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On extendability by continuity of valuations on convex polytopes

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 نشر من قبل Semyon Alesker
 تاريخ النشر 2012
  مجال البحث
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 تأليف Semyon Alesker




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There is a well known construction of weakly continuous valuations on convex compact polytopes in R^n. 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 R^n. It is shown that there is a necessary condition on the initial data for such an extension. In the case of R^3 more explicit results are obtained.



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