Brunn-Minkowski inequality
Brunn-Minkowski inequality
复制标题
DOI：
10.1007/978-94-017-1687-1_2
复制
发表时间：
2000
期刊：
影响因子：
--
通讯作者：
V. V. Buldygin-V.;A. B. Kharazishvili
中科院分区：
文献类型：
--
作者：
V. V. Buldygin-V.;A. B. Kharazishvili
这一节是我们进一步考虑的基础，专门讨论那些位于有限维拓扑向量空间中的凸集。如前所述，如果E是任意有限维（豪斯多夫）拓扑向量空间，则E同构于某个欧氏空间Rn。因此，我们可以假设，不失一般性，下面考虑的所有凸集都是Rn的子集。此外，R中的紧凸集也是我们主要感兴趣的.因此，我们有理由从这类集合的一些基本度量性质开始讨论。
This section is basic for our further considerations and is devoted to those convex sets which lie in finite-dimensional topological vector spaces. As mentioned in the previous section, ifEis an arbitrary finite-dimensional (Hausdorff) topological vector space, thenEis isomorphic to some Euclidean spaceRn. So we can assume, without loss of generality, that all convex sets under consideration below are subsets ofRn. In addition, compact convex sets inRnare of primary interest to us. Therefore, it is reasonable to start our discussion with some elementary metrical properties of such sets.