Theorems · Theorem · general topology

LipschitzOnWith.extend_lp_infty

∀ {α : Type u} [inst : PseudoMetricSpace α] {s : Set α} {ι : Type u_1} {f : α → ↥(lp (fun x => ℝ) ⊤)} {K : NNReal},
  LipschitzOnWith K f s → ∃ g, LipschitzWith K g ∧ Set.EqOn f g s

A function f : α → ℓ^∞(ι, ℝ) which is K-Lipschitz on a subset s admits a K-Lipschitz extension to the whole space. Theorem 2.2 of [Assaf Naor, Metric Embeddings and Lipschitz Extensions][Naor-2015] The same result for the case of a finite type ι is implemented in LipschitzOnWith.extend_pi.

Defined in

Mathlib.Topology.MetricSpace.Kuratowski

Cited by

0 results in Mathlib

Foundations

Depth 233 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

PseudoMetricSpace