The Egoroff theorem for measurable $\bold X$-valued functions and
operator-valued measures $\bold m: \Sigma \to L(\bold X, \bold Y)$, where
$\Sigma$ is a $\sigma$-algebra of subsets of $T \neq \emptyset$ and $\bold X$,
$\bold Y$ are both locally convex spaces, is proved. The measure is supposed to
be atomic and the convergence of functions is net.