Theorems · Definition · real analysis

BoxIntegral.HasIntegral

{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 → Prop

The predicate HasIntegral I l f vol y says that y is the integral of f over I along l w.r.t. volume vol. This means that integral sums of f tend to 𝓝 y along BoxIntegral.IntegrationParams.toFilteriUnion I ⊤.

Defined in

Mathlib.Analysis.BoxIntegral.Basic

Cited by

30 results in Mathlib

Foundations

Depth 165 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpaceFintype