ABSTRACT
The formulation of the direct integral theory of von Neumann algebras presented in this chapter differs somewhat from the usual one which is due to von Neumann. This difference manifests itself in two ways: in the introduction of the Effros Borel structure, and in the use of the direct integral theory of representations of involutive Banach algebras. In the customary formulation of the theory a field of von Neumann algebras is defined to be Borel (or measurable) if it has a Borel generating sequence for a suitable coherence. What are called Hausdorff metrics were introduced by Hausdorff in 1914, and a number of results concerning them can be found in Kuratowski’s books.
