On the Strong Law of Large Numbers for Sequences of Dependent Random Variables

New sufficient conditions for the applicability of the strong law of large numbers are established for sequences of random variables without the independence conditions. Results on strong stability of sums of dependent random variables are also obtained. No particular type of dependence between random variables of a sequence is assumed. Only conditions related to moments of random variables and their sums are used. It is shown that the results obtained are unimprovable in certain sense. These results are generalizations of some results of N. Etemadi proved under more restrictive conditions.