Theorems · Theorem · general topology

HolderOnWith.edist_le_of_le

∀ {X : Type u_1} {Y : Type u_2} [inst : PseudoEMetricSpace X] [inst_1 : PseudoEMetricSpace Y] {C r : NNReal} {f : X → Y}
  {s : Set X},
  HolderOnWith C r f s → ∀ {x y : X}, x ∈ s → y ∈ s → ∀ {d : ENNReal}, edist x y ≤ d → edist (f x) (f y) ≤ ↑C * d ^ ↑r

Defined in

Mathlib.Topology.MetricSpace.Holder

Cited by

4 results in Mathlib

Foundations

Depth 205 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

PseudoEMetricSpacePseudoEMetricSpace