Theorems · Theorem · measure theory

MeasureTheory.eLpNorm_const_smul

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

Defined in

Mathlib.MeasureTheory.Function.LpSeminorm.SMul

Cited by

4 results in Mathlib

Foundations

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

Assumes

NormedAddCommGroupNormedDivisionRingModuleNormSMulClass