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
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author Kruk, Łukasz
author_facet Kruk, Łukasz
author_sort Kruk, Łukasz
collection PubMed
description 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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spelling pubmed-74525152020-09-02 Paradoxical characterization of Lebesgue nonmeasurable sets Kruk, Łukasz Heliyon Article 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. Elsevier 2020-08-20 /pmc/articles/PMC7452515/ /pubmed/32885069 http://dx.doi.org/10.1016/j.heliyon.2020.e04652 Text en © 2020 The Author http://creativecommons.org/licenses/by-nc-nd/4.0/ This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
spellingShingle Article
Kruk, Łukasz
Paradoxical characterization of Lebesgue nonmeasurable sets
title Paradoxical characterization of Lebesgue nonmeasurable sets
title_full Paradoxical characterization of Lebesgue nonmeasurable sets
title_fullStr Paradoxical characterization of Lebesgue nonmeasurable sets
title_full_unstemmed Paradoxical characterization of Lebesgue nonmeasurable sets
title_short Paradoxical characterization of Lebesgue nonmeasurable sets
title_sort paradoxical characterization of lebesgue nonmeasurable sets
topic Article
url 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
work_keys_str_mv AT krukłukasz paradoxicalcharacterizationoflebesguenonmeasurablesets

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