Continuity Properties of Paretian Utility
Abstract : In the study of real-valued representations (Paretian utility functions) of a completely preordered space (Space of actions preordered by preferences), the continuity properties of the representation can be made to rest on the following result. R will denote the extended real line, i.e., the real line with negative infinity and positive infinity adjoined. A degenerate set is a set having at most one element. Given a subset S of R, a lacuna of S is a non-degenerate interval of R without points of S but having a lower bound and an upper bound in S; a gap of S is a maximal lacuna of S. (Author)