Abstract
In this paper, we study a general sequence of random variables under some moment conditions will follow the classical strong law of large numbers. In Chapter 1, we discuss the results of previous studies in in the sequence with special structures. These special structures contain independent, pairwise independent, extended negatively dependent (END), and asymptotically almost negatively associated (AANA). In Capter 2, we give our main results and prove. In Chapter 3, we show that how to use our main results to obtain classical strong law of large numbers when the sequence has special structures referred to Chapter 1.