Montel's Theorem
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Theorem
Let $U \subseteq \C$ be an open subset of the complex numbers.
Let $\mathcal H \left({U}\right)$ be the space of holomorphic mappings on $U$.
Then a family of mappings $\mathcal F \subseteq \mathcal H \left({U}\right)$ is normal if and only if $\mathcal F$ is locally bounded.
Proof
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Source of Name
This entry was named for Paul Antoine Aristide Montel.
Sources
- 1978: John B. Conway: Functions of One Complex Variable (2nd ed.): $\S 7.2$