compContinuousMultilinearMap — Mathlib

English

The sum of the pi-construction over a finite index set yields a multilinear map into the space of functions.

Русский

Сумма конструкций pi по конечному индексу даёт мультиляйн карту в пространство функций.

LaTeX

$$$\\text{sum of pi} = \\toMultilinearMap(\\sum f)$.$$

Lean4

/-- Composing a continuous multilinear map with a continuous linear map gives again a
continuous multilinear map. -/
def _root_.ContinuousLinearMap.compContinuousMultilinearMap (g : M₂ →L[R] M₃) (f : ContinuousMultilinearMap R M₁ M₂) :
    ContinuousMultilinearMap R M₁ M₃ :=
  { g.toLinearMap.compMultilinearMap f.toMultilinearMap with cont := g.cont.comp f.cont }

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