
Journal of Convex Analysis 21 (2014), No. 4, 11931200 Copyright Heldermann Verlag 2014 Gelfand Integral of Multifunctions Kazimierz Musial Institute of Mathematics, Wroclaw University, Pl. Grunwaldzki 2/4, 50384 Wroclaw, Poland musial@math.uni.wroc.pl It has been proven by Cascales, Kadets and Rodriguez [J. Convex Anal. 18 (2011), 873895] that each weak* scalarly integrable multifunction (with respect to a probability measure μ, whose values are compact convex subsets of a conjugate Banach space X* and the family of support functions determined by X is order bounded in L_{1}(μ), is Gelfand integrable in the family of weakly compact convex subsets of X*. A question has been posed whether a similar result holds true for multifunctions with weakly compact convex values. We prove that the answer is affirmative if X does not contain any isomorphic copy of l_{1}. If moreover the multifunction is compact valued, then it is Gelfand integrable in the family of compact convex subsets of X*. Keywords: Multifunction, Gelfand setvalued integral, Pettis setvalued integral, support function. MSC: 28B20; 28B05, 46G10, 54C60 [ Fulltextpdf (112 KB)] for subscribers only. 