A metric space associated with probability space
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...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
1993-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171293000328 |
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| Summary: | 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. |
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| ISSN: | 0161-1712 1687-0425 |