International Journal of Mathematics and Mathematical Sciences
Volume 10 (1987), Issue 1, Pages 9-16
doi:10.1155/S0161171287000024

A *-mixing convergence theorem for convex set valued processes

Abstract

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.