On sets of Vitali’s type

Cichoń, J.; Kharazishvili, A.; Węglorz, B.

doi:10.1090/S0002-9939-1993-1151809-7

On sets of Vitali’s type
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by J. Cichoń, A. Kharazishvili and B. Węglorz PDF

Proc. Amer. Math. Soc. 118 (1993), 1243-1250 Request permission

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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