Theorems · Theorem · several complex variables

Finset.analyticAt_fun_sum

∀ {α : Type u_1} {𝕜 : Type u_2} [inst : NontriviallyNormedField 𝕜] {E : Type u_3} {F : Type u_4}
  [inst_1 : NormedAddCommGroup E] [inst_2 : NormedSpace 𝕜 E] [inst_3 : NormedAddCommGroup F] [inst_4 : NormedSpace 𝕜 F]
  {f : α → E → F} {c : E} (N : Finset α), (∀ n ∈ N, AnalyticAt 𝕜 (f n) c) → AnalyticAt 𝕜 (fun a => ∑ c ∈ N, f c a) c

Eta-expanded form of Finset.analyticAt_sum Finite sums of analytic functions are analytic

Defined in

Mathlib.Analysis.Analytic.Constructions

Cited by

1 results in Mathlib

Foundations

Depth 179 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpace