Gauge integrals and selections of weakly compact valued multifunctions

Abstract

In the paper Henstock, McShane, Birkhoff and variationally multivalued integrals are studied for multifunctions taking values in the hyperspace of convex and weakly compact subsets of a general Banach space X. In particular the existence of selections integrable in the same sense of the corresponding multifunctions has been considered.

21 pages

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• Atomicity related to non-additive integrability
• Kuelbs-Steadman spaces for Banach space-valued measures
• Multifunctions determined by integrable functions
• Convergence for varying measures in the topological case
• A Girsanov Result through Birkhoff Integral
• A survey on composition operators on some function spaces
• A Girsanov result for the Pettis integral