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On sets of Vitali's type

Authors: J. Cichoń, A. Kharazishvili and B. Węglorz
Journal: Proc. Amer. Math. Soc. 118 (1993), 1243-1250
MSC: Primary 28B20; Secondary 03C62, 03E35, 54C65
MathSciNet review: 1151809
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Abstract: We consider the classical Vitali's construction of nonmeasurable subsets of the real line $ \mathbb{R}$ and investigate its analogs for various uncountable subgroups of $ \mathbb{R}$. Among other results we show that if $ G$ is an uncountable proper analytic subgroup of $ \mathbb{R}$ then there are Lebesgue measurable and Lebesgue nonmeasurable selectors for $ \mathbb{R}/G$.

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Article copyright: © Copyright 1993 American Mathematical Society