Document Type: Original Paper


Department of Statistics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Islamic Republic of Iran


Let  be a sequence of arbitrary random variables with  and , for every  and  be an array of real numbers. We will obtain two maximal inequalities for partial sums and weighted sums of random variables and also, we will prove complete convergence for weighted sums , under some conditions on  and sequence .