Weighted covering numbers of convex sets

S. Artstein-Avidan; O. Raz

doi:10.1016/j.aim.2011.02.009

Weighted covering numbers of convex sets

S. Artstein-Avidan^*, O. Raz

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

9 Scopus citations

Abstract

In this paper we define the notions of weighted covering number and weighted separation number for convex sets, and compare them to the classical covering and separation numbers. This sheds new light on the equivalence of classical covering and separation. We also provide a formula for computing these numbers via a limit of classical covering numbers in higher dimensions.

Original language	English
Pages (from-to)	730-744
Number of pages	15
Journal	Advances in Mathematics
Volume	227
Issue number	1
DOIs	https://doi.org/10.1016/j.aim.2011.02.009
State	Published - 1 May 2011
Externally published	Yes

Bibliographical note

Funding Information:
✩ Both authors were partially supported by ISF grant 865/07. This work is part of the M.Sc. thesis of the second named author. * Corresponding author. E-mail address: [email protected] (S. Artstein-Avidan).

Keywords

Convex sets
Covering numbers
Separation numbers
Weighted covering

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10.1016/j.aim.2011.02.009

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KW - Separation numbers

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Weighted covering numbers of convex sets

Abstract

Bibliographical note

Keywords

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