The Complete Convergence for Partial Sums of Interchangeable Random Variables

In this paper, we discuss the relations between the convergence of tail probability series and the existence of some type of the moment for partial sums of interchangeable random variables X_n : n ≥ 1 and positive monotone functions H(x), φ(x), we obtain a series of sufficient and equivalent results for the complete convergence of partial sums.