cpolynomialAt_uncurry_of_multilinear

English

The uncurry form of a continuous linear map yields a CPolynomialOn on the product set.

Русский

Неокурри форма непрерывного линейного отображения образует CPolynomialOn на произведении.

LaTeX

$$CPolynomialOn 𝕜 (fun p => ContinuousLinearMap.funLike.coe f p.fst p.snd) s$$

Lean4

theorem cpolynomialAt_uncurry_of_multilinear : CPolynomialAt 𝕜 (fun (p : G × (Π i, Em i)) ↦ f p.1 p.2) x :=
  f.hasFiniteFPowerSeriesOnBall_uncurry_of_multilinear.cpolynomialAt_of_mem
    (by simp only [Metric.emetric_ball_top, Set.mem_univ])

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