16 lines
430 B
Plaintext
16 lines
430 B
Plaintext
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import Mathlib.Analysis.Analytic.Meromorphic
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import Nevanlinna.analyticAt
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import Nevanlinna.divisor
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open scoped Interval Topology
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open Real Filter MeasureTheory intervalIntegral
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theorem MeromorphicAt.eventually_eq_zero_or_eventually_ne_zero
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{f : ℂ → ℂ}
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{z₀ : ℂ}
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(hf : MeromorphicAt f z₀) :
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(∀ᶠ (z : ℂ) in nhds z₀, f z = 0) ∨ ∀ᶠ (z : ℂ) in nhdsWithin z₀ {z₀}ᶜ, f z ≠ 0 := by
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sorry
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