A *-mixing convergence theorem for convex set valued processes
In this paper the concept of a *-mixing process is extended to multivalued maps from a probability space into closed, bounded convex sets of a Banach space. The main result, which requires that the Banach space be separable and reflexive, is a convergence theorem for *-mixing sequences which is anal...
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| Format: | Article |
| Language: | English |
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Wiley
1987-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171287000024 |
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| _version_ | 1832556728480169984 |
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| author | A. de Korvin R. Kleyle |
| author_facet | A. de Korvin R. Kleyle |
| author_sort | A. de Korvin |
| collection | DOAJ |
| description | In this paper the concept of a *-mixing process is extended to multivalued maps from a probability space into closed, bounded convex sets of a Banach space. The main result, which requires that the Banach space be separable and reflexive, is a convergence theorem for *-mixing sequences which is analogous to the strong law of large numbers. The impetus for studying this problem is provided by a model from information science involving the utilization of feedback data by a decision maker who is uncertain of his goals. The main result is somewhat similar to a theorem for real valued processes and is of interest in its own right. |
| format | Article |
| id | doaj-art-22b2cecad228446e987a3424d69140f8 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1987-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-22b2cecad228446e987a3424d69140f82025-02-03T05:44:27ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251987-01-0110191610.1155/S0161171287000024A *-mixing convergence theorem for convex set valued processesA. de Korvin0R. Kleyle1Department of Computer and Information Science, Indiana University – Purdue University at Indianapolis, Indianapolis, IN 46223, USADepartment of Computer and Information Science, Indiana University – Purdue University at Indianapolis, Indianapolis, IN 46223, USAIn this paper the concept of a *-mixing process is extended to multivalued maps from a probability space into closed, bounded convex sets of a Banach space. The main result, which requires that the Banach space be separable and reflexive, is a convergence theorem for *-mixing sequences which is analogous to the strong law of large numbers. The impetus for studying this problem is provided by a model from information science involving the utilization of feedback data by a decision maker who is uncertain of his goals. The main result is somewhat similar to a theorem for real valued processes and is of interest in its own right.http://dx.doi.org/10.1155/S0161171287000024decision making*-mixing processmultivalued mapsHausdorff metric. |
| spellingShingle | A. de Korvin R. Kleyle A *-mixing convergence theorem for convex set valued processes International Journal of Mathematics and Mathematical Sciences decision making *-mixing process multivalued maps Hausdorff metric. |
| title | A *-mixing convergence theorem for convex set valued processes |
| title_full | A *-mixing convergence theorem for convex set valued processes |
| title_fullStr | A *-mixing convergence theorem for convex set valued processes |
| title_full_unstemmed | A *-mixing convergence theorem for convex set valued processes |
| title_short | A *-mixing convergence theorem for convex set valued processes |
| title_sort | mixing convergence theorem for convex set valued processes |
| topic | decision making *-mixing process multivalued maps Hausdorff metric. |
| url | http://dx.doi.org/10.1155/S0161171287000024 |
| work_keys_str_mv | AT adekorvin amixingconvergencetheoremforconvexsetvaluedprocesses AT rkleyle amixingconvergencetheoremforconvexsetvaluedprocesses AT adekorvin mixingconvergencetheoremforconvexsetvaluedprocesses AT rkleyle mixingconvergencetheoremforconvexsetvaluedprocesses |