Theorems · Theorem · complex analysis
Meromorphic.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},
(∀ σ ∈ s, Meromorphic (G σ)) → Meromorphic (∑ n ∈ s, G n)- Defined in
- Mathlib.Analysis.Meromorphic.Basic
- Cited by
- 2 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.
Cites7
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 · cited by 5,195
- Meromorphicstatement and proof · cited by 108
- MeromorphicAt.sumproof · cited by 4
Cited by2
Results whose statement or proof uses this declaration.
- ValueDistribution.logCounting_sum_top_leproof · cited by 2
- Meromorphic.fun_sumproof · cited by 1