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Theorems · Theorem · measure theory

MeasureTheory.VectorMeasure.norm_measure_le_variation

∀ {X : Type u_1} {V : Type u_2} {mX : MeasurableSpace X} [inst : NormedAddCommGroup V]
  {μ : MeasureTheory.VectorMeasure X V} {E : Set X},
  autoParam (μ.variation E ≠ ⊤) MeasureTheory.VectorMeasure.norm_measure_le_variation._auto_1 →
    ‖μ E‖ ≤ μ.variation.real E
Defined in
Mathlib.MeasureTheory.VectorMeasure.Variation.Basic
Cited by
2 results in Mathlib
Foundations
Depth 173 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
NormedAddCommGroup
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MeasureTheory.dominatedFinMeasAdditive_cbmApplyMeasure · cited by 31MeasureTheory.dominatedFi…MeasureTheory.dominatedFinMeasAdditive_transpose_cbmApplyMeasure · cited by 2MeasureTheory.dominatedFi…DFunLike.coe · cited by 62936DFunLike.coeSet · cited by 53352SetReal · cited by 25697RealNormedAddCommGroup · cited by 15752NormedAddCommGroupMeasurableSpace · cited by 13106MeasurableSpaceMeasureTheory.Measure · cited by 10939MeasureTheory.MeasureENNReal · cited by 9879ENNRealTop.top · cited by 9680Top.topNorm.norm · cited by 5413Norm.normENNReal.toReal · cited by 859ENNReal.toRealMeasureTheory.Measure.real · cited by 530Measure.realMeasureTheory.VectorMeasure · cited by 451MeasureTheory.VectorMeasu…MeasureTheory.VectorMeasure.variation · cited by 125VectorMeasure.variationenorm_ne_top · cited by 82enorm_ne_topMeasureTheory.measureReal_def · cited by 68MeasureTheory.measureReal…VectorMeasure.norm_measure_le…CITED BYCITES

Cites18

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Cited by2

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