= Lyapunov condition
{c}
{title2=$s_n^{-2-\delta}\sum_i\mathbb E|Z_{n,i}|^{2+\delta}\to0$}
For independent centered <random variables> with total <variance> $s_n^2$, the Lyapunov condition requires the displayed expression to tend to zero for some $\delta>0$. The inequality $z^2\mathbf1_{\{|z|>\varepsilon s_n\}}\le |z|^{2+\delta}/(\varepsilon s_n)^\delta$ implies the <Lindeberg condition> after normalization. The <Lindeberg-Feller central limit theorem> then makes the normalized sum converge to the standard <normal distribution>.
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