International Journal of Mathematics and Mathematical Sciences
Volume 16 (1993), Issue 3, Pages 511-514

Completeness of the set of sub-σ-algebras

Xikui Wang

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

Received 4 March 1991; Revised 23 March 1992

Copyright © 1993 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.


A new metric is introduced on the set of all sub-σ-algebras of a complete probability space from functional analysis point of view. In this note, we will show that the resulting metric space is complete.