measure_theory.covering.one_dim
⟷
Mathlib.MeasureTheory.Covering.OneDim
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.
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mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451
@@ -3,8 +3,8 @@ Copyright (c) 2022 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
-import Mathbin.MeasureTheory.Covering.DensityTheorem
-import Mathbin.MeasureTheory.Measure.Lebesgue.EqHaar
+import MeasureTheory.Covering.DensityTheorem
+import MeasureTheory.Measure.Lebesgue.EqHaar
#align_import measure_theory.covering.one_dim from "leanprover-community/mathlib"@"7e5137f579de09a059a5ce98f364a04e221aabf0"
mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345
@@ -2,15 +2,12 @@
Copyright (c) 2022 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-
-! This file was ported from Lean 3 source module measure_theory.covering.one_dim
-! leanprover-community/mathlib commit 7e5137f579de09a059a5ce98f364a04e221aabf0
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathbin.MeasureTheory.Covering.DensityTheorem
import Mathbin.MeasureTheory.Measure.Lebesgue.EqHaar
+#align_import measure_theory.covering.one_dim from "leanprover-community/mathlib"@"7e5137f579de09a059a5ce98f364a04e221aabf0"
+
/-!
# Covering theorems for Lebesgue measure in one dimension
mathlib commit https://github.com/leanprover-community/mathlib/commit/9fb8964792b4237dac6200193a0d533f1b3f7423
@@ -29,6 +29,7 @@ open scoped Topology
namespace Real
+#print Real.Icc_mem_vitaliFamily_at_right /-
theorem Icc_mem_vitaliFamily_at_right {x y : ℝ} (hxy : x < y) :
Icc x y ∈ (VitaliFamily (volume : Measure ℝ) 1).setsAt x :=
by
@@ -36,6 +37,7 @@ theorem Icc_mem_vitaliFamily_at_right {x y : ℝ} (hxy : x < y) :
refine' closed_ball_mem_vitali_family_of_dist_le_mul _ _ (by linarith)
rw [dist_comm, Real.dist_eq, abs_of_nonneg] <;> linarith
#align real.Icc_mem_vitali_family_at_right Real.Icc_mem_vitaliFamily_at_right
+-/
#print Real.tendsto_Icc_vitaliFamily_right /-
theorem tendsto_Icc_vitaliFamily_right (x : ℝ) :
@@ -51,6 +53,7 @@ theorem tendsto_Icc_vitaliFamily_right (x : ℝ) :
#align real.tendsto_Icc_vitali_family_right Real.tendsto_Icc_vitaliFamily_right
-/
+#print Real.Icc_mem_vitaliFamily_at_left /-
theorem Icc_mem_vitaliFamily_at_left {x y : ℝ} (hxy : x < y) :
Icc x y ∈ (VitaliFamily (volume : Measure ℝ) 1).setsAt y :=
by
@@ -58,6 +61,7 @@ theorem Icc_mem_vitaliFamily_at_left {x y : ℝ} (hxy : x < y) :
refine' closed_ball_mem_vitali_family_of_dist_le_mul _ _ (by linarith)
rw [Real.dist_eq, abs_of_nonneg] <;> linarith
#align real.Icc_mem_vitali_family_at_left Real.Icc_mem_vitaliFamily_at_left
+-/
#print Real.tendsto_Icc_vitaliFamily_left /-
theorem tendsto_Icc_vitaliFamily_left (x : ℝ) :
mathlib commit https://github.com/leanprover-community/mathlib/commit/7e5137f579de09a059a5ce98f364a04e221aabf0
@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
! This file was ported from Lean 3 source module measure_theory.covering.one_dim
-! leanprover-community/mathlib commit fd5edc43dc4f10b85abfe544b88f82cf13c5f844
+! leanprover-community/mathlib commit 7e5137f579de09a059a5ce98f364a04e221aabf0
! Please do not edit these lines, except to modify the commit id
! if you have ported upstream changes.
