A bounded 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.
A bounded sequence $(s_n)$ of real numbers is equidistributed on an interval $[a,b]$ if for any subinterval $[c,d]$ of $[a,b]$ we have $\lim_{n\to\infty}{ \frac{|\{s_1,\dots,s_n \} \cap [c,d] |}n}={\frac{d-c}{b-a}}.$
Other related notions studied in the theory of uniform distributions are equidistribution modulo 1, discrepancy, well-distributed sequences, various kinds of distribution functions of sequences.
