Marcinkiewicz-type strong law of large numbers for double arrays of pairwise independent random variables (Q1283418)

This paper investigates the Marcinkiewicz-type strong law of large numbers for double arrays \(\{X_{ij}\}\) of pairwise independent random variables and proves that \[ \sum^m_{i=1}\sum^n_{j=1}(X_{ij}-EX_{ij})/(mn)^{1/p}\to 0,\quad\text{a.s. as }m\vee n\to\infty, \] if \(X_{ij}\) are dominated by a random variable \(X\) with \(E\{| X|^p(\log^+| X|)^3\}<\infty\). This result is an extension of \textit{B. D. Choi} and \textit{S. H. Sung}'s result [Bull. Korean Math. Soc. 22, 79-82 (1985; Zbl 0585.60043)] from the one-dimensional case to double array sequences.