Theorems · Theorem · complex analysis

meromorphicOrderAt_eq_top_iff

∀ {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}, meromorphicOrderAt f x = ⊤ ↔ ∀ᶠ (z : 𝕜) in nhdsWithin x {x}ᶜ, f z = 0

The order of a meromorphic function f at a z₀ is infinity iff f vanishes locally around z₀.

Defined in

Mathlib.Analysis.Meromorphic.Order

Cited by

20 results in Mathlib

Foundations

Depth 197 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpace