Theorems · Definition · measure theory
MeasureTheory.ennrealPreVariation
{X : Type u_1} →
[inst : MeasurableSpace X] →
(f : Set X → ENNReal) → MeasureTheory.IsSigmaSubadditiveSetFun f → f ∅ = 0 → MeasureTheory.VectorMeasure X ENNRealThe VectorMeasure X ℝ≥0∞ built from a σ-subadditive function.
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 133 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- MeasurableSpace
Around this declaration
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.
- Setstatement and proof · cited by 53,352
- MeasurableSpacestatement and proof · cited by 13,106
- ENNRealstatement and proof · cited by 9,879
- MeasurableSetproof · cited by 3,075
- MeasureTheory.VectorMeasurestatement · cited by 451
- MeasureTheory.preVariationFunproof · cited by 17
- MeasureTheory.IsSigmaSubadditiveSetFunstatement and proof · cited by 7
- MeasureTheory.preVariation.emptyproof · cited by 0
- MeasureTheory.preVariation.iUnionproof · cited by 0
Cited by11
Results whose statement or proof uses this declaration.
- MeasureTheory.VectorMeasure.enorm_measure_le_variationproof · cited by 15
- MeasureTheory.preVariationproof · cited by 5
- MeasureTheory.VectorMeasure.variation_apply_le_of_forall_enorm_leproof · cited by 3
- MeasureTheory.VectorMeasure.exists_variation_le_add'proof · cited by 2
- MeasureTheory.VectorMeasure.exists_lt_sum_of_lt_variationproof · cited by 1
- MeasureTheory.VectorMeasure.le_variationproof · cited by 1
- MeasureTheory.VectorMeasure.variation_eq_ennrealToMeasureproof · cited by 1
- MeasureTheory.ennrealPreVariation_zerostatement · cited by 1
- MeasureTheory.ennrealPreVariation.congr_simpstatement and proof · cited by 0
- MeasureTheory.preVariation_applystatement · cited by 0
- MeasureTheory.ennrealPreVariation_applystatement · cited by 0