Theorems · Theorem · functional analysis

MeasureTheory.Lp.norm_smul_le

∀ {α : Type u_1} {𝕜 : Type u_3} {E : Type u_4} {m : MeasurableSpace α} {μ : MeasureTheory.Measure α} {p q r : ENNReal}
  [hpqr : p.HolderTriple q r] [inst : NormedRing 𝕜] [inst_1 : NormedAddCommGroup E] [inst_2 : MulActionWithZero 𝕜 E]
  [inst_3 : IsBoundedSMul 𝕜 E] (f : ↥(MeasureTheory.Lp 𝕜 p μ)) (g : ↥(MeasureTheory.Lp E q μ)), ‖f • g‖ ≤ ‖f‖ * ‖g‖

Defined in

Mathlib.MeasureTheory.Function.Holder

Cited by

0 results in Mathlib

Foundations

Depth 227 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

ENNReal.HolderTripleNormedRingNormedAddCommGroupMulActionWithZeroIsBoundedSMul