François G. Dorais

Research in Logic and Foundations of Mathematics

Algebraic sums of sets in Marczewski–Burstin algebras

By F. G. Dorais and R. Filipów
Real Analysis Exchange 31 (2005), no. 1, 133–142

Using almost-invariant sets, we show that a family of Marczewski-Burstin algebras over groups are not closed under algebraic sums. We also give an application of almost-invariant sets to the difference property in the sense of de Bruijn. In particular, we show that if is a perfect Abelian Polish group then there exists a Marczewski null set such that is not Marczewski measurable, and we show that the family of Marczewski measurable real valued functions defined on does not have the difference property.