Geodesic
On the Complexity of the Family of Convex Sets in $\mathbb R^{d}$
Matematičeskie zametki, Tome 99 (2016) no. 4, pp. 537-549

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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, Khinchine's inequality.
Mots-clés : simplex 
@article{MZM_2016_99_4_a5,
     author = {V. V. Pernay},
     title = {On the {Complexity} of the {Family} of {Convex} {Sets} in $\mathbb R^{d}$},
     journal = {Matemati\v{c}eskie zametki},
     pages = {537--549},
     publisher = {mathdoc},
     volume = {99},
     number = {4},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2016_99_4_a5/}
}
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V. V. Pernay. On the Complexity of the Family of Convex Sets in $\mathbb R^{d}$. Matematičeskie zametki, Tome 99 (2016) no. 4, pp. 537-549. http://geodesic.mathdoc.fr/item/MZM_2016_99_4_a5/