V. V. Pernay, “On the Complexity of the Family of Convex Sets in <nobr>$\mathbb R^{d}$</nobr>”, Mat. Zametki, 2016, Volume 99, Issue 4,Pages <nobr>537

On the Complexity of the Family of Convex Sets in $\mathbb R^{d}$

V. V. Pernay

Lomonosov Moscow State University

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.

UDC: 517.521.5

Received: 16.09.2015
Revised: 21.11.2015

DOI: 10.4213/mzm10911