
@@ -96,7 +96,6 @@ lemma tile_reach {ϑ : Θ X} {N : ℕ} {p p' : 𝔓 X} (hp : dist_(p) (𝒬 p)
9696
← zpow_zero (2 : ℝ)]
9797
rw [Nat.cast_mul, Nat.cast_ofNat, Nat.cast_pow]
9898
gcongr --uses h12
99-
have : (2 : ℝ)^a = 2^(a : ℤ) := by rw [@zpow_natCast]
10099
ring_nf
101100
nlinarith only
102101
_ = (4 * 2 ^ (2 - 5 * (a : ℤ) ^ 2 - 2 * ↑a)) * (D * D ^ 𝔰 p) := by ring

Carleson/Calculations.lean

Lines changed: 6 additions & 8 deletions
Original file line numberDiff line numberDiff line change
@@ -199,18 +199,17 @@ lemma calculation_12 (s : ℝ) :
199199
have rightSide := calc 2 ^ (200 * a ^ 2 + 4) * (8 * ((2 : ℝ) ^ (100 * a ^ 2)) ^ s)
200200
_ = 2 ^ (200*a^2 + 4) * ((2^3)*((2 ^ (100 * a ^ 2)) ^ s)) := by
201201
norm_num
202-
_ = 2 ^ (200*a^2 + 4) * ( 2^3 * 2 ^ (100 * a ^ 2 * s) ) := by
202+
_ = 2 ^ (200*a^2 + 4) * ( 2^3 * 2 ^ (100 * a ^ 2 * s) ) := by
203203
rw [Real.rpow_mul (x:=2) (by positivity)]
204204
norm_cast
205-
_ = 2 ^ (200*a^2 + 4) * 2 ^ (3 + 100 * a ^ 2 * s) := by
205+
_ = 2 ^ (200*a^2 + 4) * 2 ^ (3 + 100 * a ^ 2 * s) := by
206206
have fact := Real.rpow_add (x:=2) (y:= 3) (z:= 100 * a ^ 2 * s) (by positivity)
207207
rw_mod_cast [fact]
208-
_ = 2^( 200*a^2 + 4 + (3 + 100 * a ^ 2 * s) ) := by
209-
have fact := Real.rpow_add (x:=2) (y:= 200*a^2 + 4) (z:= 3 + 100 * a ^ 2 * s) (by positivity)
208+
_ = 2 ^ (200*a^2 + 4 + (3 + 100 * a ^ 2 * s)) := by
210209
nth_rw 2 [Real.rpow_add]
211210
norm_cast
212211
positivity
213-
_ = 2^(7 + ((100 * a^2 * s) + (100 * a^2 * 2))) := by
212+
_ = 2 ^ (7 + ((100 * a^2 * s) + (100 * a^2 * 2))) := by
214213
congrm 2 ^ ?_
215214
linarith
216215
rw_mod_cast [leftSide]
@@ -222,7 +221,7 @@ lemma calculation_13 : (2 : ℝ) ^ (200 * (a^3) + 4*a) = (defaultA a) ^ (200*a^2
222221
rw_mod_cast [← fact]
223222
ring
224223

225-
lemma calculation_14 [PseudoMetricSpace X] [ProofData a q K σ₁ σ₂ F G] (n: ℕ) :
224+
lemma calculation_14 [PseudoMetricSpace X] [ProofData a q K σ₁ σ₂ F G] (n: ℕ) :
226225
(2 : ℝ) ^ ((Z : ℝ) * n / 2 - 201 * a ^ 3) ≤ 2 ^ ((Z : ℝ) * n / 2 - (200 * a ^ 3 + 4 * a)) := by
227226
gcongr
228227
· linarith
@@ -240,7 +239,7 @@ lemma calculation_15 [PseudoMetricSpace X] [ProofData a q K σ₁ σ₂ F G]
240239
2 ^ (zon - (200 * a^3 + 4*a)) ≤ dist := by
241240
rw [Real.rpow_sub (hx := by linarith)]
242241
rw [show dist = 2 ^ (200 * a ^ 3 + 4 * a) * dist / 2 ^ (200 * a ^ 3 + 4 * a) by simp]
243-
have := (div_le_div_iff_of_pos_right (c := 2 ^ (200 * a ^ 3 + 4 * a)) (hc := by have aIsBig := four_le_a X; positivity)).mpr h
242+
have := (div_le_div_iff_of_pos_right (c := 2 ^ (200 * a ^ 3 + 4 * a)) (hc := by positivity)).mpr h
244243
exact_mod_cast this
245244

