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2020 On the Density of the Thinnest Covering of \(\mathbb{R}^n\)
Soon-Mo Jung, Doyun Nam
Real Anal. Exchange 45(2): 387-400 (2020). DOI: 10.14321/realanalexch.45.2.0387

Abstract

Let \(K\) be a compact convex subset of \(\mathbb{R}^n\) whose Lebesgue measure is positive and which includes the origin of the coordinate system. In this paper, the density of the thinnest covering of \(\mathbb{R}^n\) by translates of \(K\) will be transformed into another form that seems easier to use. Finally, in the discussion section of this paper, we will look at the applications of the main results.

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Soon-Mo Jung. Doyun Nam. "On the Density of the Thinnest Covering of \(\mathbb{R}^n\)." Real Anal. Exchange 45 (2) 387 - 400, 2020. https://doi.org/10.14321/realanalexch.45.2.0387

Information

Published: 2020
First available in Project Euclid: 30 June 2020

zbMATH: 07229053
Digital Object Identifier: 10.14321/realanalexch.45.2.0387

Subjects:
Primary: 05B40 , 52C17
Secondary: 11H31

Keywords: covering , Density , thinnest covering

Rights: Copyright © 2020 Michigan State University Press

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Vol.45 • No. 2 • 2020
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