On extendability by continuity of valuations on convex polytopes
On extendability by continuity of valuations on convex polytopes
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凸多面体估值连续性的可扩展性
DOI：
10.1016/j.aim.2014.01.001
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发表时间：
2012
期刊：
影响因子：
--
通讯作者：
S. Alesker
中科院分区：
文献类型：
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作者：
S. Alesker
在rn中凸紧多边形上有一个众所周知的弱连续赋值构造。本文研究了这种构造的一个特殊情况下，当该构造的一个赋值通过Hausdorff度量的连续性扩展到rn的所有凸紧子集上时，证明了这种扩展的初始数据上存在一个必要条件。在r3的情况下，得到了更明确的结果。
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.