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Theorems · Theorem · measure theory

MeasureTheory.VectorMeasure.restrict_empty

∀ {α : Type u_1} {mα : MeasurableSpace α} {M : Type u_3} [inst : AddCommMonoid M] [inst_1 : TopologicalSpace M]
  (v : MeasureTheory.VectorMeasure α M), v.restrict ∅ = 0
Defined in
Mathlib.MeasureTheory.VectorMeasure.Basic
Cited by
8 results in Mathlib
Foundations
Depth 70 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
AddCommMonoidTopologicalSpace

Around this declaration

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

MeasureTheory.VectorMeasure.le_restrict_empty · cited by 1VectorMeasure.le_restrict…MeasureTheory.VectorMeasure.restrict_union · cited by 1VectorMeasure.restrict_un…MeasureTheory.VectorMeasure.variation_withDensity' · cited by 1VectorMeasure.variation_w…MeasureTheory.VectorMeasure.setIntegral_biUnion_finset · cited by 1VectorMeasure.setIntegral…MeasureTheory.VectorMeasure.restrict_le_restrict_countable_iUnion · cited by 1VectorMeasure.restrict_le…MeasureTheory.VectorMeasure.setIntegral_empty · cited by 0VectorMeasure.setIntegral…MeasureTheory.VectorMeasure.IntegrableOn.empty · cited by 0IntegrableOn.emptyMeasureTheory.VectorMeasure.norm_setIntegral_le_of_norm_le_const · cited by 0VectorMeasure.norm_setInt…DFunLike.coe · cited by 62936DFunLike.coeSet · cited by 53352SetTopologicalSpace · cited by 24529TopologicalSpaceMeasurableSpace · cited by 13106MeasurableSpaceAddCommMonoid · cited by 12281AddCommMonoidMeasurableSet · cited by 3075MeasurableSetMeasureTheory.VectorMeasure · cited by 451MeasureTheory.VectorMeasu…zero_apply · cited by 251zero_applyMeasureTheory.VectorMeasure.restrict · cited by 139VectorMeasure.restrictMeasureTheory.VectorMeasure.ext · cited by 65VectorMeasure.extMeasurableSet.empty · cited by 58MeasurableSet.emptySet.inter_empty · cited by 36Set.inter_emptyMeasureTheory.VectorMeasure.restrict_apply · cited by 26VectorMeasure.restrict_ap…MeasureTheory.VectorMeasure.empty · cited by 16VectorMeasure.emptyVectorMeasure.restrict_emptyCITED BYCITES

Cites14

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by8

Results whose statement or proof uses this declaration.