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Theorems · Definition · measure theory

MeasureTheory.VectorMeasure.variation

{X : Type u_1} →
  {mX : MeasurableSpace X} →
    {V : Type u_2} →
      [inst : TopologicalSpace V] →
        [inst_1 : ENormedAddCommMonoid V] → [T2Space V] → MeasureTheory.VectorMeasure X V → MeasureTheory.Measure X

The variation of a VectorMeasure as a Measure.

Defined in
Mathlib.MeasureTheory.VectorMeasure.Variation.Defs
Cited by
125 results in Mathlib
Foundations
Depth 171 from the axioms, rests on 4,732 definitions · uses propext, Classical.choice, Quot.sound
Assumes
TopologicalSpaceENormedAddCommMonoidT2Space

Around this declaration

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

MeasureTheory.VectorMeasure.integral · cited by 126VectorMeasure.integralMeasureTheory.VectorMeasure.Integrable · cited by 63VectorMeasure.IntegrableMeasureTheory.dominatedFinMeasAdditive_cbmApplyMeasure · cited by 31MeasureTheory.dominatedFi…MeasureTheory.VectorMeasure.enorm_measure_le_variation · cited by 15VectorMeasure.enorm_measu…MeasureTheory.VectorMeasure.variation_restrict · cited by 14VectorMeasure.variation_r…MeasureTheory.VectorMeasure.variation_le_of_forall_enorm_le · cited by 13VectorMeasure.variation_l…MeasureTheory.VectorMeasure.integral_congr_ae · cited by 11VectorMeasure.integral_co…MeasureTheory.VectorMeasure.integral_zero_vectorMeasure · cited by 11VectorMeasure.integral_ze…MeasureTheory.VectorMeasure.variation.congr_simp · cited by 9variation.congr_simpMeasureTheory.VectorMeasure.variation_zero · cited by 9VectorMeasure.variation_z…MeasureTheory.VectorMeasure.integral_undef · cited by 7VectorMeasure.integral_un…MeasureTheory.VectorMeasure.semivariation · cited by 7VectorMeasure.semivariati…MeasureTheory.VectorMeasure.enorm_integral_le_lintegral_enorm · cited by 6VectorMeasure.enorm_integ…MeasureTheory.VectorMeasure.integral_add_vectorMeasure · cited by 5VectorMeasure.integral_ad…MeasureTheory.VectorMeasure.integral_const · cited by 5VectorMeasure.integral_co…DFunLike.coe · cited by 62936DFunLike.coeSet · cited by 53352SetTopologicalSpace · cited by 24529TopologicalSpaceMeasurableSpace · cited by 13106MeasurableSpaceMeasureTheory.Measure · cited by 10939MeasureTheory.MeasureT2Space · cited by 1351T2SpaceENorm.enorm · cited by 715ENorm.enormMeasureTheory.VectorMeasure · cited by 451MeasureTheory.VectorMeasu…ENormedAddCommMonoid · cited by 32ENormedAddCommMonoidMeasureTheory.VectorMeasure.isSigmaSubadditiveSetFun_enorm · cited by 9VectorMeasure.isSigmaSuba…MeasureTheory.preVariation · cited by 5MeasureTheory.preVariationVectorMeasure.variationCITED BYCITES

Cites11

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

Cited by129

Results whose statement or proof uses this declaration.