Distributional properties of correspondences on Loeb spaces

Abstract

We present some regularity properties for the set of distributions induced by the measurable selections of a correspondence over a Loeb space, which include closedness, convexity, compactness, purification, and semicontinuity. We also note that all the properties reported in the main theorems are not satisfied by some correspondences on the unit Lebesgue interval. © 1996 Academic Press, Inc.