Theorems · Definition · real analysis

BoxIntegral.integral

{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] →
              [Fintype ι] →
                BoxIntegral.Box ι →
                  BoxIntegral.IntegrationParams → ((ι → ℝ) → E) → BoxIntegral.BoxAdditiveMap ι (E →L[ℝ] F) ⊤ → F

The integral of a function f over a box I along a filter l w.r.t. a volume vol. Returns zero on non-integrable functions.

Defined in

Mathlib.Analysis.BoxIntegral.Basic

Cited by

25 results in Mathlib

Foundations

Depth 167 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpaceFintype