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Theorems · Theorem · measure theory

MeasureTheory.lintegral_pos_iff_support

∀ {α : Type u_1} {m : MeasurableSpace α} {μ : MeasureTheory.Measure α} {f : α → ENNReal},
  Measurable f → (0 < ∫⁻ (a : α), f a ∂μ ↔ 0 < μ (Function.support f))
Defined in
Mathlib.MeasureTheory.Integral.Lebesgue.Basic
Cited by
1 results in Mathlib
Foundations
Depth 202 from the axioms · uses propext, Classical.choice, Quot.sound
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MeasureTheory.setLIntegral_pos_iff · cited by 0MeasureTheory.setLIntegra…DFunLike.coe · cited by 62936DFunLike.coeSet · cited by 53352SetMeasurableSpace · cited by 13106MeasurableSpaceMeasureTheory.Measure · cited by 10939MeasureTheory.MeasureENNReal · cited by 9879ENNRealSet.ofPred · cited by 6101Set.ofPredMeasurable · cited by 1499MeasurableMeasureTheory.lintegral · cited by 1152MeasureTheory.lintegralFunction.support · cited by 610Function.supportMeasureTheory.lintegral_pos_i…CITED BYCITES

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