Theorems · Theorem · measure theory

MeasureTheory.lpNorm_const_smul

∀ {α : Type u_1} {E : Type u_2} {m : MeasurableSpace α} {p : ENNReal} [inst : NormedAddCommGroup E] {𝕜 : Type u_3}
  [inst_1 : NormedField 𝕜] [inst_2 : Module 𝕜 E] [NormSMulClass 𝕜 E] (c : 𝕜) (f : α → E) (μ : MeasureTheory.Measure α),
  MeasureTheory.lpNorm (c • f) p μ = ↑‖c‖₊ * MeasureTheory.lpNorm f p μ

Defined in

Mathlib.MeasureTheory.Function.LpSeminorm.LpNorm

Cited by

1 results in Mathlib

Foundations

Depth 209 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedFieldModuleNormSMulClass