ThmDex – An index of mathematical definitions, results, and conjectures.
Formulation 0
Let $P = (\Omega, \mathcal{F}, \mathbb{P})$ be a D1159: Probability space such that
(i) $X : \Omega \to [0, \infty]$ is a D5101: Random unsigned basic number on $P$
Let $t \in [0, \infty]$ be an D5237: Unsigned basic number.
Then \begin{equation} t \mathbb{P}(X > t) \leq \mathbb{E}(X I_{\{ X > t \}}) \end{equation}