Open Access
2013/2014 On Partitions of the Real Line into Continuum Many Thick Subsets
A. B. Kharazishvili
Real Anal. Exchange 39(2): 459-468 (2013/2014).


Three classical constructions of Lebesgue nonmeasurable sets on the real line \(\mathbb{R}\) are envisaged from the point of view of the thickness of those sets. It is also shown, within \({\bf ZF}~\&~{\bf DC}\) theory, that the existence of a Lebesgue nonmeasurable subset of \(\mathbb{R}\) implies the existence of a partition of \(\mathbb{R}\) into continuum many thick sets.


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A. B. Kharazishvili. "On Partitions of the Real Line into Continuum Many Thick Subsets." Real Anal. Exchange 39 (2) 459 - 468, 2013/2014.


Published: 2013/2014
First available in Project Euclid: 30 June 2015

zbMATH: 1323.28002
MathSciNet: MR3365386

Primary: 28A05 , 28D05
Secondary: 03E25 , 03E30

Keywords: Bernstein set , DC axiom , Hamel basis , Luzin-Sierpiński theorem , Vitali set

Rights: Copyright © 2014 Michigan State University Press

Vol.39 • No. 2 • 2013/2014
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