Theorems · Theorem · general topology
LipschitzWith.lipschitzOnWith
∀ {α : Type u} {β : Type v} [inst : PseudoEMetricSpace α] [inst_1 : PseudoEMetricSpace β] {K : NNReal} {f : α → β}
{s : Set α}, LipschitzWith K f → LipschitzOnWith K f s- Defined in
- Mathlib.Topology.EMetricSpace.Lipschitz
- Cited by
- 16 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
- NNRealstatement and proof · cited by 4,310
- PseudoEMetricSpacestatement and proof · cited by 1,536
- LipschitzWithstatement and proof · cited by 316
- LipschitzOnWithstatement · cited by 164
Cited by16
Results whose statement or proof uses this declaration.
- LipschitzWith.dimH_image_leproof · cited by 4
- LipschitzWith.addproof · cited by 3
- LipschitzWith.comp_locallyBoundedVariationOnproof · cited by 2
- lipschitzOnWith_cfc_fun_of_subsetproof · cited by 2
- lipschitzOnWith_cfcₙ_fun_of_subsetproof · cited by 2
- LipschitzWith.hausdorffMeasure_image_leproof · cited by 2
- LipschitzWith.mulproof · cited by 1
- lipschitzOnWith_cfc_funproof · cited by 1
- lipschitzOnWith_cfcₙ_funproof · cited by 1
- LipschitzWith.locallyBoundedVariationOnproof · cited by 1
- LipschitzWith.comp_boundedVariationOnproof · cited by 0
- dist_le_of_approx_trajectories_ODEproof · cited by 0