Theorems · Theorem · complex analysis
MeromorphicAt.meromorphicAt_congr
∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_3} [inst_1 : NormedAddCommGroup E]
[inst_2 : NormedSpace 𝕜 E] {x : 𝕜} {f g : 𝕜 → E}, f =ᶠ[nhdsWithin x {x}ᶜ] g → (MeromorphicAt f x ↔ MeromorphicAt g x)If two functions agree on a punctured neighborhood, then one is meromorphic iff the other is so.
- Defined in
- Mathlib.Analysis.Meromorphic.Basic
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 190 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · 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 and proof · cited by 1,912
- Filter.EventuallyEqstatement and proof · cited by 1,912
- Filter.EventuallyEq.symmproof · cited by 408
- MeromorphicAtstatement and proof · cited by 160
- MeromorphicAt.congrproof · cited by 12
Cited by6
Results whose statement or proof uses this declaration.
- AnalyticAt.meromorphicTrailingCoeffAt_of_ne_zero_of_eq_nhdsNEproof · cited by 11
- meromorphicTrailingCoeffAt_congr_nhdsNEproof · cited by 7
- MeromorphicAt.derivproof · cited by 6
- AnalyticAt.meromorphicTrailingCoeffAt_of_eq_nhdsNEproof · cited by 4
- toMeromorphicNFAt_eventuallyEq_nhds_congrproof · cited by 1
- MeromorphicAt.update_iffproof · cited by 1