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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Hindawi Limited
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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doaj-22b2cecad228446e987a3424d69140f82020-11-24T23:08:52ZengHindawi LimitedInternational 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. |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
A. de Korvin R. Kleyle |
| 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. |
| author_facet |
A. de Korvin R. Kleyle |
| author_sort |
A. de Korvin |
| title |
A *-mixing convergence theorem for convex set valued processes |
| title_short |
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_sort |
*-mixing convergence theorem for convex set valued processes |
| publisher |
Hindawi Limited |
| series |
International Journal of Mathematics and Mathematical Sciences |
| issn |
0161-1712 1687-0425 |
| publishDate |
1987-01-01 |
| 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. |
| 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 |
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1725612639820709888 |