Theorems · Theorem · real analysis

BoxIntegral.HasIntegral.sum

∀ {ι : Type u} {E : Type v} {F : Type w} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E]
  [inst_2 : NormedAddCommGroup F] [inst_3 : NormedSpace ℝ F] {I : BoxIntegral.Box ι} [inst_4 : Fintype ι]
  {l : BoxIntegral.IntegrationParams} {vol : BoxIntegral.BoxAdditiveMap ι (E →L[ℝ] F) ⊤} {α : Type u_1} {s : Finset α}
  {f : α → (ι → ℝ) → E} {g : α → F},
  (∀ i ∈ s, BoxIntegral.HasIntegral I l (f i) vol (g i)) →
    BoxIntegral.HasIntegral I l (fun x => ∑ i ∈ s, f i x) vol (∑ i ∈ s, g i)

Defined in

Mathlib.Analysis.BoxIntegral.Basic

Cited by

1 results in Mathlib

Foundations

Depth 169 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpaceFintype