Theorems · Theorem · general topology

HolderOnWith.of_le

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

If a function is r-Hölder over a bounded set, then it is also s-Hölder when s ≤ r.

Defined in

Mathlib.Topology.MetricSpace.Holder

Cited by

2 results in Mathlib

Foundations

Depth 206 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

PseudoEMetricSpacePseudoEMetricSpace