  This paper concerns discrete-time infinite-horizon stochastic control systems
with Borel state and action spaces and universally measurable policies. We
study optimization problems on strategic measures induced by the policies in
these systems. The results are then applied to risk-neutral and risk-sensitive
Markov decision processes, as well as their partially observable counterparts,
to establish the measurability of the optimal value functions and the existence
of universally measurable, randomized or nonrandomized, $\epsilon$-optimal
policies, for a variety of average cost criteria and risk criteria. We also
extend our analysis to a class of minimax control problems and establish
similar optimality results under the axiom of analytic determinacy.
