Asymptotic normality of sums of dependent random variables, considered by B. A. Sevast'yanov

Sufficient conditions are found under which the random variable
$$ (\xi-\mathbf E\xi)/\sqrt{\mathbf E\xi} $$
is asymptotically normal, where $\displaystyle\xi=\sum_1^n\eta_i$ and $\eta_i$, $i=1,\dots,n$, are weakly dependent 0–1 random variables.