Theorems · Theorem · measure theory

MeasureTheory.integrable_average

∀ {α : Type u_1} {m : MeasurableSpace α} {μ : MeasureTheory.Measure α} {ε : Type u_8} [inst : TopologicalSpace ε]
  [inst_1 : ESeminormedAddMonoid ε] [MeasureTheory.IsFiniteMeasure μ] {f : α → ε},
  MeasureTheory.Integrable f ((μ Set.univ)⁻¹ • μ) ↔ MeasureTheory.Integrable f μ

Defined in: Mathlib.MeasureTheory.Function.L1Space.Integrable
Cited by: 0 results in Mathlib
Foundations: Depth 214 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: TopologicalSpace ESeminormedAddMonoid MeasureTheory.IsFiniteMeasure

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

DFunLike.coestatement and proof · cited by 62,936
Setstatement · cited by 53,352
TopologicalSpacestatement and proof · cited by 24,529
MeasurableSpacestatement and proof · cited by 13,106
MeasureTheory.Measurestatement and proof · cited by 10,939
ENNRealstatement · cited by 9,879
Top.topproof · cited by 9,680
Set.univstatement and proof · cited by 3,945
MeasureTheory.Integrablestatement and proof · cited by 1,367
eq_or_neproof · cited by 1,117
MeasureTheory.IsFiniteMeasurestatement and proof · cited by 1,078
smul_zeroproof · cited by 665

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