  We consider the linear programming approach for constrained and unconstrained
Markov decision processes (MDPs) under the long-run average cost criterion,
where the class of MDPs in our study have Borel state spaces and discrete
countable action spaces. Under a strict unboundedness condition on the
one-stage costs and a recently introduced majorization condition on the state
transition stochastic kernel, we study infinite-dimensional linear programs for
the average-cost MDPs and prove the absence of a duality gap and other
optimality results. Our results do not require a lower-semicontinuous MDP
model. Thus, they can be applied to countable action space MDPs where the
dynamics and one-stage costs are discontinuous in the state variable. Our
proofs make use of the continuity property of Borel measurable functions
asserted by Lusin's theorem.
