# Baire Characterisation Theorem

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## Theorem

A real-valued function $f$ defined on a Banach space $X$ is a Baire-$1$ function if and only if:

- for every non-empty closed subset $K$ of $X$, the restriction of $f$ to $K$ has a point of continuity relative to the topology of $K$.

## Proof

## Source of Name

This entry was named for René-Louis Baire.