On measurable relations

Abstract

The results in this paper supplement those in "Measurable relations" by C. J. Him-melberg [H]. Some results of that paper are extended and examples are given showing the sharpness of earlier results. In particular, examples are given showing (i) that the intersection of two weakly measurable, closed-valued relations may fail to be weakly measurable, and (ii) that Filippov's implicit function theorem may fail without appropriate restrictions either on the domain of the relation or on its values.