Surface functions of sets and integration of multivalued mappings (Q914158)

Let \(\Pi\) be the set of all polytopes in \({\mathbb{R}}^ n\) with at most \(n+1\) vertices, unit-surface and Steiner center at 0. Then for each convex compact set K in \({\mathbb{R}}^ n\) with its Steiner center at 0 there is a finite positive regular Borel measure \(\mu\) on \(\Pi\) such that \(K=\int_{\Pi}^*Md\mu\), where the star means the Aumann integral.