International Journal of Mathematics and Mathematical Sciences
Volume 16 (1993), Issue 2, Pages 277-282
doi:10.1155/S0161171293000328
A metric space associated with a probability space
Keith F. Taylor
and Xikui Wang
Department of Mathematics, University of Saskatchewan, Sask., Saskatoon S7N 0W0, Canada
Abstract
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.