## Operator-valued measurable functions.(English)Zbl 1328.46045

Summary: 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 are stronger than the weak operator topology and weaker than the Arens-Mackey topology.

### MSC:

 46L10 General theory of von Neumann algebras 47A56 Functions whose values are linear operators (operator- and matrix-valued functions, etc., including analytic and meromorphic ones) 46G10 Vector-valued measures and integration
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