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Integral properties of multifunctions with closed convex values are studied.In this more general framework not all the tools and the technique used forweakly compact convex valued multifunctions work. We pay particular attentionto the "positive multifunctions". Among them an investigation of multifunctionsdetermined by vector-valued functions is presented. Finally, decompositionresults are obtained for scalarly and gauge-defined integrals of multifunctionsand a full description of McShane integrability in terms of Henstock and Pettisintegrability is given.

Integration of multifunctions with closed convex values in arbitrary Banach spaces