Theorems · Definition · measure theory
MeasureTheory.VectorMeasure.variation
{X : Type u_1} →
{mX : MeasurableSpace X} →
{V : Type u_2} →
[inst : TopologicalSpace V] →
[inst_1 : ENormedAddCommMonoid V] → [T2Space V] → MeasureTheory.VectorMeasure X V → MeasureTheory.Measure XThe variation of a VectorMeasure as a Measure.
- Cited by
- 125 results in Mathlib
- Foundations
- Depth 171 from the axioms, rests on 4,732 definitions · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setproof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement · cited by 10,939
- T2Spacestatement and proof · cited by 1,351
- ENorm.enormproof · cited by 715
- MeasureTheory.VectorMeasurestatement and proof · cited by 451
- ENormedAddCommMonoidstatement and proof · cited by 32
- MeasureTheory.VectorMeasure.isSigmaSubadditiveSetFun_enormproof · cited by 9
- MeasureTheory.preVariationproof · cited by 5
Cited by129
Results whose statement or proof uses this declaration.
- MeasureTheory.VectorMeasure.integralproof · cited by 126
- MeasureTheory.VectorMeasure.Integrableproof · cited by 63
- MeasureTheory.dominatedFinMeasAdditive_cbmApplyMeasurestatement and proof · cited by 31
- MeasureTheory.VectorMeasure.enorm_measure_le_variationstatement and proof · cited by 15
- MeasureTheory.VectorMeasure.variation_restrictstatement and proof · cited by 14
- MeasureTheory.VectorMeasure.variation_le_of_forall_enorm_lestatement · cited by 13
- MeasureTheory.VectorMeasure.integral_congr_aestatement and proof · cited by 11
- MeasureTheory.VectorMeasure.integral_zero_vectorMeasureproof · cited by 11
- MeasureTheory.VectorMeasure.variation.congr_simpstatement and proof · cited by 9
- MeasureTheory.VectorMeasure.variation_zerostatement · cited by 9
- MeasureTheory.VectorMeasure.integral_undefproof · cited by 7
- MeasureTheory.VectorMeasure.semivariationproof · cited by 7