Theorems · Theorem · measure theory

DomMulAct.smul_Lp_const

∀ {M : Type u_1} {α : Type u_3} {E : Type u_4} [inst : MeasurableSpace α] [inst_1 : NormedAddCommGroup E]
  {μ : MeasureTheory.Measure α} {p : ENNReal} [inst_2 : SMul M α] [inst_3 : MeasureTheory.SMulInvariantMeasure M α μ]
  [inst_4 : MeasurableConstSMul M α] [inst_5 : MeasureTheory.IsFiniteMeasure μ] (c : Mᵈᵐᵃ) (a : E),
  c • (MeasureTheory.Lp.const p μ) a = (MeasureTheory.Lp.const p μ) a

Defined in

Mathlib.MeasureTheory.Function.LpSpace.DomAct.Basic

Cited by

0 results in Mathlib

Foundations

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

Assumes

MeasurableSpaceNormedAddCommGroupSMulMeasureTheory.SMulInvariantMeasureMeasurableConstSMulMeasureTheory.IsFiniteMeasure