Example 21.11.6.8CBDC69B6C55 Let $M$ be the dual vector space of $N$ and $P\subseteq M$ be a convex subset. The support function $\operatorname{Supp}_ P\in \mathrm{Conv}(N)$ of $P$ is defined as follows:
\[ \operatorname{Supp}_ P(n)\coloneqq \sup \{ \langle m,n \rangle : m\in P \} . \]
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