Baire Characterisation Theorem

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 $K$.

Source of Name

This entry was named for René-Louis Baire.