Theorems · Theorem · general topology

HolderWith.interpolate

∀ {X : Type u_1} {Y : Type u_2} [inst : PseudoEMetricSpace X] [inst_1 : PseudoEMetricSpace Y] {r : NNReal} {f : X → Y}
  {C₁ C₂ s t₁ t₂ : NNReal},
  HolderWith C₁ r f → HolderWith C₂ s f → t₁ + t₂ = 1 → HolderWith (C₁ ^ ↑t₁ * C₂ ^ ↑t₂) (r * t₁ + s * t₂) f

If a function is (C₁, r)-Hölder and (C₂, s)-Hölder, then it is (C₁ ^ t₁ * C₂ ^ t₂, r * t₁ + s * t₂)-Hölder for all t₁ t₂ : ℝ≥0 such that t₁ + t₂ = 1.

Defined in

Mathlib.Topology.MetricSpace.Holder

Cited by

0 results in Mathlib

Foundations

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

Assumes

PseudoEMetricSpacePseudoEMetricSpace