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Matematicheskie Zametki, 2016, Volume 99, Issue 4, Pages 537–549
DOI: https://doi.org/10.4213/mzm10911 (Mi mzm10911) 		 
On the Complexity of the Family of Convex Sets in $\mathbb R^{d}$

V. V. Pernay

Lomonosov Moscow State University
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DOI: https://doi.org/10.4213/mzm10911
Abstract: Estimates of quantities characterizing the complexity of the family of convex subsets of the $d$-dimensional cube $[1,n]^d$ as $n\to \infty$ are given. The geometric properties of spaces with norm generated by the generalized majorant of partial sums are studied.
Keywords: complexity of a family of subsets of a $d$-cube, generalized majorant of partial sums, convex set, simplex, Khinchine's inequality.
Received: 16.09.2015
Revised: 21.11.2015
English version:
Mathematical Notes, 2016, Volume 99, Issue 4, Pages 534–544
DOI: https://doi.org/10.1134/S0001434616030263
Bibliographic databases:
Document Type: Article
UDC: 517.521.5
Language: Russian
Citation: V. V. Pernay, “On the Complexity of the Family of Convex Sets in $\mathbb R^{d}$”, Mat. Zametki, 99:4 (2016), 537–549; Math. Notes, 99:4 (2016), 534–544
Citation in format AMSBIB
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