Theorems · Theorem · general topology

LipschitzWith.uniformEquicontinuous

∀ {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), (∀ (c : α), LipschitzWith K (f c)) → UniformEquicontinuous f

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

Defined in

Mathlib.Topology.MetricSpace.UniformConvergence

Cited by

0 results in Mathlib

Foundations

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

Assumes

PseudoEMetricSpacePseudoEMetricSpace