  Let $M$ be a type I von Neumann algebra with the center $Z,$ and let $LS(M)$
be the algebra of all locally measurable operators affiliated with $M.$ We
prove that every $Z$-linear derivation on $LS(M)$ is inner. In particular all
$Z$-linear derivations on the algebras of measurable and respectively totally
measurable operators are spatial and implemented by elements from $LS(M).$
