
Journal of Convex Analysis 27 (2020), No. 4, 12331246 Copyright Heldermann Verlag 2020 Integration of Multifunctions with Closed Convex Values in Arbitrary Banach Spaces Domenico Candeloro Dept. of Mathematics and Computer Sciences, University of Perugia, 06123 Perugia, Italy domenico.candeloro@unipg.it Luisa Di Piazza Dept. of Mathematics and Computer Sciences, University of Palermo, 90123 Palermo, Italy luisa.dipiazza@unipa.it Kazimierz Musial Institut of Mathematics, Wroclaw University, 50384 Wroclaw, Poland musial@math.uni.wroc.pl Anna Rita Sambucini Dept. of Mathematics and Computer Sciences, University of Perugia, 06123 Perugia, Italy anna.sambucini@unipg.it 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 DenjoyPettis 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 vectorvalued functions, Illinois J. Math. 38(3) (1994) 471479]. Keywords: Positive multifunction, gauge integral, decomposition theorem for multifunction, selection, measure theory. MSC: 28B20, 26E25, 26A39, 28B0, 46G10, 54C60, 54C65. [ Fulltextpdf (124 KB)] for subscribers only. 