Ali Bagheri-Bardi

Although there exist different types of (well-known) locally convex topologies on B?H?, the notion of measurability on the set of operator valued functions f : ! B?H? is unique when H is separable (see [1]). In this current discussion we observe that unlike the separable case, in the non-separable case we have to face different types of measurability. Moreover the algebraic operations ‘‘addition and product’’ are not compatible with the set of operator valued measurable functions.