ThmDex – An index of mathematical definitions, results, and conjectures.
F11339
Formulation 0
Let $P = (\Omega, \mathcal{F}, \mathbb{P})$ be a D1159: Probability space such that
(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}
Let $\varphi : (a, b) \to \mathbb{R}$ be a D5606: Subconvex real function.
Then \begin{equation} \varphi(\mathbb{E} X) \leq \mathbb{E} \varphi(X) \end{equation}