Some remarks on additive properties of invariant σ-ideals on the real line

Abstract

We consider some additive properties of invariant \(\sigma\)-ideals and \(\sigma\)-algebras of subsets of the real line \({\mathbb{R}}\). In particular, we generalize two classical Sierpinski results, concerning additive properties of measure and category on \({\mathbb{R}}\), to a large class of invariant \(\sigma\)-ideals and \(\sigma\)-algebras.