Journal of Convex Analysis 20 (2013), No. 4, 971--998
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 Painlevé-Kuratowski-Mosco 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, Painleve-Kuratowski-Mosco topology, Wijsman topology, stable type p Banach space.
MSC: 60F15, 60B12, 28B20
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