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

School of Mathematical Sciences

Tel Aviv University

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

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

Keywords

Convex sets
Covering numbers
Separation numbers
Weighted covering

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1016/j.aim.2011.02.009

Cite this

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title = "Weighted covering numbers of convex sets",

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.",

keywords = "Convex sets, Covering numbers, Separation numbers, Weighted covering",

author = "S. Artstein-Avidan and O. Raz",

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).",

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N2 - 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.

AB - 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.

KW - Convex sets

KW - Covering numbers

KW - Separation numbers

KW - Weighted covering

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DO - 10.1016/j.aim.2011.02.009

M3 - مقالة

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JO - Advances in Mathematics

JF - Advances in Mathematics

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Weighted covering numbers of convex sets

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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