ThmDex – An index of mathematical definitions, results, and conjectures.
Dilations of unsigned tail probability converge to zero
Formulation 1
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}