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

Nguyen Van Quang; Duong Xuan Giap; Bui Nguyen Tram Ngoc; Tien-Chung Hu

Abstract

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.

Author information

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

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

Keywords

Random set
gap topology
double array
compactly uniformly integrable in the Cesaro sense

Mathematics Subject Classification

60F15, 60B12, 28B20

Suggested citation

N. V. Quang, D. X. Giap, B. N. T. Ngoc, T.-C. Hu. “Some Strong Laws of Large Numbers for Double Arrays of Random Sets with Gap Topology.” Journal of Convex Analysis 26 (2019), No. 3, 719–738.