Theorems · Theorem · complex analysis

MeromorphicOn.congr_codiscreteWithin

∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_3} [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedSpace 𝕜 E] {f g : 𝕜 → E} {U : Set 𝕜},
  MeromorphicOn f U → f =ᶠ[Filter.codiscreteWithin U] g → IsOpen U → MeromorphicOn g U

If f is meromorphic on an open set U, if g agrees with f on a codiscrete subset of U, then g is also meromorphic on U.

Defined in

Mathlib.Analysis.Meromorphic.Basic

Cited by

3 results in Mathlib

Foundations

Depth 190 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpace