SLLN for Double Array of Mixing Dependence Random Sets and Fuzzy Random Sets in a Separable Banach Space

Nguyen Van Quang; Duong Xuan Giap

Abstract

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.

Author information

Contact details are reproduced from the original publication and may be historical.

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

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

Mathematics Subject Classification

60F15, 60B12, 28B20

Suggested citation

N. V. Quang, D. X. Giap. “SLLN for Double Array of Mixing Dependence Random Sets and Fuzzy Random Sets in a Separable Banach Space.” Journal of Convex Analysis 20 (2013), No. 4, 971–998.