Theorems · Theorem · general topology

LipschitzOnWith.uniformEquicontinuousOn

∀ {α : Type u_1} {β : Type u_2} {γ : Type u_3} [inst : PseudoEMetricSpace γ] [inst_1 : PseudoEMetricSpace β]
  (f : α → γ → β) (K : NNReal) {s : Set γ}, (∀ (c : α), LipschitzOnWith K (f c) s) → UniformEquicontinuousOn f s

If f : α → γ → β is a family of a functions, all of which are Lipschitz on s with the same constant, then the family is uniformly equicontinuous on s.

Defined in

Mathlib.Topology.MetricSpace.UniformConvergence

Cited by

0 results in Mathlib

Foundations

Depth 156 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

PseudoEMetricSpacePseudoEMetricSpace