Theorems · Theorem · measure theory

DomMulAct.dist_smul_Lp

∀ {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] (c : Mᵈᵐᵃ) (f g : ↥(MeasureTheory.Lp E p μ)), dist (c • f) (c • g) = dist f g

Defined in

Mathlib.MeasureTheory.Function.LpSpace.DomAct.Basic

Cited by

1 results in Mathlib

Foundations

Depth 229 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasurableSpaceNormedAddCommGroupSMulMeasureTheory.SMulInvariantMeasureMeasurableConstSMul