Theorems · Theorem · measure theory
blimsup_cthickening_ae_le_of_eventually_mul_le
∀ {α : Type u_1} [inst : PseudoMetricSpace α] [SecondCountableTopology α] [inst_2 : MeasurableSpace α] [BorelSpace α]
(μ : MeasureTheory.Measure α) [MeasureTheory.IsLocallyFiniteMeasure μ] [IsUnifLocDoublingMeasure μ] (p : ℕ → Prop)
{s : ℕ → Set α} {M : ℝ},
0 < M →
∀ {r₁ r₂ : ℕ → ℝ},
Filter.Tendsto r₁ Filter.atTop (nhdsWithin 0 (Set.Ioi 0)) →
(∀ᶠ (i : ℕ) in Filter.atTop, M * r₁ i ≤ r₂ i) →
Filter.blimsup (fun i => Metric.cthickening (r₁ i) (s i)) Filter.atTop p ≤ᵐ[μ]
Filter.blimsup (fun i => Metric.cthickening (r₂ i) (s i)) Filter.atTop pThis is really an auxiliary result en route to blimsup_cthickening_mul_ae_eq.
NB: The : Set α type ascription is present because of
https://github.com/leanprover-community/mathlib/issues/16932.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 221 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites39
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Realstatement and proof · cited by 25,697
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- Filter.Tendstostatement and proof · cited by 3,814
- LE.le.transproof · cited by 3,151
- Filter.Eventuallystatement and proof · cited by 3,134
- Filter.atTopstatement and proof · cited by 2,405
- MeasureTheory.aestatement and proof · cited by 2,352
- LT.lt.leproof · cited by 2,189
- MulZeroClass.mul_zeroproof · cited by 2,091
- le_reflproof · cited by 2,061
Cited by1
Results whose statement or proof uses this declaration.
- blimsup_cthickening_mul_ae_eqproof · cited by 2