On extendability by continuity of valuations on convex polytopes

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There is a well known construction of weakly continuous valuations on convex compact polytopes in Rn. In this paper we investigate when a special case of this construction gives a valuation which extends by continuity in the Hausdorff metric to all convex compact subsets of Rn. It is shown that there is a necessary condition on the initial data for such an extension. In the case of R3 more explicit results are obtained.

Original languageEnglish
Pages (from-to)352-380
Number of pages29
JournalAdvances in Mathematics
StatePublished - 1 Apr 2014


  • Convex sets
  • Polytopes
  • Valuations


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