Theorems · Theorem · complex analysis

meromorphicNFAt_prod

∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {x : 𝕜} {ι : Type u_3} {s : Finset ι} {f : ι → 𝕜 → 𝕜},
  (∀ i ∈ s, MeromorphicNFAt (f i) x) → {σ | σ ∈ s ∧ f σ x = 0}.Subsingleton → MeromorphicNFAt (∏ i ∈ s, f i) x

A product of meromorphic functions in normal form is in normal form if at most one of the factors vanishes.

Defined in

Mathlib.Analysis.Meromorphic.NormalForm

Cited by

3 results in Mathlib

Foundations

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

Assumes

NontriviallyNormedField