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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| _version_ | 1832565025085063168 |
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| author | Keith F. Taylor Xikui Wang |
| author_facet | Keith F. Taylor Xikui Wang |
| author_sort | Keith F. Taylor |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-60d592818d6b4be7ac7aadfb98f6bd54 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1993-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-60d592818d6b4be7ac7aadfb98f6bd542025-02-03T01:09:31ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251993-01-0116227728210.1155/S0161171293000328A metric space associated with probability spaceKeith F. Taylor0Xikui Wang1Department of Mathematics, University of Saskatchewan, Sask., Saskatoon S7N 0W0, CanadaDepartment of Mathematics, University of Saskatchewan, Sask., Saskatoon S7N 0W0, CanadaFor 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.http://dx.doi.org/10.1155/S0161171293000328σ-algebrasconditional expectationsmetric spacevon Neumann algebra. |
| spellingShingle | Keith F. Taylor Xikui Wang A metric space associated with probability space International Journal of Mathematics and Mathematical Sciences σ-algebras conditional expectations metric space von Neumann algebra. |
| title | A metric space associated with probability space |
| title_full | A metric space associated with probability space |
| title_fullStr | A metric space associated with probability space |
| title_full_unstemmed | A metric space associated with probability space |
| title_short | A metric space associated with probability space |
| title_sort | metric space associated with probability space |
| topic | σ-algebras conditional expectations metric space von Neumann algebra. |
| url | http://dx.doi.org/10.1155/S0161171293000328 |
| work_keys_str_mv | AT keithftaylor ametricspaceassociatedwithprobabilityspace AT xikuiwang ametricspaceassociatedwithprobabilityspace AT keithftaylor metricspaceassociatedwithprobabilityspace AT xikuiwang metricspaceassociatedwithprobabilityspace |