246245
lemma calculation_16 [PseudoMetricSpace X] [ProofData a q K σ₁ σ₂ F G] (s: ℤ) :
@@ -266,4 +265,3 @@ lemma calculation_7_7_4 [PseudoMetricSpace X] [ProofData a q K σ₁ σ₂ F G]
266265
· norm_num
267266
omega
268267
exact Nat.mul_le_mul this (Nat.le_add_left 1 n)
269-

Carleson/Classical/Helper.lean

Lines changed: 22 additions & 18 deletions
Original file line numberDiff line numberDiff line change
@@ -10,12 +10,13 @@ theorem Real.volume_uIoc {a b : ℝ} : volume (Set.uIoc a b) = ENNReal.ofReal |b
1010
/- Cf. proof of Real.volume_interval-/
1111
rw [Set.uIoc, volume_Ioc, max_sub_min_eq_abs]
1212

13-
lemma intervalIntegral.integral_conj' {μ : Measure ℝ} {𝕜 : Type} [RCLike 𝕜] {f : ℝ → 𝕜} {a b : ℝ}:
13+
lemma intervalIntegral.integral_conj' {μ : Measure ℝ} {𝕜 : Type*} [RCLike 𝕜] {f : ℝ → 𝕜} {a b : ℝ} :
1414
∫ x in a..b, (starRingEnd 𝕜) (f x) ∂μ = (starRingEnd 𝕜) (∫ x in a..b, f x ∂μ) := by
1515
rw [intervalIntegral_eq_integral_uIoc, integral_conj, intervalIntegral_eq_integral_uIoc,
1616
RCLike.real_smul_eq_coe_mul, RCLike.real_smul_eq_coe_mul, map_mul, RCLike.conj_ofReal]
1717

18-
lemma intervalIntegrable_of_bdd {a b : ℝ} {δ : ℝ} {g : ℝ → ℂ} (measurable_g : Measurable g) (bddg : ∀ x, ‖g x‖ ≤ δ) : IntervalIntegrable g volume a b := by
18+
lemma intervalIntegrable_of_bdd {a b : ℝ} {δ : ℝ} {g : ℝ → ℂ} (measurable_g : Measurable g)
19+
(bddg : ∀ x, ‖g x‖ ≤ δ) : IntervalIntegrable g volume a b := by
1920
apply @IntervalIntegrable.mono_fun' _ _ _ _ _ _ (fun _ ↦ δ)
2021
· exact intervalIntegrable_const
2122
· exact measurable_g.aestronglyMeasurable
@@ -24,24 +25,26 @@ lemma intervalIntegrable_of_bdd {a b : ℝ} {δ : ℝ} {g : ℝ → ℂ} (measur
2425
rw [Subtype.forall]
2526
exact fun x _ ↦ bddg x
2627

27-
lemma IntervalIntegrable.bdd_mul {F : Type} [NormedDivisionRing F] {f g : ℝ → F} {a b : ℝ} {μ : Measure ℝ}
28-
(hg : IntervalIntegrable g μ a b) (hm : AEStronglyMeasurable f μ) (hfbdd : ∃ C, ∀ x, ‖f x‖ ≤ C) : IntervalIntegrable (fun x ↦ f x * g x) μ a b := by
28+
lemma IntervalIntegrable.bdd_mul {F : Type*} [NormedDivisionRing F] {f g : ℝ → F} {a b : ℝ}
29+
{μ : Measure ℝ} (hg : IntervalIntegrable g μ a b) (hm : AEStronglyMeasurable f μ)
30+
(hfbdd : ∃ C, ∀ x, ‖f x‖ ≤ C) : IntervalIntegrable (fun x ↦ f x * g x) μ a b := by
2931
rw [intervalIntegrable_iff, IntegrableOn]
3032
apply Integrable.bdd_mul _ hm.restrict hfbdd
3133
rwa [← IntegrableOn, ← intervalIntegrable_iff]
3234

