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2005-2006 Algebraic sums of sets in Marczewski-Burstin algebras.
Francois G. Dorais, Rafał Filipów
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Real Anal. Exchange 31(1): 133-142 (2005-2006).


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.


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Francois G. Dorais. Rafał Filipów. "Algebraic sums of sets in Marczewski-Burstin algebras.." Real Anal. Exchange 31 (1) 133 - 142, 2005-2006.


Published: 2005-2006
First available in Project Euclid: 5 June 2006

zbMATH: 1106.28001
MathSciNet: MR2218194

Primary: 28A05 , 39A70

Keywords: algebraic sum , almost-invariant set , Difference property , Marczewski measurable set , Marczewski--Burstin algebra , Miller measurable set , perfect set , superperfect set

Rights: Copyright © 2005 Michigan State University Press

Vol.31 • No. 1 • 2005-2006
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