Properties
The following three conditions are equivalent:
- {an} is equidistributed modulo 1.
- For every Riemann integrable function f on ,
- For every nonzero integer k,
-
The third condition is known as Weyl's criterion. Together with the formula for the sum of a finite geometric series, the equivalence of the first and third conditions furnishes an immediate proof of the equidistribution theorem.
Read more about this topic: Equidistributed Sequence
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