Theorems · Theorem · functional analysis

MeasureTheory.Lp.smul_assoc

∀ {α : Type u_1} {𝕜' : Type u_2} {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 : Module 𝕜 E] [inst_3 : IsBoundedSMul 𝕜 E] [inst_4 : NormedRing 𝕜'] [inst_5 : Module 𝕜' E]
  [inst_6 : Module 𝕜' 𝕜] [inst_7 : IsBoundedSMul 𝕜' E] [inst_8 : IsBoundedSMul 𝕜' 𝕜] [IsScalarTower 𝕜' 𝕜 E] (c : 𝕜')
  (f : ↥(MeasureTheory.Lp 𝕜 p μ)) (g : ↥(MeasureTheory.Lp E q μ)), (c • f) • g = c • f • g

Defined in

Mathlib.MeasureTheory.Function.Holder

Cited by

0 results in Mathlib

Foundations

Depth 232 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

ENNReal.HolderTripleNormedRingNormedAddCommGroupModuleIsBoundedSMulNormedRingModuleModuleIsBoundedSMulIsBoundedSMulIsScalarTower