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bump to nightly-2023-12-05-10
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leanprover-community-bot committed Dec 5, 2023
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6 changes: 3 additions & 3 deletions Mathbin/Dynamics/Ergodic/Conservative.lean
Expand Up @@ -61,7 +61,7 @@ returns back to `s` under some iteration of `f`. -/
structure Conservative (f : α → α)
(μ : Measure α := by exact MeasureTheory.MeasureSpace.volume) extends
QuasiMeasurePreserving f μ μ : Prop where
exists_mem_image_mem :
exists_mem_iterate_mem :
∀ ⦃s⦄, MeasurableSet s → μ s ≠ 0 → ∃ x ∈ s, ∃ (m : _) (_ : m ≠ 0), (f^[m]) x ∈ s
#align measure_theory.conservative MeasureTheory.Conservative
-/
Expand All @@ -70,7 +70,7 @@ structure Conservative (f : α → α)
/-- A self-map preserving a finite measure is conservative. -/
protected theorem MeasurePreserving.conservative [IsFiniteMeasure μ] (h : MeasurePreserving f μ μ) :
Conservative f μ :=
⟨h.QuasiMeasurePreserving, fun s hsm h0 => h.exists_mem_image_mem hsm h0⟩
⟨h.QuasiMeasurePreserving, fun s hsm h0 => h.exists_mem_iterate_mem hsm h0⟩
#align measure_theory.measure_preserving.conservative MeasureTheory.MeasurePreserving.conservative
-/

Expand All @@ -80,7 +80,7 @@ namespace Conservative
/-- The identity map is conservative w.r.t. any measure. -/
protected theorem id (μ : Measure α) : Conservative id μ :=
{ to_quasiMeasurePreserving := QuasiMeasurePreserving.id μ
exists_mem_image_mem := fun s hs h0 =>
exists_mem_iterate_mem := fun s hs h0 =>
let ⟨x, hx⟩ := nonempty_of_measure_ne_zero h0
⟨x, hx, 1, one_ne_zero, hx⟩ }
#align measure_theory.conservative.id MeasureTheory.Conservative.id
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12 changes: 6 additions & 6 deletions Mathbin/Dynamics/Ergodic/MeasurePreserving.lean
Expand Up @@ -174,10 +174,10 @@ protected theorem iterate {f : α → α} (hf : MeasurePreserving f μa μa) :

variable {μ : Measure α} {f : α → α} {s : Set α}

#print MeasureTheory.MeasurePreserving.exists_mem_image_mem_of_volume_lt_mul_volume /-
#print MeasureTheory.MeasurePreserving.exists_mem_iterate_mem_of_volume_lt_mul_volume /-
/-- If `μ univ < n * μ s` and `f` is a map preserving measure `μ`,
then for some `x ∈ s` and `0 < m < n`, `f^[m] x ∈ s`. -/
theorem exists_mem_image_mem_of_volume_lt_mul_volume (hf : MeasurePreserving f μ μ)
theorem exists_mem_iterate_mem_of_volume_lt_mul_volume (hf : MeasurePreserving f μ μ)
(hs : MeasurableSet s) {n : ℕ} (hvol : μ (univ : Set α) < n * μ s) :
∃ x ∈ s, ∃ m ∈ Ioo 0 n, (f^[m]) x ∈ s :=
by
Expand All @@ -192,22 +192,22 @@ theorem exists_mem_image_mem_of_volume_lt_mul_volume (hf : MeasurePreserving f
simp only [Set.mem_preimage, Finset.mem_range] at hi hj hxi hxj
refine' ⟨(f^[i]) x, hxi, j - i, ⟨tsub_pos_of_lt hlt, lt_of_le_of_lt (j.sub_le i) hj⟩, _⟩
rwa [← iterate_add_apply, tsub_add_cancel_of_le hlt.le]
#align measure_theory.measure_preserving.exists_mem_image_mem_of_volume_lt_mul_volume MeasureTheory.MeasurePreserving.exists_mem_image_mem_of_volume_lt_mul_volume
#align measure_theory.measure_preserving.exists_mem_image_mem_of_volume_lt_mul_volume MeasureTheory.MeasurePreserving.exists_mem_iterate_mem_of_volume_lt_mul_volume
-/

