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Abstract
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International Journal of Mathematics and Mathematical Sciences
Volume 16 (1993), Issue 3, Pages 511-514
doi:10.1155/S0161171293000626

Completeness of the set of sub-σ-algebras

Xikui Wang

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

Abstract

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.