
Journal of Convex Analysis 20 (2013), No. 4, 971998 Copyright Heldermann Verlag 2013 SLLN for Double Array of Mixing Dependence Random Sets and Fuzzy Random Sets in a Separable Banach Space Nguyen Van Quang Dept. of Mathematics, Vinh University, Nghe An Province, Vietnam nvquang@hotmail.com Duong Xuan Giap Dept. of Mathematics, Vinh University, Nghe An Province, Vietnam dxgiap@gmail.com We state several convergence results on PainlevéKuratowskiMosco convergence of strong laws of large numbers for double array of φ(φ*)mixing dependence random sets or fuzzy random sets in a separable Banach space. We also obtain the SLLN for double array of φ(φ*)mixing random sets in Wijsman sense. Some related results in the literature are extended. Illustrative examples are provided. Keywords: Double array, random variable, random set, fuzzy random set, strong law of large numbers, PainleveKuratowskiMosco topology, Wijsman topology, stable type p Banach space. MSC: 60F15, 60B12, 28B20 [ Fulltextpdf (230 KB)] for subscribers only. 