Theorems · Definition · real analysis

BoxIntegral.BoxAdditiveMap.toSMul

{ι : Type u_1} →
  {I₀ : WithTop (BoxIntegral.Box ι)} →
    {E : Type u_4} →
      [inst : NormedAddCommGroup E] →
        [inst_1 : NormedSpace ℝ E] → BoxIntegral.BoxAdditiveMap ι ℝ I₀ → BoxIntegral.BoxAdditiveMap ι (E →L[ℝ] E) I₀

If f is a box-additive map, then so is the map sending I to the scalar multiplication by f I as a continuous linear map from E to itself.

Defined in

Mathlib.Analysis.BoxIntegral.Partition.Additive

Cited by

17 results in Mathlib

Foundations

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

Assumes

NormedAddCommGroupNormedSpace