Theorems · Theorem · complex analysis

MeromorphicAt.sum

∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_3} [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedSpace 𝕜 E] {ι : Type u_5} {s : Finset ι} {G : ι → 𝕜 → E} {x : 𝕜},
  (∀ σ ∈ s, MeromorphicAt (G σ) x) → MeromorphicAt (∑ n ∈ s, G n) x

Finite sums of meromorphic functions are meromorphic.

Defined in

Mathlib.Analysis.Meromorphic.Basic

Cited by

4 results in Mathlib

Foundations

Depth 192 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpace