Paradoxical characterization of Lebesgue nonmeasurable sets

Heliyon

Łukasz Kruk¹ 

[1] Corresponding author.;

关键词: Mathematics;    Lebesgue measurability;    Density point;    Nonmeasurable set;   

DOI  :  

来源: DOAJ

【 摘 要 】

We show that a set A⊆Rn is nonmeasurable in the sense of Lebesgue if and only if it has a common density point with its complement Ac. Moreover, if there exists a density point of both A and Ac, then the set of such points has a positive Lebesgue measure.

【 授权许可】

Unknown