
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 E^{2} is a subset N of S such that * the area (i.e. twodimensional Lebesgue measure) of N is 1; * for every point x of N, there is a straight line through x that meets N only at x. The existence of such a set was N was first proved in 1927 by the Polish mathematician Otton M. Nikodym. Nikodym sets are closely related to Kakeya sets (also known as Besicovitch sets). See also References * Falconer, Kenneth J. (1986). The geometry of fractal sets, Cambridge Tracts in Mathematics 85. Cambridge: Cambridge University Press, p. 100. ISBN 0521256941. MR867284 Retrieved from "http://en.wikipedia.org/" 

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