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Montel's theorem
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(Theorem)
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Suppose that $G \subset {\mathbb{C}}$ is a region.
In other words a sequence of holomorphic functions $\{ f_n \}$ has a subsequence which converges uniformly on compact subsets to a holomorphic function $f \colon G \to {\mathbb{C}}$ if and only if the set $\{ f_n \}$ is locally bounded.
- 1
- John B. Conway. Functions of One Complex Variable I. Springer-Verlag, New York, New York, 1978.
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"Montel's theorem" is owned by jirka.
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Cross-references: compact subsets, converges uniformly, subsequence, sequence, locally bounded, holomorphic functions, region
There is 1 reference to this entry.
This is version 5 of Montel's theorem, born on 2004-04-11, modified 2005-03-07.
Object id is 5754, canonical name is MontelsTheorem.
Accessed 4710 times total.
Classification:
| AMS MSC: | 30C99 (Functions of a complex variable :: Geometric function theory :: Miscellaneous) |
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Pending Errata and Addenda
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