Editing Set of uniqueness (section)

== Singular distributions ==
A closed set is a set of uniqueness if and only if there exists a [[distribution (mathematics)|distribution]] ''S'' [[support (mathematics)|support]]ed on the set (so in particular it must be singular) such that 

:<math>\lim_{n\to \infty}\widehat{S}(n)=0</math>

(<math>\hat S(n)</math> here are the Fourier coefficients). In all early examples of sets of uniqueness, the distribution in question was in fact a measure. In 1954, though, [[Ilya Piatetski-Shapiro]] constructed an example of a set of uniqueness which does not support any measure with Fourier coefficients tending to zero. In other words, the generalization of distribution is necessary.