Theorems · Theorem · complex analysis
meromorphicOn_univ
∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_3} [inst_1 : NormedAddCommGroup E]
[inst_2 : NormedSpace 𝕜 E] {f : 𝕜 → E}, MeromorphicOn f Set.univ ↔ Meromorphic fA function is meromorphic iff it is meromorphic on Set.univ.
- Defined in
- Mathlib.Analysis.Meromorphic.Basic
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 168 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- Set.univstatement and proof · cited by 3,945
- MeromorphicOnstatement and proof · cited by 141
- Meromorphicstatement and proof · cited by 108
Cited by8
Results whose statement or proof uses this declaration.
- Meromorphic.Gammaproof · cited by 2
- Meromorphic.logDeriv_mul_eventuallyEqproof · cited by 1
- Meromorphic.congr_codiscreteproof · cited by 1
- Meromorphic.logDeriv_prod_eventuallyEqproof · cited by 1
- Meromorphic.logDeriv_zpow_eventuallyEqproof · cited by 1
- Meromorphic.exists_meromorphicOrderAt_ne_top_iff_forallproof · cited by 1
- Meromorphic.logDeriv_finprod_zpow_eventuallyEqproof · cited by 0
- Meromorphic.logDeriv_finprod_eventuallyEqproof · cited by 0