A characterization of Cesàro average utility

Let X be a connected metric space, and let ⪰ weak order defined on suitable subset of N . We characterize when has Cesàro average utility representation This means that there is continuous real-valued function u such that, for all sequences x = ( n ) 1 ∞ y in the domain ⪰, we have if only limit as → value , … higher than applications to decision theory, game intergenerational social choice.