Theorems · Definition · measure theory

MeasureTheory.VectorMeasure.bound

{X : Type u_1} →
  {E : Type u_2} →
    [inst : NormedAddCommGroup E] →
      [NormedSpace ℝ E] → {mX : MeasurableSpace X} → MeasureTheory.VectorMeasure X E → NNReal

A constant bounding the norm of μ s for any set s.

Defined in: Mathlib.MeasureTheory.VectorMeasure.Variation.Semivariation
Cited by: 5 results in Mathlib
Foundations: Depth 173 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: NormedAddCommGroup NormedSpace

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

Cites9

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

Realstatement and proof · cited by 25,697
NormedAddCommGroupstatement and proof · cited by 15,752
MeasurableSpacestatement and proof · cited by 13,106
NormedSpacestatement and proof · cited by 12,499
NNRealstatement · cited by 4,310
Set.univproof · cited by 3,945
MeasureTheory.VectorMeasurestatement and proof · cited by 451
ENNReal.toNNRealproof · cited by 165
MeasureTheory.VectorMeasure.semivariationproof · cited by 7

Cited by5

Results whose statement or proof uses this declaration.

MeasureTheory.VectorMeasure.semivariation_apply_le_boundstatement · cited by 1
MeasureTheory.VectorMeasure.nnnorm_apply_le_boundstatement and proof · cited by 1
MeasureTheory.VectorMeasure.norm_apply_le_boundstatement · cited by 1
MeasureTheory.VectorMeasure.enorm_apply_le_boundstatement · cited by 1
MeasureTheory.VectorMeasure.integrable_vectorMeasure_prodMk_leftproof · cited by 0