Theorems · Theorem · measure theory

MeasureTheory.eLpNorm_const_smul_le

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

Defined in

Mathlib.MeasureTheory.Function.LpSeminorm.SMul

Cited by

3 results in Mathlib

Foundations

Depth 207 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedRingMulActionWithZeroIsBoundedSMul