On the continuity of the vector valued and set valued conditional expectations
In this paper we study the dependence of the vector valued conditional expectation (for both single valued and set valued random variables), on the σ–field and random variable that determine it. So we prove that it is continuous for the L1(X) convergence of the sub–σ–fields and of the random variabl...
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| Format: | Article |
| Language: | English |
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Wiley
1989-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S016117128900061X |
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| _version_ | 1832551086126268416 |
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| author | Nikolaos S. Papageorgiou |
| author_facet | Nikolaos S. Papageorgiou |
| author_sort | Nikolaos S. Papageorgiou |
| collection | DOAJ |
| description | In this paper we study the dependence of the vector valued conditional expectation (for both single valued and set valued random variables), on the σ–field and random variable that determine it. So we prove that it is continuous for the L1(X) convergence of the sub–σ–fields and of the random variables. We also present a sufficient condition for the L1(X)–convergence of the sub–σ–fields. Then we extend the work to the set valued conditional expectation using the Kuratowski–Mosco (K–M) convergence and the convergence in the Δ–metric. We also prove a property of the set valued conditional expectation. |
| format | Article |
| id | doaj-art-ed3ca21149ad403d9fdf0822c70f7bf1 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1989-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-ed3ca21149ad403d9fdf0822c70f7bf12025-02-03T06:05:06ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251989-01-0112347748610.1155/S016117128900061XOn the continuity of the vector valued and set valued conditional expectationsNikolaos S. Papageorgiou0University of California, 1015 Department of Mathematics, Davis, California 95616, USAIn this paper we study the dependence of the vector valued conditional expectation (for both single valued and set valued random variables), on the σ–field and random variable that determine it. So we prove that it is continuous for the L1(X) convergence of the sub–σ–fields and of the random variables. We also present a sufficient condition for the L1(X)–convergence of the sub–σ–fields. Then we extend the work to the set valued conditional expectation using the Kuratowski–Mosco (K–M) convergence and the convergence in the Δ–metric. We also prove a property of the set valued conditional expectation.http://dx.doi.org/10.1155/S016117128900061X |
| spellingShingle | Nikolaos S. Papageorgiou On the continuity of the vector valued and set valued conditional expectations International Journal of Mathematics and Mathematical Sciences |
| title | On the continuity of the vector valued and set valued conditional expectations |
| title_full | On the continuity of the vector valued and set valued conditional expectations |
| title_fullStr | On the continuity of the vector valued and set valued conditional expectations |
| title_full_unstemmed | On the continuity of the vector valued and set valued conditional expectations |
| title_short | On the continuity of the vector valued and set valued conditional expectations |
| title_sort | on the continuity of the vector valued and set valued conditional expectations |
| url | http://dx.doi.org/10.1155/S016117128900061X |
| work_keys_str_mv | AT nikolaosspapageorgiou onthecontinuityofthevectorvaluedandsetvaluedconditionalexpectations |