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

limN→∞ #{n<=N: a<xn<b} / N = (b-a) /|I|
That is, asymptotically the number of xn'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.

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