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Theorems · Theorem · measure theory

MeasureTheory.VectorMeasure.integrableOn_univ

∀ {X : Type u_2} {E : Type u_3} {F : Type u_4} {mX : MeasurableSpace X} [inst : NormedAddCommGroup E]
  [inst_1 : NormedAddCommGroup F] {μ : MeasureTheory.VectorMeasure X F} {f : X → E},
  μ.IntegrableOn f Set.univ ↔ μ.Integrable f
Defined in
Mathlib.MeasureTheory.VectorMeasure.SetIntegral
Cited by
1 results in Mathlib
Foundations
Depth 179 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
NormedAddCommGroupNormedAddCommGroup
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Around this declaration

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

MeasureTheory.VectorMeasure.Integrable.integrableOn · cited by 2Integrable.integrableOnNormedAddCommGroup · cited by 15752NormedAddCommGroupMeasurableSpace · cited by 13106MeasurableSpaceSet.univ · cited by 3945Set.univMeasureTheory.VectorMeasure · cited by 451MeasureTheory.VectorMeasu…MeasureTheory.VectorMeasure.Integrable · cited by 63VectorMeasure.IntegrableMeasureTheory.VectorMeasure.IntegrableOn · cited by 19VectorMeasure.IntegrableOnMeasureTheory.VectorMeasure.restrict_univ · cited by 4VectorMeasure.restrict_un…VectorMeasure.integrableOn_un…CITED BYCITES

Cites7

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Cited by1

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