Theorems · Theorem · general topology

LipschitzOnWith.of_le_add_mul

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

For functions to ℝ, it suffices to prove f x ≤ f y + K * dist x y; this version assumes 0≤K.

Defined in

Mathlib.Topology.MetricSpace.Lipschitz

Cited by

2 results in Mathlib

Foundations

Depth 154 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

PseudoMetricSpace