Theorems · Theorem · general topology

lipschitzOnWith_iff_dist_le_mul

∀ {α : Type u} {β : Type v} [inst : PseudoMetricSpace α] [inst_1 : PseudoMetricSpace β] {K : NNReal} {s : Set α}
  {f : α → β}, LipschitzOnWith K f s ↔ ∀ x ∈ s, ∀ y ∈ s, dist (f x) (f y) ≤ ↑K * dist x y

Defined in

Mathlib.Topology.MetricSpace.Lipschitz

Cited by

3 results in Mathlib

Foundations

Depth 148 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

PseudoMetricSpacePseudoMetricSpace