On weighted averages of double sequences

The well known Kolmogorov strong law of large numbers states the following. If X1, X2, . . . are independent identically distributed (i.i.d.) random variables with finite expectation and EX1 = 0, then the average (X1 + · · ·+Xn)/n converges to 0 almost surely (a.s.). However, if we consider a double sequence, then we need another condition. Actually, if (Xij) is a double sequence of i.i.d. random variables with EX11 = 0, then E |X11| log |X11| <∞ implies that (∑m i=1 ∑n j=1Xij ) /(mn)