Theorems · Theorem · measure theory

MeasureTheory.MemLp.eLpNormEssSup_indicator_norm_ge_eq_zero

∀ {α : Type u_1} {β : Type u_2} {m : MeasurableSpace α} {μ : MeasureTheory.Measure α} [inst : NormedAddCommGroup β]
  {f : α → β},
  MeasureTheory.MemLp f ⊤ μ →
    MeasureTheory.StronglyMeasurable f → ∃ M, MeasureTheory.eLpNormEssSup ({x | M ≤ ↑‖f x‖₊}.indicator f) μ = 0

Defined in: Mathlib.MeasureTheory.Function.UniformIntegrable
Cited by: 1 results in Mathlib
Foundations: Depth 206 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: NormedAddCommGroup

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Cites47

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

DFunLike.coeproof · cited by 62,936
Realstatement and proof · 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.ofPredstatement and proof · cited by 6,101
Norm.normproof · cited by 5,413
LE.le.transproof · cited by 3,151
Filter.Eventuallyproof · cited by 3,134
MeasureTheory.aeproof · cited by 2,352

Cited by1

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MeasureTheory.MemLp.eLpNorm_indicator_norm_ge_leproof · cited by 1