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In mathematics, the equidistribution theorem is the statement that the sequence
is uniformly distributed on the circle R / Z {\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 μ = d θ 2 π {\displaystyle \mu ={\frac {d\theta }{2\pi }}}.
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