Theorems · Theorem · general topology

MemHolder.smul_iff

∀ {X : Type u_1} {Y : Type u_2} [inst : MetricSpace X] [inst_1 : NormedAddCommGroup Y] {r : NNReal} {f : X → Y}
  {𝕜 : Type u_3} [inst_2 : SeminormedRing 𝕜] [inst_3 : Module 𝕜 Y] [NormSMulClass 𝕜 Y] {c : 𝕜},
  ‖c‖₊ ≠ 0 → (MemHolder r (c • f) ↔ MemHolder r f)

Defined in

Mathlib.Topology.MetricSpace.HolderNorm

Cited by

1 results in Mathlib

Foundations

Depth 208 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MetricSpaceNormedAddCommGroupSeminormedRingModuleNormSMulClass