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}