On the strong law of large numbers for sums of pairwise independent random variables

The strong law of large numbers with the norming sequence n1/y, 1 < [gamma] < 2, is proved for sums of pairwise independent identically distributed random variables Xi, I = 1, 2, ..., with finite EX1[gamma](log+ X1[tau]) for some positive [tau] > 4[gamma] - 6 (instead of [tau] = [gamma] in the paper of Li Gang, 1988). It is known that [tau] cannot be negative in this theorem.