Theorems · Theorem · general topology
LipschitzOnWith.extend_real
∀ {α : Type u} [inst : PseudoMetricSpace α] {f : α → ℝ} {s : Set α} {K : NNReal},
LipschitzOnWith K f s → ∃ g, LipschitzWith K g ∧ Set.EqOn f g sA function f : α → ℝ which is K-Lipschitz on a subset s admits a K-Lipschitz extension
to the whole space.
- Defined in
- Mathlib.Topology.MetricSpace.Lipschitz
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 155 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- PseudoMetricSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites37
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
- Set.Elemproof · cited by 7,166
- Set.rangeproof · cited by 4,705
- NNRealstatement and proof · cited by 4,310
- add_zeroproof · cited by 2,707
- Set.Nonemptyproof · cited by 2,627
- MulZeroClass.mul_zeroproof · cited by 2,091
- le_antisymmproof · cited by 2,068
- le_reflproof · cited by 2,061
- iInfproof · cited by 1,690
- PseudoMetricSpacestatement and proof · cited by 1,550
Cited by3
Results whose statement or proof uses this declaration.
- LipschitzOnWith.extend_piproof · cited by 1
- LipschitzOnWith.ae_differentiableWithinAt_of_mem_of_realproof · cited by 1
- LipschitzOnWith.extend_lp_inftyproof · cited by 0