Theorems · Definition · real analysis

BoxIntegral.integralSum

{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} →
                ((ι → ℝ) → E) → BoxIntegral.BoxAdditiveMap ι (E →L[ℝ] F) ⊤ → BoxIntegral.TaggedPrepartition I → F

The integral sum of f : ℝⁿ → E over a tagged prepartition π w.r.t. box-additive volume vol with codomain E →L[ℝ] F is the sum of vol J (f (π.tag J)) over all boxes of π.

Defined in

Mathlib.Analysis.BoxIntegral.Basic

Cited by

32 results in Mathlib

Foundations

Depth 164 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpace