Theorems · Theorem · complex analysis

MeromorphicNFOn.divisor_nonneg_iff_analyticOnNhd

∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_2} [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedSpace 𝕜 E] {f : 𝕜 → E} {U : Set 𝕜},
  MeromorphicNFOn f U → (0 ≤ MeromorphicOn.divisor f U ↔ AnalyticOnNhd 𝕜 f U)

If a function is meromorphic in normal form on U, then its divisor is non-negative iff it is analytic.

Defined in

Mathlib.Analysis.Meromorphic.NormalForm

Cited by

2 results in Mathlib

Foundations

Depth 208 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpace