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