\begin{definition}[Definition:Epigraph]
Let $f: S \to \overline \R$ be an extended real-valued function.
The '''epigraph''' of $f$ is the set:
:$\map {\operatorname {epi} } f := \set {\tuple {x, \alpha} \in S \times \R: \map f x \le \alpha}$
\end{definition}