Definition 18.4.1 (Support Function).label Let $\dpn{E, F}{\lambda}$ be a duality over $\real$ and $A \subset E$ be non-empty, then the mapping
\[H_{A}: F \to (-\infty, \infty] \quad y \mapsto \sup_{x \in A}\dpn{x, y}{\lambda}\]
the support function of $A$ with respect to $\dpn{E, F}{\lambda}$.
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