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Theorems · Theorem · measure theory

MeasureTheory.VectorMeasure.restrict_toSignedMeasure

∀ {α : Type u_1} {mα : MeasurableSpace α} {μ : MeasureTheory.Measure α} [inst : MeasureTheory.IsFiniteMeasure μ]
  {s : Set α},
  MeasurableSet s → MeasureTheory.VectorMeasure.restrict μ.toSignedMeasure s = (μ.restrict s).toSignedMeasure
Defined in
Mathlib.MeasureTheory.VectorMeasure.Basic
Cited by
1 results in Mathlib
Foundations
Depth 197 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
MeasureTheory.IsFiniteMeasure
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Around this declaration

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

MeasureTheory.VectorMeasure.setIntegral_toSignedMeasure · cited by 1VectorMeasure.setIntegral…DFunLike.coe · cited by 62936DFunLike.coeSet · cited by 53352SetReal · cited by 25697RealMeasurableSpace · cited by 13106MeasurableSpaceMeasureTheory.Measure · cited by 10939MeasureTheory.MeasureMeasurableSet · cited by 3075MeasurableSetMeasureTheory.Measure.restrict · cited by 1646Measure.restrictMeasureTheory.IsFiniteMeasure · cited by 1078MeasureTheory.IsFiniteMea…MeasureTheory.Measure.real · cited by 530Measure.realMeasureTheory.VectorMeasure · cited by 451MeasureTheory.VectorMeasu…MeasurableSet.inter · cited by 167MeasurableSet.interMeasureTheory.VectorMeasure.restrict · cited by 139VectorMeasure.restrictMeasureTheory.VectorMeasure.ext · cited by 65VectorMeasure.extMeasureTheory.Measure.toSignedMeasure · cited by 36Measure.toSignedMeasureMeasureTheory.measureReal_restrict_apply · cited by 29MeasureTheory.measureReal…VectorMeasure.restrict_toSign…CITED BYCITES

Cites17

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Cited by1

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