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\documentclass{article}
\usepackage{thmbox}
\newtheorem[M]{proposition}{Proposition}[section]
\begin{document}
\begin{proposition}
Let $M$ be a martingale, then $(\phi(M_t))_{t \geq 0}$ is a
sub-martingale for all convex functions $\phi$ such that $\phi(M_t)$
is integrable for all $t$.
\end{proposition}
\begin{proof}
This follows from Jensen's inequality for conditional expectations,
see any standard text book on this subject.
\end{proof}
\end{document}