Noncommutative Vitali-Hahn-Saks Theorem holds precisely for finite $W^{\ast }$-algebras

E. Chetcuti, J. Hamhalter

It is shown that the bona fide generalization of the Vitali-Hahn-Saks Theorem to von Neumann algebras is possible if, and only if, the algebra is finite. This settles the problem o…