-/
@@ -14,6 +14,9 @@ import Mathbin.MeasureTheory.Measure.Lebesgue.EqHaar
/-!
# Covering theorems for Lebesgue measure in one dimension
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
We have a general theory of covering theorems for doubling measures, developed notably
in `density_theorems.lean`. In this file, we expand the API for this theory in one dimension,
by showing that intervals belong to the relevant Vitali family.
mathlib commit https://github.com/leanprover-community/mathlib/commit/58a272265b5e05f258161260dd2c5d247213cbd3
@@ -34,6 +34,7 @@ theorem Icc_mem_vitaliFamily_at_right {x y : ℝ} (hxy : x < y) :
rw [dist_comm, Real.dist_eq, abs_of_nonneg] <;> linarith
#align real.Icc_mem_vitali_family_at_right Real.Icc_mem_vitaliFamily_at_right
+#print Real.tendsto_Icc_vitaliFamily_right /-
theorem tendsto_Icc_vitaliFamily_right (x : ℝ) :
Tendsto (fun y => Icc x y) (𝓝[>] x) ((VitaliFamily (volume : Measure ℝ) 1).filterAt x) :=
by
@@ -45,6 +46,7 @@ theorem tendsto_Icc_vitaliFamily_right (x : ℝ) :
rw [closed_ball_eq_Icc]
exact Icc_subset_Icc (by linarith) hy.2
#align real.tendsto_Icc_vitali_family_right Real.tendsto_Icc_vitaliFamily_right
+-/
theorem Icc_mem_vitaliFamily_at_left {x y : ℝ} (hxy : x < y) :
Icc x y ∈ (VitaliFamily (volume : Measure ℝ) 1).setsAt y :=
@@ -54,6 +56,7 @@ theorem Icc_mem_vitaliFamily_at_left {x y : ℝ} (hxy : x < y) :
rw [Real.dist_eq, abs_of_nonneg] <;> linarith
#align real.Icc_mem_vitali_family_at_left Real.Icc_mem_vitaliFamily_at_left
+#print Real.tendsto_Icc_vitaliFamily_left /-
theorem tendsto_Icc_vitaliFamily_left (x : ℝ) :
Tendsto (fun y => Icc y x) (𝓝[<] x) ((VitaliFamily (volume : Measure ℝ) 1).filterAt x) :=
by
@@ -65,6 +68,7 @@ theorem tendsto_Icc_vitaliFamily_left (x : ℝ) :
rw [closed_ball_eq_Icc]
exact Icc_subset_Icc hy.1 (by linarith)
#align real.tendsto_Icc_vitali_family_left Real.tendsto_Icc_vitaliFamily_left
+-/
end Real
mathlib commit https://github.com/leanprover-community/mathlib/commit/5f25c089cb34db4db112556f23c50d12da81b297
@@ -38,10 +38,10 @@ theorem tendsto_Icc_vitaliFamily_right (x : ℝ) :
Tendsto (fun y => Icc x y) (𝓝[>] x) ((VitaliFamily (volume : Measure ℝ) 1).filterAt x) :=
by
refine' (VitaliFamily.tendsto_filterAt_iff _).2 ⟨_, _⟩
- · filter_upwards [self_mem_nhdsWithin]with y hy using Icc_mem_vitali_family_at_right hy
+ · filter_upwards [self_mem_nhdsWithin] with y hy using Icc_mem_vitali_family_at_right hy
· intro ε εpos
have : x ∈ Ico x (x + ε) := ⟨le_refl _, by linarith⟩
- filter_upwards [Icc_mem_nhdsWithin_Ioi this]with y hy
+ filter_upwards [Icc_mem_nhdsWithin_Ioi this] with y hy
rw [closed_ball_eq_Icc]
exact Icc_subset_Icc (by linarith) hy.2
#align real.tendsto_Icc_vitali_family_right Real.tendsto_Icc_vitaliFamily_right
@@ -58,10 +58,10 @@ theorem tendsto_Icc_vitaliFamily_left (x : ℝ) :
Tendsto (fun y => Icc y x) (𝓝[<] x) ((VitaliFamily (volume : Measure ℝ) 1).filterAt x) :=
by
refine' (VitaliFamily.tendsto_filterAt_iff _).2 ⟨_, _⟩
- · filter_upwards [self_mem_nhdsWithin]with y hy using Icc_mem_vitali_family_at_left hy
+ · filter_upwards [self_mem_nhdsWithin] with y hy using Icc_mem_vitali_family_at_left hy
· intro ε εpos
have : x ∈ Ioc (x - ε) x := ⟨by linarith, le_refl _⟩
- filter_upwards [Icc_mem_nhdsWithin_Iio this]with y hy
+ filter_upwards [Icc_mem_nhdsWithin_Iio this] with y hy
rw [closed_ball_eq_Icc]
exact Icc_subset_Icc hy.1 (by linarith)
#align real.tendsto_Icc_vitali_family_left Real.tendsto_Icc_vitaliFamily_left
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -22,7 +22,7 @@ by showing that intervals belong to the relevant Vitali family.
