International Journal of Mathematics and Mathematical Sciences
Volume 10 (1987), Issue 1, Pages 9-16
A -mixing convergence theorem for convex set valued processes
Department of Computer and Information Science, Indiana University – Purdue University at Indianapolis, Indianapolis 46223, IN, USA
Received 27 May 1986; Revised 27 August 1986
Copyright © 1987 A. de Korvin and R. Kleyle. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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.