Utility Functions and the 'Lin' Operation for Convex Sets

摘要

This note contributes to utility theory by sharpening a recent example of Kannai (Existence of a Utility in Infinite Dimensional Partially Ordered Spaces) and Perles, and to the geometry of infinite-dimensional convex sets by settling a problem raised in a previous work by the author concerning the iteration of the 'lin' operation. The reduction of the first matter to the second is described. The actual construction appears in section 2. Section 3 mentions two unsolved problems. (Author)