Theorems · Theorem · complex analysis
MeromorphicAt.fun_sum
∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_3} [inst_1 : NormedAddCommGroup E]
[inst_2 : NormedSpace 𝕜 E] {ι : Type u_5} {s : Finset ι} {G : ι → 𝕜 → E} {x : 𝕜},
(∀ σ ∈ s, MeromorphicAt (G σ) x) → MeromorphicAt (fun z => ∑ n ∈ s, G n z) xFinite sums of meromorphic functions are meromorphic.
- Defined in
- Mathlib.Analysis.Meromorphic.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 193 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- Finsetstatement and proof · cited by 13,712
- NormedSpacestatement and proof · cited by 12,499
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- Finset.sumstatement and proof · cited by 5,195
- Finset.sum_applyproof · cited by 234
- MeromorphicAtstatement and proof · cited by 160
- MeromorphicAt.sumproof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- MeromorphicOn.fun_sumproof · cited by 0