Dierentiable Selections of SetValued Mappings and Asymptotic Behaviour of Random Sets in Innite Dimensions

darymathematikhuberlinde We consider setvalued mappings acting between two linear normed spaces and having convex closed images Our aim is to construct selections with direc tional dierentiability properties up to the second order using certain tangen tial approximations of the mapping The constructions preserve measurability and lead to a directionally dierentiable Castaing representation of measurable multifunctions admitting the required tangential approximation A generalized setvalued central limit theorem for random sets in innite dimensional spaces is presented The results yield asymptotic distributions of measurable selections forming the Castaing representation of the multifunctio