Integration of Multifunctions with Closed Convex Values in Arbitrary Banach Spaces

Integral properties of multifunctions with closed convex values are studied. In this more general framework not all the tools and the technique used for weakly compact convex valued multifunctions work. We prove that positive Denjoy-Pettis integrable multifunctions are Pettis integrable and we obtain a full description of McShane integrability in terms of Henstock and Pettis integrability, finishing the problem started by D. H. Fremlin in 1994 [The Henstock and McShane integrals of vector-valued functions, Illinois J. Math. 38(3) (1994) 471–479].