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

(i)	$X, Y : \Omega \to \mathbb{R}$ are each a D3161: Random real number on $P$
(ii)	\begin{equation} \mathbb{E} |X|, \mathbb{E} |Y| < \infty \end{equation}
(iii)	\begin{equation} X \overset{a.s.}{\leq} Y \end{equation}

Then \begin{equation} \mathbb{E}(X) \leq \mathbb{E}(Y) \end{equation}