Theorems · Theorem · functional analysis

MeasureTheory.MemLp.smul

∀ {𝕜 : Type u_1} {α : Type u_2} {E : Type u_3} {m : MeasurableSpace α} {μ : MeasureTheory.Measure α}
  [inst : NormedRing 𝕜] [inst_1 : NormedAddCommGroup E] [inst_2 : MulActionWithZero 𝕜 E] [IsBoundedSMul 𝕜 E]
  {p q r : ENNReal} {f : α → E} {φ : α → 𝕜},
  MeasureTheory.MemLp f q μ → MeasureTheory.MemLp φ p μ → ∀ [hpqr : p.HolderTriple q r], MeasureTheory.MemLp (φ • f) r μ

Defined in

Mathlib.MeasureTheory.Function.LpSeminorm.CompareExp

Cited by

13 results in Mathlib

Foundations

Depth 215 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedRingNormedAddCommGroupMulActionWithZeroIsBoundedSMulENNReal.HolderTriple