Theorems · Theorem · measure theory

DomAddAct.vadd_Lp_add

∀ {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 : VAdd M α] [inst_3 : MeasureTheory.VAddInvariantMeasure M α μ]
  [inst_4 : MeasurableConstVAdd M α] (c : Mᵈᵃᵃ) (f g : ↥(MeasureTheory.Lp E p μ)), c +ᵥ f + g = (c +ᵥ f) + (c +ᵥ g)

Defined in

Mathlib.MeasureTheory.Function.LpSpace.DomAct.Basic

Cited by

1 results in Mathlib

Foundations

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

Assumes

MeasurableSpaceNormedAddCommGroupVAddMeasureTheory.VAddInvariantMeasureMeasurableConstVAdd