33-
lemma IntervalIntegrable.mul_bdd {F : Type} [NormedField F] {f g : ℝ → F} {a b : ℝ} {μ : Measure ℝ}
34-
(hf : IntervalIntegrable f μ a b) (hm : AEStronglyMeasurable g μ) (hgbdd : ∃ C, ∀ x, ‖g x‖ ≤ C) : IntervalIntegrable (fun x ↦ f x * g x) μ a b := by
35+
lemma IntervalIntegrable.mul_bdd {F : Type*} [NormedField F] {f g : ℝ → F} {a b : ℝ}
36+
{μ : Measure ℝ} (hf : IntervalIntegrable f μ a b) (hm : AEStronglyMeasurable g μ)
37+
(hgbdd : ∃ C, ∀ x, ‖g x‖ ≤ C) : IntervalIntegrable (fun x ↦ f x * g x) μ a b := by
3538
conv => pattern (fun x ↦ f x * g x); ext x; rw [mul_comm]
3639
exact hf.bdd_mul hm hgbdd
3740

38-
lemma IntegrableOn.sub {α : Type} {β : Type} {m : MeasurableSpace α}
39-
{μ : Measure α} [NormedAddCommGroup β] {s : Set α} {f g : α → β} (hf : IntegrableOn f s μ) (hg : IntegrableOn g s μ) : IntegrableOn (f - g) s μ := by
41+
lemma IntegrableOn.sub {α : Type*} {β : Type*} {m : MeasurableSpace α} {μ : Measure α}
42+
[NormedAddCommGroup β] {s : Set α} {f g : α → β}
43+
(hf : IntegrableOn f s μ) (hg : IntegrableOn g s μ) : IntegrableOn (f - g) s μ := by
4044
apply Integrable.sub <;> rwa [← IntegrableOn]
4145

42-
43-
lemma ConditionallyCompleteLattice.le_biSup {α : Type} [ConditionallyCompleteLinearOrder α] {ι : Type} [Nonempty ι]
44-
{f : ι → α} {s : Set ι} {a : α} (hfs : BddAbove (f '' s)) (ha : ∃ i ∈ s, f i = a) :
46+
lemma ConditionallyCompleteLattice.le_biSup {α : Type*} [ConditionallyCompleteLinearOrder α]
47+
{ι : Type*} {f : ι → α} {s : Set ι} {a : α} (hfs : BddAbove (f '' s)) (ha : ∃ i ∈ s, f i = a) :
4548
a ≤ ⨆ i ∈ s, f i := by
4649
apply ConditionallyCompleteLattice.le_csSup
4750
· --TODO: improve this
@@ -75,15 +78,16 @@ lemma ConditionallyCompleteLattice.le_biSup {α : Type} [ConditionallyCompleteLi
7578
simp only [Set.mem_range, exists_prop] at hx
7679
rwa [hx.2] at fia
7780

78-
79-
/-Adapted from mathlib Function.Periodic.exists_mem_Ico₀-/
80-
theorem Function.Periodic.exists_mem_Ico₀' {α : Type} {β : Type} {f : α → β} {c : α}
81-
[LinearOrderedAddCommGroup α] [Archimedean α] (h : Periodic f c) (hc : 0 < c) (x : α) : ∃ (n : ℤ), (x - n • c) ∈ Set.Ico 0 c ∧ f x = f (x - n • c) :=
81+
/- Adapted from mathlib Function.Periodic.exists_mem_Ico₀ -/
82+
theorem Function.Periodic.exists_mem_Ico₀' {α β : Type*} {f : α → β} {c : α}
83+
[LinearOrderedAddCommGroup α] [Archimedean α] (h : Periodic f c) (hc : 0 < c) (x : α) :
84+
∃ (n : ℤ), (x - n • c) ∈ Set.Ico 0 c ∧ f x = f (x - n • c) :=
8285
let ⟨n, H, _⟩ := existsUnique_zsmul_near_of_pos' hc x
8386
⟨n, H, (h.sub_zsmul_eq n).symm⟩
8487

