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Kuelbs–Li Inequalities and Metric Entropy of Convex Hulls

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  • Oliver Kley

    (Friedrich-Schiller-Universität Jena)

Abstract

Let T be a precompact subset of a Hilbert space. We make use of a precise link between the absolutely convex hull $\operatorname{aco}(T)$ and the reproducing kernel Hilbert space of a Gaussian random variable constructed from T. Firstly, we avail ourselves of it for optimality considerations concerning the well-known Kuelbs–Li inequalities. Secondly, this enables us to apply small deviation results to the problem of estimating the metric entropy of $\operatorname{aco}(T)$ in dependence of the metric entropy of T.

Suggested Citation

  • Oliver Kley, 2013. "Kuelbs–Li Inequalities and Metric Entropy of Convex Hulls," Journal of Theoretical Probability, Springer, vol. 26(3), pages 649-665, September.
    • Handle: RePEc:spr:jotpro:v:26:y:2013:i:3:d:10.1007_s10959-012-0408-5
    DOI: 10.1007/s10959-012-0408-5
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    References listed on IDEAS

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    1. Aurzada, Frank & Lifshits, Mikhail, 2008. "Small deviation probability via chaining," Stochastic Processes and their Applications, Elsevier, vol. 118(12), pages 2344-2368, December.
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