Real Analysis Exchange

A note on algebraic sums of subsets of the real line.

Jacek Cichoń and Andrzej Jasiński

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Abstract

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.

Article information

Source
Real Anal. Exchange, Volume 28, Number 2 (2002), 493-500.

Dates
First available in Project Euclid: 20 July 2007

Permanent link to this document
https://projecteuclid.org/euclid.rae/1184963812

Mathematical Reviews number (MathSciNet)
MR2010332

Zentralblatt MATH identifier
1052.28001

Subjects
Primary: 03E15: Descriptive set theory [See also 28A05, 54H05] 28A05: Classes of sets (Borel fields, $\sigma$-rings, etc.), measurable sets, Suslin sets, analytic sets [See also 03E15, 26A21, 54H05]
Secondary: 26A21: Classification of real functions; Baire classification of sets and functions [See also 03E15, 28A05, 54C50, 54H05]

Keywords
Lebesgue measure Baire property Borel sets null sets algebraic sums

Citation

Cichoń, Jacek; Jasiński, Andrzej. A note on algebraic sums of subsets of the real line. Real Anal. Exchange 28 (2002), no. 2, 493--500. https://projecteuclid.org/euclid.rae/1184963812


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References

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