Completeness of the set of sub-σ-algebras
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.
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
1993-01-01
|
| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171293000626 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1841524491601051648 |
|---|---|
| author | Xikui Wang |
| author_facet | Xikui Wang |
| author_sort | Xikui Wang |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-cede7dd7f8a2491c9b561fc1e2fbd5f0 |
| 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-cede7dd7f8a2491c9b561fc1e2fbd5f02025-02-03T05:53:13ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251993-01-0116351151410.1155/S0161171293000626Completeness of the set of sub-σ-algebrasXikui Wang0Department of Mathematics, University of Saskatchewan, Sask., Saskatoon S7N 0W0, CanadaA 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.http://dx.doi.org/10.1155/S0161171293000626conditional expectationmetricSidăk operatorBanach lattice. |
| spellingShingle | Xikui Wang Completeness of the set of sub-σ-algebras International Journal of Mathematics and Mathematical Sciences conditional expectation metric Sidăk operator Banach lattice. |
| title | Completeness of the set of sub-σ-algebras |
| title_full | Completeness of the set of sub-σ-algebras |
| title_fullStr | Completeness of the set of sub-σ-algebras |
| title_full_unstemmed | Completeness of the set of sub-σ-algebras |
| title_short | Completeness of the set of sub-σ-algebras |
| title_sort | completeness of the set of sub σ algebras |
| topic | conditional expectation metric Sidăk operator Banach lattice. |
| url | http://dx.doi.org/10.1155/S0161171293000626 |
| work_keys_str_mv | AT xikuiwang completenessofthesetofsubsalgebras |