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ON THE CONTINUITY PROPERTIES OF PARETIAN UTILITY,
CALIFORNIA UNIV BERKELEY
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