Mathlib Map

Theorems · Definition · measure theory

MeasureTheory.VectorMeasure.restrict

{α : Type u_1} →
  {mα : MeasurableSpace α} →
    {M : Type u_3} →
      [inst : AddCommMonoid M] →
        [inst_1 : TopologicalSpace M] → MeasureTheory.VectorMeasure α M → Set α → MeasureTheory.VectorMeasure α M

The restriction of a vector measure on some set.

Defined in
Mathlib.MeasureTheory.VectorMeasure.Basic
Cited by
139 results in Mathlib
Foundations
Depth 67 from the axioms, rests on 1,302 definitions · uses propext, Classical.choice, Quot.sound
Assumes
AddCommMonoidTopologicalSpace

Around this declaration

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

MeasureTheory.SignedMeasure.toJordanDecomposition · cited by 34SignedMeasure.toJordanDec…MeasureTheory.VectorMeasure.restrict_apply · cited by 26VectorMeasure.restrict_ap…MeasureTheory.VectorMeasure.IntegrableOn · cited by 19VectorMeasure.IntegrableOnMeasureTheory.VectorMeasure.restrict_not_measurable · cited by 14VectorMeasure.restrict_no…MeasureTheory.VectorMeasure.variation_restrict · cited by 14VectorMeasure.variation_r…MeasureTheory.VectorMeasure.restrict_le_restrict_iff · cited by 12VectorMeasure.restrict_le…MeasureTheory.SignedMeasure.toMeasureOfZeroLE · cited by 11SignedMeasure.toMeasureOf…MeasureTheory.VectorMeasure.withDensity · cited by 11VectorMeasure.withDensityMeasureTheory.SignedMeasure.toMeasureOfLEZero · cited by 10SignedMeasure.toMeasureOf…MeasureTheory.SignedMeasure.toSignedMeasure_toJordanDecomposition · cited by 10SignedMeasure.toSignedMea…MeasureTheory.VectorMeasure.nonneg_of_zero_le_restrict · cited by 9VectorMeasure.nonneg_of_z…MeasureTheory.VectorMeasure.setIntegral_eq_zero_of_not_measurableSet · cited by 9VectorMeasure.setIntegral…MeasureTheory.VectorMeasure.restrict_empty · cited by 8VectorMeasure.restrict_em…MeasureTheory.VectorMeasure.zero_le_restrict_subset · cited by 8VectorMeasure.zero_le_res…MeasureTheory.VectorMeasure.integral_indicator · cited by 7VectorMeasure.integral_in…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…VectorMeasure.restrictCITED BYCITES

Cites7

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

Cited by148

Results whose statement or proof uses this declaration.