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Theorems · Theorem · measure theory

MeasureTheory.VectorMeasure.enorm_measure_le_variation

∀ {X : Type u_1} {V : Type u_2} {mX : MeasurableSpace X} [inst : TopologicalSpace V] [inst_1 : ENormedAddCommMonoid V]
  [inst_2 : T2Space V] (μ : MeasureTheory.VectorMeasure X V) (E : Set X), ‖μ E‖ₑ ≤ μ.variation E
Defined in
Mathlib.MeasureTheory.VectorMeasure.Variation.Basic
Cited by
15 results in Mathlib
Foundations
Depth 172 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.variation_restrict · cited by 14VectorMeasure.variation_r…MeasureTheory.VectorMeasure.variation_add_le · cited by 4VectorMeasure.variation_a…MeasureTheory.VectorMeasure.variation_transpose_le · cited by 4VectorMeasure.variation_t…MeasurableEmbedding.variation_map · cited by 3MeasurableEmbedding.varia…MeasureTheory.VectorMeasure.variation_dirac · cited by 2VectorMeasure.variation_d…MeasureTheory.VectorMeasure.norm_measure_le_variation · cited by 2VectorMeasure.norm_measur…MeasureTheory.VectorMeasure.enorm_apply_le_semivariation · cited by 2VectorMeasure.enorm_apply…MeasureTheory.Measure.variation_toSignedMeasure · cited by 2Measure.variation_toSigne…MeasureTheory.VectorMeasure.variation_apply_eq_zero · cited by 1VectorMeasure.variation_a…MeasureTheory.VectorMeasure.variation_eq_zero · cited by 1VectorMeasure.variation_e…MeasureTheory.VectorMeasure.variation_transpose_eq_smul · cited by 1VectorMeasure.variation_t…MeasureTheory.VectorMeasure.absolutelyContinuous · cited by 0VectorMeasure.absolutelyC…MeasureTheory.VectorMeasure.variation_prod_le · cited by 0VectorMeasure.variation_p…MeasureTheory.VectorMeasure.semivariation_le_variation · cited by 0VectorMeasure.semivariati…MeasureTheory.SignedMeasure.totalVariation_eq_variation · cited by 0SignedMeasure.totalVariat…DFunLike.coe · cited by 62936DFunLike.coeSet · cited by 53352SetTopologicalSpace · cited by 24529TopologicalSpaceMeasurableSpace · cited by 13106MeasurableSpaceMeasureTheory.Measure · cited by 10939MeasureTheory.MeasureENNReal · cited by 9879ENNRealBot.bot · cited by 4720Bot.botMeasurableSet · cited by 3075MeasurableSetFinset.sum_congr · cited by 2323Finset.sum_congrT2Space · cited by 1351T2SpaceENorm.enorm · cited by 715ENorm.enormMeasureTheory.VectorMeasure · cited by 451MeasureTheory.VectorMeasu…Finset.sum_singleton · cited by 251Finset.sum_singletonMeasureTheory.measure_empty · cited by 169MeasureTheory.measure_emp…MeasureTheory.VectorMeasure.variation · cited by 125VectorMeasure.variationVectorMeasure.enorm_measure_l…CITED BYCITES

Cites25

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Cited by15

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