Equidistribution theorem

In mathematics, the equidistribution theorem is the statement that the sequence

a, 2a, 3a, ... mod 1

is uniformly distributed on the circle ${\displaystyle \mathbb {R} /\mathbb {Z} }$, when a is an irrational number. It is a special case of the ergodic theorem where one takes the normalized angle measure ${\displaystyle \mu ={\frac {d\theta }{2\pi }}}$.