Theorems · Theorem · complex analysis
MeromorphicOn.toMeromorphicNFOn_eq_self_on_nhdsNE
∀ {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} {U : Set 𝕜},
MeromorphicOn f U → x ∈ U → toMeromorphicNFOn f U =ᶠ[nhdsWithin x {x}ᶜ] fIf f is meromorphic on U and x ∈ U, then f and its conversion to normal
form on U agree in a punctured neighborhood of x.
- Defined in
- Mathlib.Analysis.Meromorphic.NormalForm
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 204 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- Compl.complstatement and proof · cited by 2,925
- nhdsWithinstatement · cited by 1,912
- Filter.EventuallyEqstatement · cited by 1,912
- Filter.univ_mem'proof · cited by 1,672
- Filter.mp_memproof · cited by 1,537
- AnalyticAtproof · cited by 321
- MeromorphicOnstatement and proof · cited by 141
- AnalyticAt.meromorphicNFAtproof · cited by 16
Cited by3
Results whose statement or proof uses this declaration.
- MeromorphicOn.extract_zeros_polesproof · cited by 4
- meromorphicOrderAt_toMeromorphicNFOnproof · cited by 2
- toMeromorphicNFOn_eq_toMeromorphicNFAt_on_nhdsproof · cited by 2