85-
/-Adapted from mathlib Function.Periodic.exists_mem_Ico₀-/
86-
theorem Function.Periodic.exists_mem_Ico' {α : Type} {β : Type} {f : α → β} {c : α}
87-
[LinearOrderedAddCommGroup α] [Archimedean α] (h : Periodic f c) (hc : 0 < c) (x a: α) : ∃ (n : ℤ), (x - n • c) ∈ Set.Ico a (a + c) ∧ f x = f (x - n • c) :=
88+
/- Adapted from mathlib Function.Periodic.exists_mem_Ico₀ -/
89+
theorem Function.Periodic.exists_mem_Ico' {α β : Type*} {f : α → β} {c : α}
90+
[LinearOrderedAddCommGroup α] [Archimedean α] (h : Periodic f c) (hc : 0 < c) (x a: α) :
91+
∃ (n : ℤ), (x - n • c) ∈ Set.Ico a (a + c) ∧ f x = f (x - n • c) :=
8892
let ⟨n, H, _⟩ := existsUnique_sub_zsmul_mem_Ico hc x a
8993
⟨n, H, (h.sub_zsmul_eq n).symm⟩

Carleson/Defs.lean

Lines changed: 1 addition & 1 deletion
Original file line numberDiff line numberDiff line change
@@ -320,7 +320,7 @@ lemma enorm_K_sub_le [ProperSpace X] [IsFiniteMeasureOnCompacts (volume : Measur
320320

321321
lemma integrableOn_K_Icc [IsOpenPosMeasure (volume : Measure X)]
322322
[IsFiniteMeasureOnCompacts (volume : Measure X)] [ProperSpace X]
323-
[Regular (volume : Measure X)] [IsOneSidedKernel a K] {x : X} {r R : ℝ} (hr : r > 0) :
323+
[IsOneSidedKernel a K] {x : X} {r R : ℝ} (hr : r > 0) :
324324
IntegrableOn (K x) {y | dist x y ∈ Icc r R} volume := by
325325
use Measurable.aestronglyMeasurable (measurable_K_right x)
326326
rw [hasFiniteIntegral_def]

Carleson/ForestOperator/Forests.lean

Lines changed: 1 addition & 2 deletions
Original file line numberDiff line numberDiff line change
@@ -373,8 +373,7 @@ theorem forest_operator' {n : ℕ} (𝔉 : Forest X n) {f : X → ℂ} {A : Set
373373
fun_prop
374374
· apply h'A.subset support_indicator_subset
375375
gcongr
376-
· have := (q_mem_Ioc (X := X)).2
377-
simp only [sub_nonneg, ge_iff_le, inv_le_inv₀ zero_lt_two (q_pos X)]
376+
· simp only [sub_nonneg, ge_iff_le, inv_le_inv₀ zero_lt_two (q_pos X)]
378377
exact (q_mem_Ioc (X := X)).2
379378
· exact le_rfl
380379
calc

Carleson/ForestOperator/PointwiseEstimate.lean

Lines changed: 1 addition & 3 deletions
Original file line numberDiff line numberDiff line change
@@ -714,9 +714,7 @@ lemma second_tree_pointwise (hu : u ∈ t) (hL : L ∈ 𝓛 (t u)) (hx : x ∈ L
714714
have x'p : x' ∈ 𝓘 p := (Grid.le_def.mp Lle).1 hx'
715715
refine le_iSup₂_of_le (𝓘 p) x'p <| le_iSup₂_of_le x xp <|
716716
le_iSup₂_of_le (𝔰 p') ⟨s_ineq, scale_mem_Icc.2⟩ <| le_iSup_of_le ?_ ?_
717-
· have : ((D : ℝ≥0∞) ^ (𝔰 p' - 1)).toReal = D ^ (s₂ - 1) := by
718-
rw [sp', ← ENNReal.toReal_zpow]; simp
719-
apply le_upperRadius; convert d1
717+
· apply le_upperRadius; convert d1
720718
· convert le_rfl; change (Icc (𝔰 p) _).toFinset = _; rw [sp, sp']
721719
apply subset_antisymm
722720
· rw [← Finset.toFinset_coe (t.σ u x), toFinset_subset_toFinset]

Carleson/ForestOperator/RemainingTiles.lean

Lines changed: 1 addition & 1 deletion
Original file line numberDiff line numberDiff line change
@@ -229,7 +229,7 @@ lemma square_function_count (hJ : J ∈ 𝓙₆ t u₁) (s' : ℤ) :
229229
⨍⁻ x in J, (∑ I ∈ {I : Grid X | s I = s J - s' ∧ Disjoint (I : Set X) (𝓘 u₁) ∧
230230
¬ Disjoint (J : Set X) (ball (c I) (8 * D ^ s I)) },
231231
(ball (c I) (8 * D ^ s I)).indicator 1 x) ^ 2 ∂volume ≤ C7_6_4 a s' := by
232-
cases' lt_or_ge (↑S + s J) s' with hs' hs'
232+
rcases lt_or_ge (↑S + s J) s' with hs' | hs'
233233
· suffices ({I : Grid X | s I = s J - s' ∧ Disjoint (I : Set X) (𝓘 u₁) ∧
234234
¬ Disjoint (J : Set X) (ball (c I) (8 * D ^ s I)) } : Finset (Grid X)) = ∅ by
235235
rw [this]

Carleson/Psi.lean

Lines changed: 8 additions & 5 deletions
Original file line numberDiff line numberDiff line change
@@ -26,10 +26,12 @@ private lemma D_pow0' (r : ℤ) : 0 < (D : ℝ) ^ r := by positivity
2626
private lemma cDx0 {c x : ℝ} (hc : c > 0) (hx : 0 < x) : c * D * x > 0 := by positivity
2727
end
2828

29+
/-- The function `ψ` used as a basis for a dyadic partition of unity. -/
2930
def ψ (D : ℕ) (x : ℝ) : ℝ :=
3031
max 0 <| min 1 <| min (4 * D * x - 1) (2 - 4 * x)
3132

32-
set_option hygiene false
33+
set_option hygiene false in
34+
@[inherit_doc]
3335
scoped[ShortVariables] notation "ψ" => ψ (defaultD a)
3436

3537
lemma zero_le_ψ (D : ℕ) (x : ℝ) : 0 ≤ ψ D x :=
@@ -140,8 +142,9 @@ lemma lipschitzWith_ψ' (hD : 1 ≤ D) (a b : ℝ) : ‖ψ D a - ψ D b‖ ≤ 4
140142
repeat rw [ENNReal.toReal_ofReal (by positivity)] at lipschitz
141143
norm_cast
142144

143-
/- the one or two numbers `s` where `ψ (D ^ (-s) * x)` is possibly nonzero -/
144-
variable (D) in def nonzeroS (x : ℝ) : Finset ℤ :=
145+
variable (D) in
146+
/-- the one or two numbers `s` where `ψ (D ^ (-s) * x)` is possibly nonzero -/
147+
def nonzeroS (x : ℝ) : Finset ℤ :=
145148
Finset.Icc ⌊(1 + logb D (2 * x))⌋ ⌈logb D (4 * x)⌉
146149

147150
---------------------------------------------
@@ -519,7 +522,6 @@ lemma nnnorm_Ks_le {s : ℤ} {x y : X} :
519522
/-- Needed for Lemma 7.5.5. -/
520523
lemma enorm_Ks_le {s : ℤ} {x y : X} :
521524
‖Ks s x y‖ₑ ≤ C2_1_3 a / volume (ball x (D ^ s)) * ‖ψ (D ^ (-s) * dist x y)‖ₑ := by
522-
have : 0 ≤ C2_1_3 a / volume (ball x (D ^ s)) := by unfold C2_1_3; positivity
523525
by_cases hK : Ks s x y = 0
524526
· rw [hK, enorm_zero]; exact zero_le _
525527
rw [Ks, enorm_mul]; nth_rw 2 [← enorm_norm]; rw [norm_real, enorm_norm]
@@ -649,7 +651,8 @@ private lemma norm_Ks_sub_Ks_le₀₀ {s : ℤ} {x y y' : X} (hK : Ks s x y ≠
649651
have : (dist y y' / dist x y) ^ (a : ℝ)⁻¹ ≤ (dist y y' / D ^ s * (4 * D)) ^ (a : ℝ)⁻¹ := by
650652
apply Real.rpow_le_rpow (div_nonneg dist_nonneg dist_nonneg) this (by positivity)
651653
rw [Real.mul_rpow (div_nonneg dist_nonneg (Ds0 X s).le) (fourD0 D1).le] at this
652-
apply le_trans <| mul_le_mul this (div_vol_le₀ C_K_pos_real hK) (by simp; positivity) (by positivity)
654+
apply le_trans <| mul_le_mul this (div_vol_le₀ C_K_pos_real hK)
655+
(by simp only [C_K, coe_rpow, NNReal.coe_ofNat, defaultA]; positivity) (by positivity)
653656
rw [(by ring : (dist y y' / D ^ s) ^ (a : ℝ)⁻¹ * (4 * D) ^ (a : ℝ)⁻¹ *
654657
(2 ^ (2 * a + 100 * a ^ 3) * C_K a / volume.real (ball x (D ^ s))) =
655658
(4 * D) ^ (a : ℝ)⁻¹ * 2 ^ (2 * a + 100 * a ^ 3) * C_K a / volume.real (ball x (D ^ s)) *

Carleson/TileExistence.lean

Lines changed: 11 additions & 14 deletions
Original file line numberDiff line numberDiff line change
@@ -186,7 +186,7 @@ lemma chain_property_set_has_bound (k : ℤ):
186186
· exact fun s a ↦ subset_iUnion₂_of_subset s a fun ⦃a⦄ a ↦ a
187187

188188
variable (X) in
189-
def zorn_apply_maximal_set (k : ℤ):
189+
lemma zorn_apply_maximal_set (k : ℤ):
190190
∃ s ∈ property_set X k, ∀ s' ∈ property_set X k, s ⊆ s' → s' = s := by
191191
have := zorn_subset (property_set X k) (chain_property_set_has_bound X k)
192192
simp_rw [maximal_iff] at this; convert this using 6; exact eq_comm
@@ -300,20 +300,20 @@ lemma I_induction_proof {k:ℤ} (hk:-S ≤ k) (hneq : ¬ k = -S) : -S ≤ k - 1
300300
linarith [lt_of_le_of_ne hk fun a_1 ↦ hneq (id a_1.symm)]
301301

302302
mutual
303-
def I1 {k:ℤ} (hk : -S ≤ k) (y : Yk X k) : Set X :=
303+
def I1 {k : ℤ} (hk : -S ≤ k) (y : Yk X k) : Set X :=
304304
if hk': k = -S then
305305
ball y (D^(-S:ℤ))
306306
else
307307
let hk'' : -S < k := lt_of_le_of_ne hk fun a_1 ↦ hk' (id a_1.symm)
308-
have h1: 0 ≤ S + (k - 1) := by linarith
308+
have h1 : 0 ≤ S + (k - 1) := by linarith
309309
have : (S + (k-1)).toNat < (S + k).toNat := by
310310
rw [Int.lt_toNat,Int.toNat_of_nonneg h1]
311311
linarith
312312
⋃ (y': Yk X (k-1)),
313313
⋃ (_ : y' ∈ Yk X (k-1) ↓∩ ball (y:X) (D^k)), I3 (I_induction_proof hk hk') y'
314314
termination_by (3 * (S+k).toNat, sizeOf y)
315315

316-
def I2 {k:ℤ} (hk : -S ≤ k) (y : Yk X k) : Set X :=
316+
def I2 {k : ℤ} (hk : -S ≤ k) (y : Yk X k) : Set X :=
317317
if hk': k = -S then
318318
ball y (2 * D^(-S:ℤ))
319319
else
@@ -344,25 +344,22 @@ lemma I1_subset_I3 {k : ℤ} (hk : -S ≤ k) (y:Yk X k) :
344344
left
345345
exact hi
346346

