Theorems · Theorem · complex analysis

tendsto_zero_of_meromorphicOrderAt_pos

∀ {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},
  0 < meromorphicOrderAt f x → Filter.Tendsto f (nhdsWithin x {x}ᶜ) (nhds 0)

If the order of a meromorphic function is positive, then this function converges to zero at this point. See also the iff version tendsto_zero_iff_meromorphicOrderAt_pos.

Defined in

Mathlib.Analysis.Meromorphic.Order

Cited by

4 results in Mathlib

Foundations

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

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpace