In a recent paper Bures
proved a result concerning the classification of tensor products of a family of
semi-finite W∗-algebras and showed that it constituted a non-commutative extension
of the main part of Kakutani’s theorem on infinite product measures. In
this paper these results are extended, first by removing the semi-finiteness
restriction, and secondly by completing the analogy with Kakutani’s
Theorem.