Theorems · Theorem · real analysis

BoxIntegral.integral_add

∀ {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} {f g : (ι → ℝ) → E} {vol : BoxIntegral.BoxAdditiveMap ι (E →L[ℝ] F) ⊤},
  BoxIntegral.Integrable I l f vol →
    BoxIntegral.Integrable I l g vol →
      BoxIntegral.integral I l (f + g) vol = BoxIntegral.integral I l f vol + BoxIntegral.integral I l g vol

Defined in

Mathlib.Analysis.BoxIntegral.Basic

Cited by

0 results in Mathlib

Foundations

Depth 171 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpaceFintype