Theorems · Theorem · complex analysis
MeromorphicAt.analyticAt
∀ {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}, MeromorphicAt f x → ContinuousAt f x → AnalyticAt 𝕜 f xIf a function is both meromorphic and continuous at a point, then it is analytic there.
- Defined in
- Mathlib.Analysis.Meromorphic.Order
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 201 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites35
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
- Top.topproof · cited by 9,680
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- nhdsproof · cited by 5,554
- Filter.Eventuallyproof · cited by 3,134
- Compl.complproof · cited by 2,925
- nhdsWithinproof · cited by 1,912
- Filter.univ_mem'proof · cited by 1,672
- Filter.mp_memproof · cited by 1,537
- WithTop.someproof · cited by 1,128
- ContinuousAtstatement and proof · cited by 697
Cited by2
Results whose statement or proof uses this declaration.
- MeromorphicOn.eventually_analyticAtproof · cited by 1
- AnalyticAt.of_meromorphicOrderAt_posproof · cited by 0