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* * * * * * * * * * * * * * * * * * *Elementary proof of the equidistribution theorem

I'm looking for references to (as many as possible) elementary proofs of the Weyl's equidistribution theorem, i.e., the statement that the sequence $\alpha, 2\alpha, 3\alpha, \ldots \mod 1$ is uniformly distributed on the unit interval. With "elementary" I mean that it does not make use of complex analysis in particular the Weyl's criterion.

Thank you very much.
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Elementary proof of the equidistribution theorem* * * * * * * * * * * * * * * * * * *

I'm looking for references to (as many as possible) elementary proofs of the Weyl's equidistribution theorem, i.e., the statement that the sequence $\alpha, 2\alpha, 3\alpha, \ldots \mod 1$ is uniformly distributed on the unit interval. With "elementary" I mean that it does not make use of complex analysis in particular the Weyl's criterion.

Thank you very much.
show/hide this revision's text 1

Elementary proof of the equidistribution theorem

I'm looking for references to (as many as possible) elementary proofs of the Weyl's equidistribution theorem, i.e., the statement that the sequence $\alpha, 2\alpha, 3\alpha, \ldots \mod 1$ is uniformly distributed on the unit interval. With "elementary" I mean that it does not make use of complex analysis in particular the Weyl's criterion.

Thank you very much.