EXACT SEQUENCES FOR SUMS OF PAIRWISE I.I.D. RANDOM VARIABLES

In this paper, X, X$_{1}$, X$_{2}$, .. will denote any sequence of pairwise independent random variables with common distribution, and b$_{1}$, b$_{2}$.. will denote any sequence of constants. Using Chung [2, Theorem 4.2.5] and the same idea as in Chow and Robbins [1, Lemma 1 and 2] we have the following lemma.