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
nvquang@hotmail.com
Duong Xuan Giap
Dept. of Mathematics, Vinh University, Nghe An, Viet Nam
dxgiap@gmail.com
Bui Nguyen Tram Ngoc
Dept. of Primary School and Preschool, Dong Nai University, Dong Nai, Viet Nam
bntramngoc@gmail.com
Tien-Chung Hu
Dept. of Mathematics, Tsing Hua University, Hsinchu, Taiwan
tchu@math.nthu.edu.tw
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
[ Fulltext-pdf (153 KB)] for subscribers only.