Theorems · Theorem · complex analysis
MeromorphicNFOn.meromorphicOn
∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_2} [inst_1 : NormedAddCommGroup E]
[inst_2 : NormedSpace 𝕜 E] {f : 𝕜 → E} {U : Set 𝕜}, MeromorphicNFOn f U → MeromorphicOn f UIf a function is meromorphic in normal form on U, then it is meromorphic on
U.
- Defined in
- Mathlib.Analysis.Meromorphic.NormalForm
- Cited by
- 13 results in Mathlib
- Foundations
- Depth 199 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- MeromorphicOnstatement · cited by 141
- MeromorphicNFOnstatement and proof · cited by 35
- MeromorphicNFAt.meromorphicAtproof · cited by 7
Cited by13
Results whose statement or proof uses this declaration.
- MeromorphicOn.extract_zeros_polesproof · cited by 4
- Function.FactorizedRational.meromorphicOrderAt_eqproof · cited by 3
- Meromorphic.Gammaproof · cited by 2
- MeromorphicOn.divisor_of_toMeromorphicNFOnproof · cited by 2
- MeromorphicNFOn.divisor_nonneg_iff_analyticOnNhdproof · cited by 2
- MeromorphicOn.log_norm_meromorphicTrailingCoeffAt_extract_zeros_polesproof · cited by 1
- Function.FactorizedRational.divisorproof · cited by 1
- MeromorphicOn.exists_canonicalDecompproof · cited by 1
- Complex.CanonicalDecomp.divisor_eq_divisorproof · cited by 1
- toMeromorphicNFOn_eq_selfproof · cited by 0
- MeromorphicOn.meromorphicTrailingCoeffAt_extract_zeros_polesproof · cited by 0
- MeromorphicNFOn.zero_set_eq_divisor_supportproof · cited by 0