Let $X \in \mathsf{Random}[0, \infty)$ be a D5452: Random unsigned real number such that
(i) | \begin{equation} \mathbb{E} X < \infty \end{equation} |
Then
\begin{equation}
\lim_{\lambda \to \infty, \, \lambda \in \mathbb{R}} \lambda \mathbb{P}(X \geq \lambda) = 0
\end{equation}