Journal of Convex Analysis 27 (2020), No. 4, 1233--1246
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, 50-384 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 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].
Keywords: Positive multifunction, gauge integral, decomposition theorem for multifunction, selection, measure theory.
MSC: 28B20, 26E25, 26A39, 28B0, 46G10, 54C60, 54C65.
[ Fulltext-pdf (124 KB)] for subscribers only.