A sequence {x_{n}} is *uniformly distributed* in an interval I if for all a,b in I,

lim_{N→∞} #{n<=N: a<x_{n}<b} / N = (b-a) /|I|

That is,

asymptotically the number of x

_{n}'s in any subinterval is proportional to its length.

A uniformly distributed sequence behaves in many ways like a sequence chosen by the uniform distribution. Indeed, almost always a sequence chosen according to the uniform distribution will be uniformly distributed.