Let $f : \{ 1, 2, 3, \ldots \} \to \{1, 2, 3, \ldots \}$ be a D5406: Positive integer function such that

(i)	\begin{equation} \lim_{n \to \infty} f(n) = \infty \end{equation}
(ii)	$\{ X_{n, m} \}_{n \geq 1, \, 1 \leq m \leq f(n)}$ be a D5163: Random real triangular array
(iii)	$X_{n, 1}, \; \ldots, \; X_{n, f(n)}$ is an D2713: Independent random collection for each $n \in \{ 1, 2, 3, \ldots \}$
(iv)	\begin{equation} \forall \, n \in \{ 1, 2, 3, \ldots \} : \forall \, m \in \{ 1, 2, \ldots, f(n) \} : \mathbb{E} |X_{n, m}|^2 < \infty \end{equation}
(v)	\begin{equation} \mu_{n, m} : = \mathbb{E} X_{n, m} \end{equation}
(vi)	\begin{equation} \sigma^2_{n, m} : = \text{Var} X_{n, m} \end{equation}
(vii)	\begin{equation} s^2_n : = \sum_{m = 1}^{f(n)} \sigma^2_{n, m} \end{equation}
(viii)	\begin{equation} \forall \, \varepsilon > 0 : \lim_{n \to \infty} \frac{1}{s^2_n} \sum_{m = 1}^{f(n)} \mathbb{E} (|X_{n, m} - \mu_{n, m}|^2 I_{\{ |X_{n, m} - \mu_{n, m}| > \varepsilon s_n \}}) = 0 \end{equation}

Then \begin{equation} \lim_{n \to \infty} \sum_{m = 1}^{f(n)} \frac{X_{n, m} - \mu_{n, m}}{s_n} \overset{d}{=} \text{Gaussian}(0, 1) \end{equation}