Marcinkiewicz‐type strong law of large numbers for double arrays of pairwise independent random variables

Abstract

Let {Xij} be a double sequence of pairwise independent random variables. If P{|Xmn| ≥ t} ≤ P{|X| ≥ t} for all nonnegative real numbers t and , for 1 < p < 2, then we prove that urn:x-wiley:01611712:media:ijmm690634:ijmm690634-math-0002 Under the weak condition of E|X|plog+|X| < ∞, it converges to 0 in L1. And the results can be generalized to an r‐dimensional array of random variables under the conditions , respectively, thus, extending Choi and Sung′s result [1] of the one‐dimensional case.