Research Article

Nonmeasurable Vitali set: variations on theme

Published in: Quaestiones Mathematicae
Volume 46 , issue 4 , 2023 , pages: 775–779

DOI: 10.2989/16073606.2022.2041759

Author(s): Angelo Bella University of Catania, Italy (EU) , Daniele Puglisi University of Catania, Italy (EU) , Alfonso Villani University of Catania, Italy (EU)

Keywords: Primary: Primary: 28C10 , Secondary: Secondary: 43A05 , Vitali set , Lebesgue measure , analitic and coanalitic sets

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Abstract

We extend Vitali’s procedure to get nonmeasurable sets. Answering a question of Kharazishvili [4], we present a relatively simple argument for passing from singletons to finite sets. Our result is actually much stronger, as it covers even the case of compact choices.

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