Resumen de Convergence of weighted sums of random variables and uniform integrability concerning the weights

Manuel Hilario Ordóñez Cabrera

• Let $\{a_{nk}\}, n, k\in\mathbb{N}$ be an array of real constants, and let $\{X_n\}$ be a sequence of random variables. The concept of $\{a_{nk}\}$-uniform integrability of $\{X_n\}$ is defined and two characterizations of this concept are established. Limit theorems for weighted sums $\sum_ka_{nk}(X_k - EX_k)$ are obtained, when the sequence $\{X_n\}$ is $\{a_{nk}\}$-uniformly integrable.