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2000/2001 Measure Zero Sets Whose Algebraic Sum Is Non-Measurable
Krzysztof Ciesielski
Real Anal. Exchange 26(2): 919-922 (2000/2001).


In this note we will show that for every natural number $n>0$ there exists an $S\subset[0,1]$ such that its $n$-th algebraic sum $nS=S+\cdots +S$ is a nowhere dense measure zero set, but its $n+1$-st algebraic sum $nS+S$ is neither measurable nor it has the Baire property. In addition, the set $S$ will be also a Hamel base, that is, a linear base of $\mathbb{R}$ over $\mathbb{Q}$.


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Krzysztof Ciesielski. "Measure Zero Sets Whose Algebraic Sum Is Non-Measurable." Real Anal. Exchange 26 (2) 919 - 922, 2000/2001.


Published: 2000/2001
First available in Project Euclid: 27 June 2008

zbMATH: 1009.28004
MathSciNet: MR1844407

Primary: 28A05

Keywords: algebraic sum , measurability , sets

Rights: Copyright © 2000 Michigan State University Press

Vol.26 • No. 2 • 2000/2001
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