Abstract
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, if E is an arbitrary finite-dimensional (Hausdorff) topological vector space, then E is isomorphic to some Euclidean space R n. So we can assume, without loss of generality, that all convex sets under consideration below are subsets of R n. In addition, compact convex sets in R n are of primary interest to us. Therefore, it is reasonable to start our discussion with some elementary metrical properties of such sets.
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© 2000 Springer Science+Business Media Dordrecht
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Buldygin, V.V., Kharazishvili, A.B. (2000). Brunn-Minkowski inequality. In: Geometric Aspects of Probability Theory and Mathematical Statistics. Mathematics and Its Applications, vol 514. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-1687-1_2
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DOI: https://doi.org/10.1007/978-94-017-1687-1_2
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-5505-7
Online ISBN: 978-94-017-1687-1
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