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In mathematics, a sequence of real numbers is said to be equidistributed, or uniformly distributed, if the proportion of terms falling in a subinterval is proportional to the length of that interval. Such sequences are studied in Diophantine approximation theory and have applications to Monte Carlo integration. ==Definition== A sequence of real numbers is said to be ''equidistributed'' on a non-degenerate interval () if for any subinterval () of () we have : (Here, the notation |∩()| 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 is a sequence of random variables; rather, it is a determinate sequence of real numbers. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Equidistributed sequence」の詳細全文を読む スポンサード リンク
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