Occupation measures in average cost Markov decision processes

We consider the average cost Markov decision processes (MDPʹs) with general state and action spaces. Extending the idea in Borkarʹs excellent paper [3, 4], we define an extended occupation measure associated with the class of policies for MDPʹs and an annexed index (called a power), by which the validity for optimization is measured. Also, by construction of an extended occupation measure, the policy with robustness for the cost function is given. The proofs are done without continuity and compactness and universally and/or analytically measurable policies are unnecessary to describe the results, which are new in this paper.