open Set MeasureTheory IsUnifLocDoublingMeasure Filter
-open Topology
+open scoped Topology
namespace Real
mathlib commit https://github.com/leanprover-community/mathlib/commit/f51de8769c34652d82d1c8e5f8f18f8374782bed
@@ -4,12 +4,12 @@ Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
! This file was ported from Lean 3 source module measure_theory.covering.one_dim
-! leanprover-community/mathlib commit 5f6e827d81dfbeb6151d7016586ceeb0099b9655
+! leanprover-community/mathlib commit fd5edc43dc4f10b85abfe544b88f82cf13c5f844
! Please do not edit these lines, except to modify the commit id
! if you have ported upstream changes.
-/
import Mathbin.MeasureTheory.Covering.DensityTheorem
-import Mathbin.MeasureTheory.Measure.HaarLebesgue
+import Mathbin.MeasureTheory.Measure.Lebesgue.EqHaar
/-!
# Covering theorems for Lebesgue measure in one dimension
mathlib commit https://github.com/leanprover-community/mathlib/commit/d95bef0d215ea58c0fd7bbc4b151bf3fe952c095
@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
! This file was ported from Lean 3 source module measure_theory.covering.one_dim
-! leanprover-community/mathlib commit f2ce6086713c78a7f880485f7917ea547a215982
+! leanprover-community/mathlib commit 5f6e827d81dfbeb6151d7016586ceeb0099b9655
! Please do not edit these lines, except to modify the commit id
! if you have ported upstream changes.
-/
@@ -20,7 +20,7 @@ by showing that intervals belong to the relevant Vitali family.
-/
-open Set MeasureTheory IsDoublingMeasure Filter
+open Set MeasureTheory IsUnifLocDoublingMeasure Filter
open Topology
mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc
@@ -2,15 +2,12 @@
Copyright (c) 2022 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-
-! This file was ported from Lean 3 source module measure_theory.covering.one_dim
-! leanprover-community/mathlib commit fd5edc43dc4f10b85abfe544b88f82cf13c5f844
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathlib.MeasureTheory.Covering.DensityTheorem
import Mathlib.MeasureTheory.Measure.Lebesgue.EqHaar
+#align_import measure_theory.covering.one_dim from "leanprover-community/mathlib"@"fd5edc43dc4f10b85abfe544b88f82cf13c5f844"
+
/-!
# Covering theorems for Lebesgue measure in one dimension
The unported dependencies are
algebra.order.module
init.core
linear_algebra.free_module.finite.rank
algebra.order.monoid.cancel.defs
algebra.abs
algebra.group_power.lemmas
init.data.list.basic
linear_algebra.free_module.rank
algebra.order.monoid.cancel.basic
init.data.list.default
topology.subset_properties
init.logic
The following 1 dependencies have changed in mathlib3 since they were ported, which may complicate porting this file