Weyl's criterion states that a sequence $(x_n) \subset [0,1]$ is equidistributed if and only if $\lim_{n \to \infty} \frac{1}{n}\sum_{j = 0}^{n-1}e^{2\pi i \ell x_j} = 0$ for ever non-zero integer $\ell$. I was wondering if anyone knows of a criterion similar to this one which characterizes when a sequence $(x_n) \subset [0,1]$ is dense in $[0,1]$? I find this formula particularly interesting because of the strong resemblance to Fourier series (which can in fact be used to prove the criterion), so I would be very pleased if anyone knows an answer which keeps this in mind.
Thanks in advance.