期刊名称：International Journal of Mathematics and Mathematical Sciences
印刷版ISSN：0161-1712
电子版ISSN：1687-0425
出版年度：1993
卷号：16
DOI：10.1155/S0161171293000328
出版社：Hindawi Publishing Corporation
摘要：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.