347-
lemma I1_subset_I2 {k:ℤ} (hk : -S ≤ k) (y:Yk X k) :
347+
@[nolint unusedHavesSuffices]
348+
lemma I1_subset_I2 {k : ℤ} (hk : -S ≤ k) (y : Yk X k) :
348349
I1 hk y ⊆ I2 hk y := by
349-
rw [I1,I2]
350-
if hk_s : k = -S then
351-
intro y'
352-
rw [dif_pos hk_s,dif_pos hk_s]
350+
rw [I1, I2]
351+
split_ifs with hk_s
352+
· intro y'
353353
apply ball_subset_ball
354354
nth_rw 1 [← one_mul (D^(-S:ℤ):ℝ)]
355355
gcongr
356356
norm_num
357-
else
358-
rw [dif_neg hk_s, dif_neg hk_s]
359-
simp only [iUnion_subset_iff]
357+
· simp only [iUnion_subset_iff]
360358
intro y' hy' z hz
361359
simp only [mem_iUnion, exists_prop, exists_and_left]
362360
use y'
363361
rw [and_iff_left hz]
364-
revert hy'
365-
apply ball_subset_ball
362+
apply ball_subset_ball _ hy'
366363
nth_rw 1 [← one_mul (D^k : ℝ)]
367364
gcongr
368365
norm_num

Carleson/ToMathlib/Analysis/Convolution.lean

Lines changed: 3 additions & 3 deletions
Original file line numberDiff line numberDiff line change
@@ -40,7 +40,7 @@ protected theorem AEStronglyMeasurable.convolution [NormedSpace ℝ F] [AddGroup
4040

4141
/-- This implies both of the following theorems `convolutionExists_of_memLp_memLp` and
4242
`enorm_convolution_le_eLpNorm_mul_eLpNorm`. -/
43-
lemma lintegral_enorm_convolution_integrand_le_eLpNorm_mul_eLpNorm [NormedSpace ℝ F] [AddGroup G]
43+
lemma lintegral_enorm_convolution_integrand_le_eLpNorm_mul_eLpNorm [AddGroup G]
4444
[MeasurableAdd₂ G] [MeasurableNeg G] {μ : Measure G} [SFinite μ] [μ.IsNegInvariant]
4545
[μ.IsAddLeftInvariant] {p q : ENNReal} (hpq : p.IsConjExponent q)
4646
(hL : ∀ (x y : G), ‖L (f x) (g y)‖ ≤ ‖f x‖ * ‖g y‖)
@@ -57,7 +57,7 @@ lemma lintegral_enorm_convolution_integrand_le_eLpNorm_mul_eLpNorm [NormedSpace
5757

5858
/-- If `MemLp f p μ` and `MemLp g q μ`, where `p` and `q` are Hölder conjugates, then the
5959
convolution of `f` and `g` exists everywhere. -/
60-
theorem ConvolutionExists.of_memLp_memLp [NormedSpace ℝ F] [AddGroup G] [MeasurableAdd₂ G]
60+
theorem ConvolutionExists.of_memLp_memLp [AddGroup G] [MeasurableAdd₂ G]
6161
[MeasurableNeg G] (μ : Measure G) [SFinite μ] [μ.IsNegInvariant] [μ.IsAddLeftInvariant]
6262
[μ.IsAddRightInvariant] {p q : ENNReal} (hpq : p.IsConjExponent q)
6363
(hL : ∀ (x y : G), ‖L (f x) (g y)‖ ≤ ‖f x‖ * ‖g y‖) (hf : AEStronglyMeasurable f μ)
@@ -71,7 +71,7 @@ theorem ConvolutionExists.of_memLp_memLp [NormedSpace ℝ F] [AddGroup G] [Measu
7171
by `eLpNorm f p μ * eLpNorm g q μ`. -/
7272
theorem enorm_convolution_le_eLpNorm_mul_eLpNorm [NormedSpace ℝ F] [AddGroup G]
7373
[MeasurableAdd₂ G] [MeasurableNeg G] (μ : Measure G) [SFinite μ] [μ.IsNegInvariant]
74-
[μ.IsAddLeftInvariant] [μ.IsAddRightInvariant] {p q : ENNReal} (hpq : p.IsConjExponent q)
74+
[μ.IsAddLeftInvariant] {p q : ENNReal} (hpq : p.IsConjExponent q)
7575
(hL : ∀ (x y : G), ‖L (f x) (g y)‖ ≤ ‖f x‖ * ‖g y‖)
7676
(hf : AEStronglyMeasurable f μ) (hg : AEStronglyMeasurable g μ) (x₀ : G) :
7777
‖(f ⋆[L, μ] g) x₀‖ₑ ≤ eLpNorm f p μ * eLpNorm g q μ :=

0 commit comments

Comments
 (0)