NON-COMMUTATIVE VITALI-HAHN-SAKS THEOREM HOLDS PRECISELY FOR FINITE W*-ALGEBRAS
Emmanuel Chetcuti, Jan Hamhalter · The Quarterly Journal of Mathematics · 2008
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 on the non-commutative Vitali–Hahn–Saks theorem completely and provides new means of characterizing finite von Neumann algebras.