A metric space associated with probability space

Keith F. Taylor and Xikui Wang

International Journal of Mathematics and Mathematical Sciences, 1993, vol. 16, 1-6

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 II 1 -factor are briefly discussed.

Date: 1993
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:815482

DOI: 10.1155/S0161171293000328

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