Theorems · Theorem · real analysis
LipschitzOnWith.locallyBoundedVariationOn
∀ {E : Type u_2} [inst : PseudoEMetricSpace E] {f : ℝ → E} {C : NNReal} {s : Set ℝ},
LipschitzOnWith C f s → LocallyBoundedVariationOn f s- Cited by
- 3 results in Mathlib
- Foundations
- Depth 156 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- PseudoEMetricSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- Realstatement and proof · cited by 25,697
- NNRealstatement and proof · cited by 4,310
- PseudoEMetricSpacestatement and proof · cited by 1,536
- LipschitzOnWithstatement and proof · cited by 164
- LocallyBoundedVariationOnstatement · cited by 41
- Set.mapsTo_idproof · cited by 8
- monotoneOn_idproof · cited by 3
- LipschitzOnWith.comp_locallyBoundedVariationOnproof · cited by 2
- MonotoneOn.locallyBoundedVariationOnproof · cited by 1
Cited by3
Results whose statement or proof uses this declaration.
- LipschitzWith.locallyBoundedVariationOnproof · cited by 1
- LipschitzOnWith.ae_differentiableWithinAt_of_mem_realproof · cited by 0
- LipschitzOnWith.ae_differentiableWithinAt_realproof · cited by 0