A Characterization of Cesàro Average Utility

Let X be a connected metric space, let N be the set of natural numbers, and let > be a preference order defined on a suitable subset of X^N. I characterize when > has a Cesàro average utility representation. This means that there is a continuous function u from X into the real numbers, such that one sequence in X^N is preferred to another sequence if it yields a higher limit, as n goes to infinity, of the average utility over the first n terms in the sequence. This has applications to decision theory and inter-generational social choice