Paradoxical characterization of Lebesgue nonmeasurable sets

We show that a set [Formula: see text] is nonmeasurable in the sense of Lebesgue if and only if it has a common density point with its complement [Formula: see text]. Moreover, if there exists a density point of both A and [Formula: see text] , then the set of such points has a positive Lebesgue mea...

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Detalles Bibliográficos
Autor principal: Kruk, Łukasz
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Elsevier 2020
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7452515/
https://www.ncbi.nlm.nih.gov/pubmed/32885069
http://dx.doi.org/10.1016/j.heliyon.2020.e04652
Descripción
Sumario:We show that a set [Formula: see text] is nonmeasurable in the sense of Lebesgue if and only if it has a common density point with its complement [Formula: see text]. Moreover, if there exists a density point of both A and [Formula: see text] , then the set of such points has a positive Lebesgue measure.

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