Operator-valued measurable functions

Abstract

Let $\Omega$ be a measurable space and $\mathcal{M}$ be a $\sigma$-finite von Neumann algebra which is also a second dual space. On the set of functions from $\Omega$ into $\mathcal{M}$, it is supposed to give a criterion to illustrate $\tau$-measurability where $\tau$ runs over some well-known locally convex topologies on $\mathcal{M}$ which is stronger than weak operator topology and weaker than the Arens-Mackey topology.