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Journal of Convex Analysis 26 (2019), No. 3, 719--738
Copyright Heldermann Verlag 2019

Some Strong Laws of Large Numbers for Double Arrays of Random Sets with Gap Topology

Nguyen Van Quang
Dept. of Mathematics, Vinh University, Nghe An, Viet Nam

Duong Xuan Giap
Dept. of Mathematics, Vinh University, Nghe An, Viet Nam

Bui Nguyen Tram Ngoc
Dept. of Primary School and Preschool, Dong Nai University, Dong Nai, Viet Nam

Tien-Chung Hu
Dept. of Mathematics, Tsing Hua University, Hsinchu, Taiwan

The aim of this paper is to state some strong laws of large numbers for a double array of independent (or pairwise independent) random sets with the gap topology under various settings. Our results improve some previously reported results. Some illustrative examples are provided.

Keywords: Random set, gap topology, double array, compactly uniformly integrable in the Cesaro sense.

MSC: 60F15, 60B12, 28B20

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