Theorems · Theorem · measure theory

MeasureTheory.memLp_finsetSum

∀ {α : Type u_1} {ε' : Type u_4} {m : MeasurableSpace α} [inst : TopologicalSpace ε']
  [inst_1 : ESeminormedAddCommMonoid ε'] {p : ENNReal} {μ : MeasureTheory.Measure α} [ContinuousAdd ε'] {ι : Type u_5}
  (s : Finset ι) {f : ι → α → ε'},
  (∀ i ∈ s, MeasureTheory.MemLp (f i) p μ) → MeasureTheory.MemLp (fun a => ∑ i ∈ s, f i a) p μ

Defined in

Mathlib.MeasureTheory.Function.LpSeminorm.TriangleInequality

Cited by

3 results in Mathlib

Foundations

Depth 220 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceESeminormedAddCommMonoidContinuousAdd