Paradoxical characterization of Lebesgue nonmeasurable sets
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.
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| Format: | Article |
| Language: | English |
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Elsevier
2020-08-01
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| Series: | Heliyon |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2405844020314961 |