We study different concepts of the convergence of sequences with multidimensional indices. Emphasis is placed on the use of Etemadi's subsequence method in the study of almost sure convergence of random fields. An improvement of the SLLN for pairwise independent random variables is also obtained.
"On Etemadi's subsequences and the strong law of large numbers for random fields." Rocky Mountain J. Math. 45 (5) 1555 - 1563, 2015. https://doi.org/10.1216/RMJ-2015-45-5-1555