Paradoxical characterization of Lebesgue nonmeasurable sets
Łukasz Kruk · Heliyon · 2020
We show that a set A ⊆ R n is nonmeasurable in the sense of Lebesgue if and only if it has a common density point with its complement A c . Moreover, if there exists a density point of both A and A c , then the set of such points has a positive Lebesgue measure.