In this paper we consider stochastic equilibrium problems involving parameter of probability measures. Employing the fixed point theorem of Knaster, Kuratowski, Mazurkiewicz, and Fan (KKM-Fan), conditions for the existence of solutions to such problems are established. We then propose new metric concepts on the underlying stochastic spaces and study some properties corresponding to these metrics. Afterwards, we study sufficient conditions for the solution mappings of such problems, that are closed, upper (lower) semicontinuous and continuous with respect to the mentioned metrics.
Finally, the special cases of stochastic optimization problems are taken into account as the applications.