Bulletin of the
Korean Mathematical Society BKMS

Let $\{a_{ni}, u_n\le i\le v_n, n\ge 1\}$ be an array of constants. Let $\{X_{ni}, u_n\le i\le v_n, n\ge 1\}$ be $\{a_{ni}\}$-uniformly integrable random variables. Weak laws for the weighted sums $\sum_{i=u_n}^{v_n} a_{ni}X_{ni}$ are obtained.

Keywords: weak law of large numbers, weighted sums, $r$-mean convergence, convergence in probability, arrays, uniform integrability

MSC numbers: 60F05, 60F25