  Given a von Neumann algebra $M$ with a faithful normal semi-finite trace
$\tau,$ let $L(M, \tau)$ be the algebra of all $\tau$-measurable operators
affiliated with $M.$ We prove that if $A$ is a locally convex reflexive
complete metrizable solid $\ast$-subalgebra in $L(M, \tau),$ which can be
embedded into a locally bounded weak Fr\'{e}chet $M$-bimodule, then any
derivation on $A$ is inner.
