Theorems · Theorem · functional analysis

MeasureTheory.ae_bdd_liminf_atTop_rpow_of_eLpNorm_bdd

∀ {α : Type u_1} {E : Type u_4} {m0 : MeasurableSpace α} {μ : MeasureTheory.Measure α} [inst : NormedAddCommGroup E]
  [inst_1 : MeasurableSpace E] [OpensMeasurableSpace E] {R : NNReal} {p : ENNReal} {f : ℕ → α → E},
  (∀ (n : ℕ), Measurable (f n)) →
    (∀ (n : ℕ), MeasureTheory.eLpNorm (f n) p μ ≤ ↑R) →
      ∀ᵐ (x : α) ∂μ, Filter.liminf (fun n => ‖f n x‖ₑ ^ p.toReal) Filter.atTop < ⊤

Defined in: Mathlib.MeasureTheory.Function.LpSeminorm.Basic
Cited by: 1 results in Mathlib
Foundations: Depth 210 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: NormedAddCommGroup MeasurableSpace OpensMeasurableSpace

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Cites47

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Realstatement · cited by 25,697
NormedAddCommGroupstatement and proof · cited by 15,752
MeasurableSpacestatement and proof · cited by 13,106
MeasureTheory.Measurestatement and proof · cited by 10,939
ENNRealstatement and proof · cited by 9,879
Top.topstatement and proof · cited by 9,680
Set.ofPredproof · cited by 6,101
NNRealstatement and proof · cited by 4,310
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

Cited by1

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MeasureTheory.ae_bdd_liminf_atTop_of_eLpNorm_bddproof · cited by 1