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 $M.$ Weprove that every $Z$-linear derivation on $LS(M)$ is inner. In particular all$Z$-linear derivations on the algebras of measurable and respectively totallymeasurable operators are spatial and implemented by elements from $LS(M).$
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机译：设$ M $为中心为Z的I型冯·诺伊曼代数，并令LS（M）$为与M关联的所有可本地度量的算子的代数。我们证明，每个$ Z $线性推导于$ LS（M）$是内部的。特别是在可测算子和完全可测算子的代数上的所有$ Z $线性推导都是空间的，并由$ LS（M）中的元素实现。
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