  This paper presents sufficient conditions for the existence of stationary
optimal policies for average-cost Markov Decision Processes with Borel state
and action sets and with weakly continuous transition probabilities. The
one-step cost functions may be unbounded, and action sets may be noncompact.
The main contributions of this paper are: (i) general sufficient conditions for
the existence of stationary discount-optimal and average-cost optimal policies
and descriptions of properties of value functions and sets of optimal actions,
(ii) a sufficient condition for the average-cost optimality of a stationary
policy in the form of optimality inequalities, and (iii) approximations of
average-cost optimal actions by discount-optimal actions.
