Let $X_1, X_2, X_3, \ldots \in \text{Random}(\mathbb{R})$ 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} \mathbb{E} |X_1| < \infty \end{equation}

Then \begin{equation} \lim_{N \to \infty} \frac{1}{N} \sum_{n = 1}^N X_n \overset{a.s.}{=} \mathbb{E} X_1 \end{equation}

Let $X_1, X_2, X_3, \ldots \in \text{Random}(\mathbb{R})$ 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} \mathbb{E} |X_1| < \infty \end{equation}

Then \begin{equation} \mathbb{P} \left( \lim_{N \to \infty} \frac{1}{N} \sum_{n = 1}^N X_n = \mathbb{E} X_1 \right) = 1 \end{equation}