Lie derivations on the algebra of measurable operators affiliated with a type I finite von Neumann algebra

Let $M$ be a type I finite von Neumann algebra and let $S(M)$ be the algebra of all measurable operators affiliated with $M$. We prove that every Lie derivation on $S(M)$ has standard form, that is, it is decomposed into the sum of a derivation and a center-valued trace.