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

(i)	$X_{n, 1}, \ldots, X_{n, n}$ is an D2713: Independent random collection for each $n \in 1, 2, 3, \ldots$
(ii)	$\lambda_1, \lambda_2, \lambda_3, \ldots \in (0, \infty)$ are each a D993: Real number
(iii)	\begin{equation} \lim_{n \to \infty} \lambda_n = \infty \end{equation}
(iv)	\begin{equation} \lim_{n \to \infty} \sum_{m = 1}^n \mathbb{P}(|X_{n, m}| > \lambda_n) = 0 \end{equation}
(v)	\begin{equation} \lim_{n \to \infty} \frac{1}{\lambda^2_n} \sum_{m = 1}^n \mathbb{E} (|X_{n, m}|^2 I_{\{ |X_{n, m}| \leq \lambda_n \}}) = 0 \end{equation}

Then \begin{equation} \sum_{m = 1}^n \frac{X_{n, m} - \mathbb{E} (X_{n, m} I_{\{ |X_{n, m}| \leq \lambda_n \}})}{\lambda_n} \overset{p}{\longrightarrow} 0 \quad \text{ as } \quad n \to \infty \end{equation}