Let $\{ X_{n, m} \}_{n \geq 1, \, 1 \leq m \leq M_n}$ be a D5163: Random real triangular array such that

(i)	$X_{n, 1}, \dots, X_{n, M_n}$ is an D2713: Independent random collection for each $n \geq 1$
(ii)	$\mathbb{E} X_{n, m} = 0$
(iii)	$\sigma^2_{n, m} : = \text{Var} X_{n, m} \in (0, \infty)$
(iv)	\begin{equation} s^2_n : = \sum_{m = 1}^{M_n} \sigma^2_{n, m} = 1 \end{equation}
(v)	\begin{equation} \forall \, \varepsilon > 0 : \lim_{n \to \infty} \sum_{m = 1}^{M_n} \mathbb{E}( |X_{n, m}|^2 I_{\{ |X_{n, m}| > \varepsilon \}} ) = 0 \end{equation}

Then \begin{equation} \sum_{m = 1}^{M_n} X_{n, m} \overset{d}{\longrightarrow} \text{Gaussian}(0, 1) \quad \text{ as } \quad n \to \infty \end{equation}