Theorems · Theorem · real analysis

BoxIntegral.Integrable.to_subbox_aux

∀ {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 J : BoxIntegral.Box ι} [inst_4 : Fintype ι]
  {l : BoxIntegral.IntegrationParams} {f : (ι → ℝ) → E} {vol : BoxIntegral.BoxAdditiveMap ι (E →L[ℝ] F) ⊤}
  [CompleteSpace F],
  BoxIntegral.Integrable I l f vol →
    ∀ (hJ : J ≤ I),
      ∃ y,
        BoxIntegral.HasIntegral J l f vol y ∧
          Filter.Tendsto (BoxIntegral.integralSum f vol)
            (BoxIntegral.IntegrationParams.toFilteriUnion I (BoxIntegral.Prepartition.single I J hJ)) (nhds y)

Defined in

Mathlib.Analysis.BoxIntegral.Basic

Cited by

2 results in Mathlib

Foundations

Depth 177 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpaceFintypeCompleteSpace