Theorems · Theorem · several complex variables

ContinuousMultilinearMap.cpolynomialOn_uncurry_compContinuousLinearMap

∀ {𝕜 : Type u_1} {G : Type u_4} [inst : NontriviallyNormedField 𝕜] [inst_1 : NormedAddCommGroup G]
  [inst_2 : NormedSpace 𝕜 G] {ι : Type u_5} {Em : ι → Type u_6} {Fm : ι → Type u_7}
  [inst_3 : (i : ι) → NormedAddCommGroup (Em i)] [inst_4 : (i : ι) → NormedSpace 𝕜 (Em i)]
  [inst_5 : (i : ι) → NormedAddCommGroup (Fm i)] [inst_6 : (i : ι) → NormedSpace 𝕜 (Fm i)] [inst_7 : Fintype ι]
  {t : Set (((i : ι) → Fm i →L[𝕜] Em i) × ContinuousMultilinearMap 𝕜 Em G)},
  CPolynomialOn 𝕜 (fun p => p.2.compContinuousLinearMap p.1) t

Defined in

Mathlib.Analysis.Analytic.CPolynomial

Cited by

0 results in Mathlib

Foundations

Depth 190 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpaceFintype