Theorems · Theorem · complex analysis

analyticOrderAt_eq_top

∀ {𝕜 : Type u_1} {E : Type u_2} [inst : NontriviallyNormedField 𝕜] [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedSpace 𝕜 E] {f : 𝕜 → E} {z₀ : 𝕜}, analyticOrderAt f z₀ = ⊤ ↔ ∀ᶠ (z : 𝕜) in nhds z₀, f z = 0

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

Defined in

Mathlib.Analysis.Analytic.Order

Cited by

12 results in Mathlib

Foundations

Depth 195 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpace