Let $X_1, X_2, X_3, \ldots \in \text{Random}(\Omega \to \mathbb{R})$ each be a D3161: Random real number such that

(i)	$X_1, X_2, X_3, \ldots$ is an D3358: I.I.D. random collection
(ii)	\begin{equation} \lim_{x \to \infty} x \mathbb{P}(|X_1| > x) = 0 \end{equation}
(iii)	\begin{equation} \mu_N : = \mathbb{E}(X_1 I_{\{ |X_1| \leq N \}}) \end{equation}

Then \begin{equation} \sum_{n = 1}^N \frac{X_n - \mu_N}{N} \overset{p}{\longrightarrow} 0 \quad \text{ as } \quad N \to \infty \end{equation}