ThmDex – An index of mathematical definitions, results, and conjectures.
F9601
Formulation 2
Let $P = (\Omega, \mathcal{F}, \mathbb{P})$ be a D1159: Probability space such that
(i) $X : \Omega \to [0, \infty]$ is a D4381: Random basic number on $P$
Let $\lambda > 0$ be a D993: Real number.
Then \begin{equation} \mathbb{P}(X \geq \lambda) \leq \frac{1}{\lambda} \int_{\Omega} X(\omega) \, \mathbb{P}(d \omega) \end{equation}