Real Analysis Exchange

Covering the circle with random open sets.

Jinghu Yu

Full-text: Open access

Abstract

The Dvoretzky covering problem is to cover the circle with random intervals. We consider the covering of the circle with random open sets. We find a necessary and sufficient condition for the circle to be covered almost surely when each open set is composed of a finite number of intervals which are separated by a positive distance.

Article information

Source
Real Anal. Exchange, Volume 29, Number 1 (2003), 341-354.

Dates
First available in Project Euclid: 9 June 2006

Permanent link to this document
https://projecteuclid.org/euclid.rae/1149860198

Mathematical Reviews number (MathSciNet)
MR2061316

Zentralblatt MATH identifier
1073.60009

Subjects
Primary: 60D05: Geometric probability and stochastic geometry [See also 52A22, 53C65] 52C17: Packing and covering in $n$ dimensions [See also 05B40, 11H31] 28A80: Fractals [See also 37Fxx]

Keywords
Dovretzky covering

Citation

Yu, Jinghu. Covering the circle with random open sets. Real Anal. Exchange 29 (2003), no. 1, 341--354. https://projecteuclid.org/euclid.rae/1149860198


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