Convex Sets and Minimal Sublinear Functions

We show that, given a closed convex set $K$ containing the origin in its interior, the support function of the set $\{y\in K^* \mid \mbox{ there exists } x\in K\mbox{ such that } \langle x,y \rangle =1\}$ is the pointwise smallest among all sublinear functions $\sigma$ such that $K=\{x \mid \sigma(x)\leq 1\}$.

en

http://eprints.lse.ac.uk/31765/