Theorems · Theorem · general topology

HolderOnWith.comp

∀ {X : Type u_1} {Y : Type u_2} {Z : Type u_3} [inst : PseudoEMetricSpace X] [inst_1 : PseudoEMetricSpace Y]
  [inst_2 : PseudoEMetricSpace Z] {s : Set X} {Cg rg : NNReal} {g : Y → Z} {t : Set Y},
  HolderOnWith Cg rg g t →
    ∀ {Cf rf : NNReal} {f : X → Y},
      HolderOnWith Cf rf f s → Set.MapsTo f s t → HolderOnWith (Cg * Cf ^ ↑rg) (rg * rf) (g ∘ f) s

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

PseudoEMetricSpacePseudoEMetricSpacePseudoEMetricSpace