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This paper is devoted to derivations on the algebra $S(M)$ of all measurableoperators 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 resultis valid for derivation on the algebra $S(M,\tau)$ of $\tau$-measurableoperators equipped with the measure topology $t_{\tau}$.

Innerness of continuous derivations on algebras of measurable operators affiliated with finite von Neumann algebras