Theorems · Theorem · several complex variables

analyticAt_finprod

∀ {𝕜 : Type u_2} [inst : NontriviallyNormedField 𝕜] {E : Type u_3} [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedSpace 𝕜 E] {α : Type u_9} {A : Type u_10} [inst_3 : NormedCommRing A] [inst_4 : NormedAlgebra 𝕜 A]
  {f : α → E → A} {c : E}, (∀ (a : α), AnalyticAt 𝕜 (f a) c) → AnalyticAt 𝕜 (∏ᶠ (n : α), f n) c

Finproducts of analytic functions are analytic

Defined in

Mathlib.Analysis.Analytic.Constructions

Cited by

2 results in Mathlib

Foundations

Depth 193 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedCommRingNormedAlgebra