The existence of martingale selectors for a multivalued supermartin-gale with continuous parameter is proved.We also prove the weak regularity of multivalued supermartingales.Using the regularity of Banach-valued martingales,we show a multivalued supermartingale has a cadlag modiication under Kuratowski convergence. x1. Introduction Multivalued martingales and supermartingales with discrete par...

For a large number of those working in topology, functional analysis, multivalued analysis, approximation theory, convex geometry, mathematical economics, control theory, and several other areas, the year 1956 has always been strongly connected with the publication by Ernest Michael of two fundamental papers on continuous selections which appeared in the Annals of Mathematics [4] [5]. With suff...

In this paper we study multivalued martingales in continuous time. First we show that every multivalued martingale in continuous time can be represented as the closure of a sequence of martingale selections. Then we prove two results concerning the cadlag modifications of continuous time multivalued martingales, in Kuratowski-Mosco convergence and in convergence in the Hausdorff metric respecti...

A natural strengthening of the completeness hypothesis, called B-completeness, allows us to extend to ωμ-metric spaces some properties of complete metric spaces which fail to hold if only the completeness condition is assumed. In this way we achieve some results on hyperspace theory, dealing with supercompleteness and with selections of multivalued functions. The notion of B-completeness is inv...