Theorems · Theorem · measure theory

MeasureTheory.integrable_finsetSum

∀ {α : Type u_1} {m : MeasurableSpace α} {μ : MeasureTheory.Measure α} {ε' : Type u_8} [inst : TopologicalSpace ε']
  [inst_1 : ESeminormedAddCommMonoid ε'] [ContinuousAdd ε'] {ι : Type u_9} (s : Finset ι) {f : ι → α → ε'},
  (∀ i ∈ s, MeasureTheory.Integrable (f i) μ) → MeasureTheory.Integrable (fun a => ∑ i ∈ s, f i a) μ

Defined in

Mathlib.MeasureTheory.Function.L1Space.Integrable

Cited by

6 results in Mathlib

Foundations

Depth 209 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceESeminormedAddCommMonoidContinuousAdd