Definition
A bounded sequence {s1, s2, s3, …} of real numbers is said to be equidistributed on an interval if for any subinterval of we have
(Here, the notation |{s1,…,sn }∩| denotes the number of elements, out of the first n elements of the sequence, that are between c and d.)
For example, if a sequence is equidistributed in, since the interval occupies 1/5 of the length of the interval, as n becomes large, the proportion of the first n members of the sequence which fall between 0.5 and 0.9 must approach 1/5. Loosely speaking, one could say that each member of the sequence is equally likely to fall anywhere in its range. However, this is not to say that {sn} is a sequence of random variables; rather, it is a determinate sequence of real numbers.
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