Regular Castaing Representations of Multifunctions with Applications to Stochastic Programming

We consider set valued mappings de ned on a topological space with convex closed images in IRn The measurability of a multifunction is characterized by the existence of a Castaing representation for it a countable set of measurable selections that pointwise ll up the graph of the multifunction Our aim is to construct a Castaing representation which inherits the regularity properties of the multifunction The con struction uses Steiner points A notion of a generalized Steiner point is introduced A Castaing representation called regular is de ned by using generalized Steiner se lections All selections are measurable continuous resp H older continuous or di rectionally di erentiable if the multifunction has the corresponding properties The results are applied to various multifunctions arising in stochastic programming In particular statements about the asymptotic behavior of measurable selections of so lution sets via the delta method are obtained