Theorems · Theorem · complex analysis

MeromorphicAt.finprod

∀ {𝕜 : Type u_1} {𝕜' : Type u_2} [inst : NontriviallyNormedField 𝕜] [inst_1 : NontriviallyNormedField 𝕜']
  [inst_2 : NormedAlgebra 𝕜 𝕜'] {ι : Type u_5} {F : ι → 𝕜 → 𝕜'} {x : 𝕜},
  (∀ (i : ι), MeromorphicAt (F i) x) → MeromorphicAt (∏ᶠ (i : ι), F i) x

Finprods of meromorphic functions are meromorphic.

Defined in

Mathlib.Analysis.Meromorphic.Basic

Cited by

5 results in Mathlib

Foundations

Depth 191 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNontriviallyNormedFieldNormedAlgebra