2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/166556Let $M$ 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).$12 pagesOperator AlgebrasFunctional Analysis46L57, 46L50, 46L55. 46L60text