Theorems · Theorem · complex analysis

MeromorphicNFAt.eventuallyEq_nhdsNE_iff_eventuallyEq_nhds

∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_2} [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedSpace 𝕜 E] {f : 𝕜 → E} {x : 𝕜} {g : 𝕜 → E},
  MeromorphicNFAt f x → MeromorphicNFAt g x → (f =ᶠ[nhdsWithin x {x}ᶜ] g ↔ f =ᶠ[nhds x] g)

Local identity theorem: two meromorphic functions in normal form agree in a neighborhood iff they agree in a pointed neighborhood. See ContinuousAt.eventuallyEq_nhds_iff_eventuallyEq_nhdsNE for the analogous statement for continuous functions.

Defined in

Mathlib.Analysis.Meromorphic.NormalForm

Cited by

1 results in Mathlib

Foundations

Depth 201 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpace