冯•诺依曼代数的可测算子的性质

In this article, some properties of measurable operators associated with a von Neumann algebra are considered. The concept of step operator is defined and it is proved that any positive measurable operator can be strongly approximated by some step operators on its domain, which means that any positive measurable operator can be strongly approximated by some projections on its domain. In addition, the measurability of composition operator of measurable operator and bounded operator is discussed.