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Theorems · Theorem · measure theory

MeasureTheory.VectorMeasure.variation_zero

∀ {X : Type u_1} {V : Type u_2} {mX : MeasurableSpace X} [inst : TopologicalSpace V] [inst_1 : ENormedAddCommMonoid V]
  [inst_2 : T2Space V], MeasureTheory.VectorMeasure.variation 0 = 0
Defined in
Mathlib.MeasureTheory.VectorMeasure.Variation.Basic
Cited by
9 results in Mathlib
Foundations
Depth 174 from the axioms · 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_zero_vectorMeasure · cited by 11VectorMeasure.integral_ze…MeasureTheory.VectorMeasure.variation_restrict_le · cited by 5VectorMeasure.variation_r…MeasureTheory.VectorMeasure.variation_map_le · cited by 4VectorMeasure.variation_m…MeasureTheory.VectorMeasure.variation_smul · cited by 2VectorMeasure.variation_s…MeasureTheory.VectorMeasure.variation_eq_zero · cited by 1VectorMeasure.variation_e…MeasureTheory.VectorMeasure.variation_WithDensity_le · cited by 1VectorMeasure.variation_W…MeasureTheory.VectorMeasure.Integrable.zero_vectorMeasure · cited by 0Integrable.zero_vectorMea…MeasureTheory.VectorMeasure.variation_finsetSum_le · cited by 0VectorMeasure.variation_f…MeasureTheory.Measure.variation_withDensityᵥ · cited by 0Measure.variation_withDen…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…zero_apply · cited by 251zero_applyMeasureTheory.VectorMeasure.variation · cited by 125VectorMeasure.variationenorm_zero · cited by 44enorm_zeroENormedAddCommMonoid · cited by 32ENormedAddCommMonoidMeasureTheory.VectorMeasure.isSigmaSubadditiveSetFun_enorm · cited by 9VectorMeasure.isSigmaSuba…MeasureTheory.preVariation.congr_simp · cited by 2preVariation.congr_simpMeasureTheory.preVariation_zero · cited by 1MeasureTheory.preVariatio…VectorMeasure.variation_zeroCITED BYCITES

Cites15

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Cited by9

Results whose statement or proof uses this declaration.