Theorems · Theorem · general topology

HolderWith.smul

∀ {X : Type u_1} {Y : Type u_2} [inst : PseudoMetricSpace X] [inst_1 : SeminormedAddCommGroup Y] {C r : NNReal}
  {f : X → Y} {α : Type u_4} [inst_2 : SeminormedAddCommGroup α] [inst_3 : SMulZeroClass α Y] [IsBoundedSMul α Y]
  (a : α), HolderWith C r f → HolderWith (C * ‖a‖₊) r (a • f)

Defined in

Mathlib.Topology.MetricSpace.Holder

Cited by

2 results in Mathlib

Foundations

Depth 201 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

PseudoMetricSpaceSeminormedAddCommGroupSeminormedAddCommGroupSMulZeroClassIsBoundedSMul