/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (m «expr ≠ » 0) -/
#print MeasureTheory.MeasurePreserving.exists_mem_image_mem /-
#print MeasureTheory.MeasurePreserving.exists_mem_iterate_mem /-
/-- A self-map preserving a finite measure is conservative: if `μ s ≠ 0`, then at least one point
`x ∈ s` comes back to `s` under iterations of `f`. Actually, a.e. point of `s` comes back to `s`
infinitely many times, see `measure_theory.measure_preserving.conservative` and theorems about
`measure_theory.conservative`. -/
theorem exists_mem_image_mem [IsFiniteMeasure μ] (hf : MeasurePreserving f μ μ)
theorem exists_mem_iterate_mem [IsFiniteMeasure μ] (hf : MeasurePreserving f μ μ)
(hs : MeasurableSet s) (hs' : μ s ≠ 0) : ∃ x ∈ s, ∃ (m : _) (_ : m ≠ 0), (f^[m]) x ∈ s :=
by
rcases ENNReal.exists_nat_mul_gt hs' (measure_ne_top μ (univ : Set α)) with ⟨N, hN⟩
rcases hf.exists_mem_image_mem_of_volume_lt_mul_volume hs hN with ⟨x, hx, m, hm, hmx⟩
exact ⟨x, hx, m, hm.1.ne', hmx⟩
#align measure_theory.measure_preserving.exists_mem_image_mem MeasureTheory.MeasurePreserving.exists_mem_image_mem
#align measure_theory.measure_preserving.exists_mem_image_mem MeasureTheory.MeasurePreserving.exists_mem_iterate_mem
-/

end MeasurePreserving
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14 changes: 7 additions & 7 deletions lake-manifest.json
Expand Up @@ -4,7 +4,7 @@
[{"url": "https://github.com/leanprover/std4",
"type": "git",
"subDir": null,
"rev": "2e4a3586a8f16713f16b2d2b3af3d8e65f3af087",
"rev": "9e37a01f8590f81ace095b56710db694b5bf8ca0",
"name": "std",
"manifestFile": "lake-manifest.json",
"inputRev": "main",
Expand All @@ -13,7 +13,7 @@
{"url": "https://github.com/leanprover-community/quote4",
"type": "git",
"subDir": null,
"rev": "d3a1d25f3eba0d93a58d5d3d027ffa78ece07755",
"rev": "ccba5d35d07a448fab14c0e391c8105df6e2564c",
"name": "Qq",
"manifestFile": "lake-manifest.json",
"inputRev": "master",
Expand All @@ -22,7 +22,7 @@
{"url": "https://github.com/leanprover-community/aesop",
"type": "git",
"subDir": null,
"rev": "c7cff4551258d31c0d2d453b3f9cbca757d445f1",
"rev": "3141402ba5a5f0372d2378fd75a481bc79a74ecf",
"name": "aesop",
"manifestFile": "lake-manifest.json",
"inputRev": "master",
Expand All @@ -49,19 +49,19 @@
{"url": "https://github.com/leanprover-community/mathlib4.git",
"type": "git",
"subDir": null,
"rev": "c72f4d06b1f28f07f7d049118aa2dd1402406346",
"rev": "373c9fe4f3de086924aca34042affa7d3bb95475",
"name": "mathlib",
"manifestFile": "lake-manifest.json",
"inputRev": "c72f4d06b1f28f07f7d049118aa2dd1402406346",
"inputRev": "373c9fe4f3de086924aca34042affa7d3bb95475",
"inherited": true,
"configFile": "lakefile.lean"},
{"url": "https://github.com/leanprover-community/lean3port.git",
"type": "git",
"subDir": null,
"rev": "bd7d116652bdf500a4d1458904bec2948332787b",
"rev": "0bc6ffa967946527c6d3dd0bf2ff5b122bce1c4d",
"name": "lean3port",
"manifestFile": "lake-manifest.json",
"inputRev": "bd7d116652bdf500a4d1458904bec2948332787b",
"inputRev": "0bc6ffa967946527c6d3dd0bf2ff5b122bce1c4d",
"inherited": false,
"configFile": "lakefile.lean"}],
"name": "mathlib3port",
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4 changes: 2 additions & 2 deletions lakefile.lean
Expand Up @@ -4,7 +4,7 @@ open Lake DSL System
-- Usually the `tag` will be of the form `nightly-2021-11-22`.
-- If you would like to use an artifact from a PR build,
-- it will be of the form `pr-branchname-sha`.
def tag : String := "nightly-2023-12-03-06"
def tag : String := "nightly-2023-12-05-10"
def releaseRepo : String := "leanprover-community/mathport"
def oleanTarName : String := "mathlib3-binport.tar.gz"

Expand Down Expand Up @@ -38,7 +38,7 @@ target fetchOleans (_pkg) : Unit := do
untarReleaseArtifact releaseRepo tag oleanTarName libDir
return .nil

require lean3port from git "https://github.com/leanprover-community/lean3port.git"@"bd7d116652bdf500a4d1458904bec2948332787b"
require lean3port from git "https://github.com/leanprover-community/lean3port.git"@"0bc6ffa967946527c6d3dd0bf2ff5b122bce1c4d"

@[default_target]
lean_lib Mathbin where
Expand Down
2 changes: 1 addition & 1 deletion lean-toolchain
@@ -1 +1 @@
leanprover/lean4:v4.3.0
leanprover/lean4:v4.4.0-rc1

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