# 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.

## Source of Name

This entry was named for Paul Antoine Aristide Montel.