Abstract:The extension theorem of bounded, weakly compact, convex set valued and weakly countably additive measures is established through a discussion of convexity, compactness and existence of selection of the set valued measures; meanwhile, a characterization is obtained for continuous, weakly compact and convex set valued measures which can be represented by Pettis-Aumann-type integral.
Keywords: set valued functions, set valued measures, Pettis-Aumann integral
AMS Subject Classification: 28A45, 46G10