International Journal of Mathematics and Mathematical Sciences
Volume 16 (1993), Issue 2, Pages 277-282

A metric space associated with probability space

Keith F. Taylor and Xikui Wang

Department of Mathematics, University of Saskatchewan, Sask., Saskatoon S7N 0W0, Canada

Received 7 January 1992

Copyright © 1993 Keith F. Taylor and Xikui Wang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


For a complete probability space (Ω,,P), the set of all complete sub-σ-algebras of , S(), is given a natural metric and studied. The questions of when S() is compact or connected are awswered and the important subset consisting of all continuous sub-σ-algebras is shown to be closed. Connections with Christensen's metric on the von Neumann subalgebras of a Type II1-factor are briefly discussed.