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Theorems · Theorem · measure theory

MeasureTheory.VectorMeasure.restrict_inter_add_diff

Deprecated since 2026-06-03Use MeasureTheory.VectorMeasure.restrict_inter_add_sdiff instead.

∀ {α : Type u_1} {mα : MeasurableSpace α} {M : Type u_4} [inst : TopologicalSpace M] [inst_1 : AddCommMonoid M]
  [T2Space M] [inst_3 : ContinuousAdd M] {v : MeasureTheory.VectorMeasure α M} {s t : Set α},
  MeasurableSet s → MeasurableSet t → v.restrict (s ∩ t) + v.restrict (s \ t) = v.restrict s

Alias of MeasureTheory.VectorMeasure.restrict_inter_add_sdiff.

Defined in
Mathlib.MeasureTheory.VectorMeasure.Basic
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0 results in Mathlib
Foundations
Depth 96 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
TopologicalSpaceAddCommMonoidT2SpaceContinuousAdd
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Set · cited by 53352SetTopologicalSpace · cited by 24529TopologicalSpaceMeasurableSpace · cited by 13106MeasurableSpaceAddCommMonoid · cited by 12281AddCommMonoidMeasurableSet · cited by 3075MeasurableSetT2Space · cited by 1351T2SpaceContinuousAdd · cited by 777ContinuousAddMeasureTheory.VectorMeasure · cited by 451MeasureTheory.VectorMeasu…MeasureTheory.VectorMeasure.restrict · cited by 139VectorMeasure.restrictMeasureTheory.VectorMeasure.restrict_inter_add_sdiff · cited by 3VectorMeasure.restrict_in…VectorMeasure.restrict_inter_…CITED BYCITES

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