Open Access
2004-2005 More tales of two (s)-ities.
Kenneth Schilling
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Real Anal. Exchange 30(2): 861-866 (2004-2005).


In any complete separable metric space, the Boolean algebra $(s)/(s_0)$ of Marczewski sets modulo the Marczewski null sets is complete. Using this fact, we show that a simple construction solves two known problems in real analysis: the existence of an $(s_0)$-set which is not Lebesgue measurable and does not have the Baire property, and a function which is not $(s)$-measurable, but whose graph is an $(s_0)$-set. Using a similar idea, we also present a short proof that the Boolean algebra of universally measurable sets modulo the sets universally of measure zero is not complete.


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Kenneth Schilling. "More tales of two (s)-ities.." Real Anal. Exchange 30 (2) 861 - 866, 2004-2005.


Published: 2004-2005
First available in Project Euclid: 15 October 2005

zbMATH: 1108.28003
MathSciNet: MR2177443

Primary: 28A05
Secondary: 03G05

Keywords: Baire property , Complete Boolean Algebra , Marczewski Measurable , Universally Measurable

Rights: Copyright © 2004 Michigan State University Press

Vol.30 • No. 2 • 2004-2005
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