Open Access
2002/2003 A note on algebraic sums of subsets of the real line.
Jacek Cichoń, Andrzej Jasiński
Author Affiliations +
Real Anal. Exchange 28(2): 493-500 (2002/2003).


We investigate the algebraic sums of sets for a large class of invariant \(\sigma\)-ideals and \(\sigma\)-fields of subsets of the real line. We give a simple example of two Borel subsets of the real line such that its algebraic sum is not a Borel set. Next we show a similar result to Proposition 2 from A. Kharazishvili paper \cite{S2}. Our results are obtained for ideals with coanalytical bases.


Download Citation

Jacek Cichoń. Andrzej Jasiński. "A note on algebraic sums of subsets of the real line.." Real Anal. Exchange 28 (2) 493 - 500, 2002/2003.


Published: 2002/2003
First available in Project Euclid: 20 July 2007

zbMATH: 1052.28001
MathSciNet: MR2010332

Primary: 03E15 , 28A05
Secondary: 26A21

Keywords: algebraic sums , Baire property , Borel sets , Lebesgue measure , null sets

Rights: Copyright © 2002 Michigan State University Press

Vol.28 • No. 2 • 2002/2003
Back to Top