Nikodym set

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In mathematics, a Nikodym set is the seemingly paradoxical result of a construction in measure theory. A Nikodym set in the unit square S in the Euclidean plane E2 is a subset N of S such that

The existence of such a set as N was first proved in 1927 by the Polish mathematician Otto M. Nikodym. Nikodym sets are closely related to Kakeya sets (also known as Besicovitch sets).

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