Regular castaing representations of multifunctions with applications to stochastic programming

We consider set-valued mappings defined on a topological space with closed convex images in R-n. The measurability of a multifunction is characterized by the existence of a Castaing representation for it: a countable set of m easurable selections that pointwise fills up the graph of the multifunction . Our aim is to construct a Castaing representation which inherits the regu larity properties of the multifunction. The construction uses Steiner point s. A notion of a generalized Steiner point is introduced. A Castaing repres entation called regular is defined by using generalized Steiner selections. All selections are measurable, continuous, resp., Holder-continuous, or di rectionally differentiable, if the multifunction has the corresponding prop erties. The results are applied to various multifunctions arising in stocha stic programming. In particular, statements about the asymptotic behavior o f measurable selections of solution sets via the delta-method are obtained.