In mathematics, a Nikodym set is a subset of the unit square in
Subsequently, constructions were found of Nikodym sets having continuum many exceptional lines for each point, and Kenneth Falconer found analogues in higher dimensions.
The existence of Nikodym sets is sometimes compared with the Banach–Tarski paradox.
There is, however, an important difference between the two: the Banach–Tarski paradox relies on non-measurable sets.
Mathematicians have also researched Nikodym sets over finite fields (as opposed to