The aim of this paper is to develop some measure-theoretic methods for the study of large economic systems with individual-specific randomness and multiple optimal actions. In particular, for a suitably formulated continuum of correspondences, an exact version of the law of large numbers in...

For choice with deterministic consequences, the standard rationality hypothesis is ordinality, i.e., maximization of a weak preference ordering. For choice under risk (resp. uncertainty), preferences are assumed to be represented by the objectively (resp. subjectively) expected value of a von...