Real Analysis Exchange
- Real Anal. Exchange
- Volume 31, Number 1 (2005), 133-142.
Algebraic sums of sets in Marczewski-Burstin algebras.
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 $G$ is a perfect Abelian Polish group then there exists a Marczewski null set $A \subseteq G$ such that $A+A$ is not Marczewski measurable, and we show that the family of Marczewski measurable real valued functions defined on $G$ does not have the difference property.
Real Anal. Exchange, Volume 31, Number 1 (2005), 133-142.
First available in Project Euclid: 5 June 2006
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Dorais, Francois G.; Filipów, Rafał. Algebraic sums of sets in Marczewski-Burstin algebras. Real Anal. Exchange 31 (2005), no. 1, 133--142. https://projecteuclid.org/euclid.rae/1149516801