Theorems · Theorem · several complex variables

Finset.analyticWithinAt_fun_prod

∀ {α : Type u_1} {𝕜 : Type u_2} [inst : NontriviallyNormedField 𝕜] {E : Type u_3} [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedSpace 𝕜 E] {A : Type u_9} [inst_3 : NormedCommRing A] [inst_4 : NormedAlgebra 𝕜 A] {f : α → E → A}
  {c : E} {s : Set E} (N : Finset α),
  (∀ n ∈ N, AnalyticWithinAt 𝕜 (f n) s c) → AnalyticWithinAt 𝕜 (fun z => ∏ n ∈ N, f n z) s c

Finite products of analytic functions are analytic

Defined in

Mathlib.Analysis.Analytic.Constructions

Cited by

3 results in Mathlib

Foundations

Depth 189 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedCommRingNormedAlgebra