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Theorems · Theorem · measure theory

MeasureTheory.Integrable.of_finite

∀ {α : Type u_1} {β : Type u_2} {m : MeasurableSpace α} {μ : MeasureTheory.Measure α} [inst : NormedAddCommGroup β]
  [Finite α] [MeasurableSingletonClass α] [MeasureTheory.IsFiniteMeasure μ] {f : α → β}, MeasureTheory.Integrable f μ
Defined in
Mathlib.MeasureTheory.Function.L1Space.Integrable
Cited by
4 results in Mathlib
Foundations
Depth 204 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
NormedAddCommGroupFiniteMeasurableSingletonClassMeasureTheory.IsFiniteMeasure
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

PMF.integral_eq_sum · cited by 1PMF.integral_eq_sumMeasureTheory.Integrable.of_subsingleton · cited by 0Integrable.of_subsingletonZMod.dft_eq_fourier · cited by 0ZMod.dft_eq_fourierMeasureTheory.Integrable.of_isEmpty · cited by 0Integrable.of_isEmptyNormedAddCommGroup · cited by 15752NormedAddCommGroupMeasurableSpace · cited by 13106MeasurableSpaceMeasureTheory.Measure · cited by 10939MeasureTheory.MeasureFinite · cited by 3029FiniteMeasureTheory.Integrable · cited by 1367MeasureTheory.IntegrableMeasureTheory.IsFiniteMeasure · cited by 1078MeasureTheory.IsFiniteMea…MeasurableSingletonClass · cited by 230MeasurableSingletonClassMeasureTheory.AEStronglyMeasurable.of_discrete · cited by 5AEStronglyMeasurable.of_d…MeasureTheory.HasFiniteIntegral.of_finite · cited by 3HasFiniteIntegral.of_fini…Integrable.of_finiteCITED BYCITES

Cites9

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

Cited by4

Results whose statement or proof uses this declaration.