Theorems · Theorem · general topology

HolderOnWith.interpolate_const

∀ {X : Type u_1} {Y : Type u_2} [inst : PseudoEMetricSpace X] [inst_1 : PseudoEMetricSpace Y] {r : NNReal} {f : X → Y}
  {C s t₁ t₂ : NNReal} {A : Set X},
  HolderOnWith C r f A → HolderOnWith C s f A → t₁ + t₂ = 1 → HolderOnWith C (r * t₁ + s * t₂) f A

If a function is (C, r)-Hölder and (C, s)-Hölder, then it is (C, r * t₁ + s * t₂)-Hölder for all t₁ t₂ : ℝ≥0 such that t₁ + t₂ = 1.

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