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Theorems · Theorem · measure theory

MeasureTheory.VectorMeasure.isSigmaSubadditiveSetFun_enorm

∀ {X : Type u_1} {mX : MeasurableSpace X} {V : Type u_2} [inst : TopologicalSpace V] [inst_1 : ENormedAddCommMonoid V]
  [T2Space V] (μ : MeasureTheory.VectorMeasure X V), MeasureTheory.IsSigmaSubadditiveSetFun fun x => ‖μ x‖ₑ

The norm of a vector measure is σ-subadditive on measurable sets.

Defined in
Mathlib.MeasureTheory.VectorMeasure.Variation.Defs
Cited by
9 results in Mathlib
Foundations
Depth 131 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 · cited by 125VectorMeasure.variationMeasureTheory.VectorMeasure.enorm_measure_le_variation · cited by 15VectorMeasure.enorm_measu…MeasureTheory.VectorMeasure.variation_zero · cited by 9VectorMeasure.variation_z…MeasureTheory.VectorMeasure.variation_apply_le_of_forall_enorm_le · cited by 3VectorMeasure.variation_a…MeasureTheory.VectorMeasure.variation_neg · cited by 3VectorMeasure.variation_n…MeasureTheory.VectorMeasure.exists_variation_le_add' · cited by 2VectorMeasure.exists_vari…MeasureTheory.VectorMeasure.exists_lt_sum_of_lt_variation · cited by 1VectorMeasure.exists_lt_s…MeasureTheory.VectorMeasure.le_variation · cited by 1VectorMeasure.le_variationMeasureTheory.VectorMeasure.variation_eq_ennrealToMeasure · cited by 1VectorMeasure.variation_e…MeasureTheory.VectorMeasure.variation_apply · cited by 0VectorMeasure.variation_a…DFunLike.coe · cited by 62936DFunLike.coeSet · cited by 53352SetTopologicalSpace · cited by 24529TopologicalSpaceMeasurableSpace · cited by 13106MeasurableSpaceAddCommMonoid · cited by 12281AddCommMonoidMeasurableSet · cited by 3075MeasurableSetDisjoint · cited by 2201DisjointSummationFilter.unconditional · cited by 2068SummationFilter.unconditi…T2Space · cited by 1351T2Spacetsum · cited by 1148tsumENorm.enorm · cited by 715ENorm.enormFunction.onFun · cited by 570Function.onFunPairwise · cited by 516PairwiseSubtype.prop · cited by 505Subtype.propMeasureTheory.VectorMeasure · cited by 451MeasureTheory.VectorMeasu…VectorMeasure.isSigmaSubaddit…CITED BYCITES

Cites19

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Cited by10

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