16 lines
527 B
Lean4
16 lines
527 B
Lean4
import Mathlib.Analysis.Meromorphic.Basic
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open MeromorphicOn Metric Real Set Classical
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variable
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{𝕜 : Type*} [NontriviallyNormedField 𝕜]
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{E : Type*} [NormedAddCommGroup E] [NormedSpace 𝕜 E]
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{U : Set 𝕜} {f g : 𝕜 → E} {a : WithTop E} {a₀ : E}
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/-- Finite sums of meromorphic functions are meromorphic. -/
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@[fun_prop]
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theorem MeromorphicAt.sum {ι : Type*} {s : Finset ι} {f : ι → 𝕜 → E} {x : 𝕜}
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(h : ∀ σ, MeromorphicAt (f σ) x) :
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MeromorphicAt (∑ n ∈ s, f n) x := by
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sorry
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