Let $P = (\Omega, \mathcal{F}, \mathbb{P})$ be a D1159: Probability space such that
Let $\varphi : (a, b) \to \mathbb{R}$ be a D5606: Subconvex real function.
| (i) | $(a, b) \subseteq [-\infty, \infty]$ is an D5146: Open basic interval |
| (ii) | $X : \Omega \to (a, b)$ is a D3161: Random real number on $P$ |
| (iii) | \begin{equation} \mathbb{E} |X| < \infty \end{equation} |
Then
\begin{equation}
\varphi(\mathbb{E} X)
\leq \mathbb{E} \varphi(X)
\end{equation}