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Theorems · Theorem · measure theory

MeasureTheory.integrable_zero

∀ (α : Type u_1) {m : MeasurableSpace α} (ε' : Type u_8) [inst : TopologicalSpace ε'] [inst_1 : ESeminormedAddMonoid ε']
  (μ : MeasureTheory.Measure α), MeasureTheory.Integrable 0 μ
Defined in
Mathlib.MeasureTheory.Function.L1Space.Integrable
Cited by
22 results in Mathlib
Foundations
Depth 198 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
TopologicalSpaceESeminormedAddMonoid

Around this declaration

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

MeasureTheory.integrable_condExp · cited by 28MeasureTheory.integrable_…MeasureTheory.integrable_finsetSum' · cited by 10MeasureTheory.integrable_…MeasureTheory.condExp_zero · cited by 9MeasureTheory.condExp_zeroMeasureTheory.condExp_nonneg · cited by 7MeasureTheory.condExp_non…MeasureTheory.setToFun_zero · cited by 6MeasureTheory.setToFun_ze…MeasureTheory.withDensityᵥ_zero · cited by 5MeasureTheory.withDensity…InformationTheory.klDiv_self · cited by 4InformationTheory.klDiv_s…MeasureTheory.SimpleFunc.integrable_approxOn_range · cited by 4SimpleFunc.integrable_app…MeasureTheory.SignedMeasure.eq_singularPart · cited by 3SignedMeasure.eq_singular…MeasureTheory.integrableOn_zero · cited by 3MeasureTheory.integrableO…MeasureTheory.locallyIntegrable_zero · cited by 2MeasureTheory.locallyInte…MeasureTheory.tendsto_integral_approxOn_of_measurable_of_range_subset · cited by 2MeasureTheory.tendsto_int…MeasureTheory.condExp_ae_eq_restrict_zero · cited by 2MeasureTheory.condExp_ae_…MeasureTheory.Integrable.of_subsingleton_codomain · cited by 1Integrable.of_subsingleto…MeasureTheory.SignedMeasure.haveLebesgueDecomposition_mk · cited by 1SignedMeasure.haveLebesgu…TopologicalSpace · cited by 24529TopologicalSpaceMeasurableSpace · cited by 13106MeasurableSpaceMeasureTheory.Measure · cited by 10939MeasureTheory.MeasureMeasureTheory.Integrable · cited by 1367MeasureTheory.IntegrableESeminormedAddMonoid · cited by 133ESeminormedAddMonoidMeasureTheory.integrable_zeroCITED BYCITES

Cites5

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Cited by22

Results whose statement or proof uses this declaration.