  This paper is devoted to derivations on the algebra $S(M)$ of all measurable
operators affiliated with a finite von Neumann algebra $M.$ We prove that if
$M$ is a finite von Neumann algebra with a faithful normal semi-finite trace
$\tau$, equipped with the locally measure topology $t,$ then every
$t$-continuous derivation $D:S(M)\rightarrow S(M)$ is inner. A similar result
is valid for derivation on the algebra $S(M,\tau)$ of $\tau$-measurable
operators equipped with the measure topology $t_{\tau}$.
