Corollary 13.2.8.label Let $C,D\suf\R^{n}$ be nonempty closed convex sets then $h_{C}\leq h_{D}\iff C\suf D$ (on $\R^{n}$ or $\mathbb{S}^{n-1}$). In particular $h_{C}=h_{D}\iff C=D$

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