Theorems · Theorem · complex analysis

meromorphicOrderAt_congr

∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_2} [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedSpace 𝕜 E] {f₁ f₂ : 𝕜 → E} {x : 𝕜},
  f₁ =ᶠ[nhdsWithin x {x}ᶜ] f₂ → meromorphicOrderAt f₁ x = meromorphicOrderAt f₂ x

Meromorphic functions that agree in a punctured neighborhood of z₀ have the same order at z₀.

Defined in

Mathlib.Analysis.Meromorphic.Order

Cited by

15 results in Mathlib

Foundations

Depth 198 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpace