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

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.