30 lines
751 B
Plaintext
30 lines
751 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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import Nevanlinna.meromorphicAt
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import Nevanlinna.meromorphicOn_divisor
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import Nevanlinna.stronglyMeromorphicOn
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import Nevanlinna.mathlibAddOn
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open scoped Interval Topology
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open Real Filter MeasureTheory intervalIntegral
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theorem MeromorphicOn.order_ne_top
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{f : ℂ → ℂ}
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{U : Set ℂ}
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(h₁U : IsConnected U)
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(h₁f : MeromorphicOn f U) :
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(∃ z₀ : U, (h₁f z₀.1 z₀.2).order ≠ ⊤) ↔ (∀ z : U, (h₁f z.1 z.2).order ≠ ⊤) := by
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constructor
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· intro h
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obtain ⟨h₁z₀, h₂z₀⟩ := h
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intro hz
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sorry
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· intro h
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obtain ⟨w, hw⟩ := h₁U.nonempty
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use ⟨w, hw⟩
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exact h ⟨w, hw⟩
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