Theorems · Theorem · complex analysis

MeromorphicOn.divisor_support_finite_of_subset

∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {U : Set 𝕜} {E : Type u_2} [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedSpace 𝕜 E] {f : 𝕜 → E} {V : Set 𝕜},
  MeromorphicOn f U → IsCompact U → V ⊆ U → (MeromorphicOn.divisor f V).support.Finite

If f is meromorphic on a compact set U and V ⊆ U, then the divisor of f on V has finite support.

Defined in

Mathlib.Analysis.Meromorphic.Divisor

Cited by

1 results in Mathlib

Foundations

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

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpace