Weyl criterion
= Weyl criterion
{c}
A sequence $(x_n)$ in $\mathbb R/\mathbb Z$ is an <equidistributed sequence> if and only if $N^{-1}\sum_{n=0}^{N-1}e^{2\pi i m x_n}\to0$ for every nonzero integer $m$. Approximation of continuous functions by <trigonometric polynomials> proves the criterion.