Theorems · Definition · real analysis
BoundedVariationOn
{α : Type u_1} → [LinearOrder α] → {E : Type u_2} → [PseudoEMetricSpace E] → (α → E) → Set α → PropA function has bounded variation on a set s if its total variation there is finite.
- Cited by
- 65 results in Mathlib
- Foundations
- Depth 148 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- Top.topproof · cited by 9,680
- LinearOrderstatement and proof · cited by 8,572
- PseudoEMetricSpacestatement and proof · cited by 1,536
- eVariationOnproof · cited by 90
Cited by68
Results whose statement or proof uses this declaration.
- LocallyBoundedVariationOnproof · cited by 41
- BoundedVariationOn.vectorMeasurestatement and proof · cited by 11
- BoundedVariationOn.ofDualstatement and proof · cited by 11
- BoundedVariationOn.vectorMeasure_Iccstatement and proof · cited by 6
- BoundedVariationOn.tendsto_leftLimstatement and proof · cited by 5
- BoundedVariationOn.locallyBoundedVariationOnstatement and proof · cited by 5
- MonotoneOn.eVariationOn_eqproof · cited by 4
- BoundedVariationOn.tendsto_eVariationOn_Ici_zero_of_filterstatement and proof · cited by 3
- BoundedVariationOn.tendsto_eVariationOn_Ico_zerostatement and proof · cited by 3
- BoundedVariationOn.vectorMeasure_Iocstatement and proof · cited by 3
- BoundedVariationOn.bilinear_compstatement and proof · cited by 3
- BoundedVariationOn.monostatement and proof · cited by 3