Bulletin of the
Korean Mathematical Society BKMS

In this paper we establish the weak law of large numbers for randomly weighted partial sums of random variables and study conditions imposed on the triangular array of random weights $\{ W_{nj} : 1 \le j \le n ,\ n \ge 1 \}$ and on the triangular array of random variables $\{ X_{nj} : 1 \le j \le n ,\ n \ge 1 \}$ which ensure that $\sum_{j=1}^{n}~W_{nj} | X_{nj} - B_{nj} |$ converges in probability to 0, where $\{ B_{nj} : 1 \le j \le n ,\ n \ge 1 \}$ is a centering array of constants or random variables.

Keywords: weak law of large numbers, randomly weighted partial sums, triangular arrays of random variables, bounded in probability, convergence in probability

MSC numbers: 60F05, 60E15