Let $P = (\Omega, \mathcal{F}, \mathbb{P})$ be a D1159: Probability space such that

(i)	$X : \Omega \to [-\infty, \infty]$ is a D4381: Random basic number on $P$

Then $\mathbb{P}(|X| < \infty) = 1$ if and only if

(1)	\begin{equation} \mathbb{P}(X^+ < \infty) = 1 \end{equation}
(2)	\begin{equation} \mathbb{P}(X^- < \infty) = 1 \end{equation}