Theorems · Theorem · complex analysis
meromorphic_congr_codiscrete
∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_3} [inst_1 : NormedAddCommGroup E]
[inst_2 : NormedSpace 𝕜 E] {f g : 𝕜 → E}, f =ᶠ[Filter.codiscrete 𝕜] g → (Meromorphic f ↔ Meromorphic g)If two functions differ only on a discrete set, then one is meromorphic iff so is the other.
- Defined in
- Mathlib.Analysis.Meromorphic.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 192 from the axioms · uses propext, Classical.choice, Quot.sound
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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
- Filter.EventuallyEqstatement and proof · cited by 1,912
- Filter.EventuallyEq.symmproof · cited by 408
- Meromorphicstatement and proof · cited by 108
- Filter.codiscretestatement and proof · cited by 34
- Meromorphic.congr_codiscreteproof · cited by 1
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