Theorems · Theorem · measure theory
MeasureTheory.SignedMeasure.null_of_totalVariation_zero
∀ {α : Type u_1} [inst : MeasurableSpace α] (s : MeasureTheory.SignedMeasure α) {i : Set α},
s.totalVariation i = 0 → s i = 0- Cited by
- 3 results in Mathlib
- Foundations
- Depth 178 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.
Cites22
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Setstatement and proof · cited by 53,352
- Realstatement · cited by 25,697
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- ENNRealstatement and proof · cited by 9,879
- MeasurableSetproof · cited by 3,075
- sub_selfproof · cited by 996
- ENNReal.toRealproof · cited by 859
- MeasureTheory.Measure.realproof · cited by 530
- MeasureTheory.SignedMeasurestatement and proof · cited by 108
- Pi.add_applyproof · cited by 61
Cited by3
Results whose statement or proof uses this declaration.
- MeasureTheory.SignedMeasure.mutuallySingular_ennreal_iffproof · cited by 2
- MeasureTheory.SignedMeasure.absolutelyContinuous_ennreal_iffproof · cited by 1
- MeasureTheory.SignedMeasure.mutuallySingular_iffproof · cited by 0