Metric discrepancy results for subsequences of {θ k x}

摘要

We determine the set of possible constants appearing in the law of the iterated logarithm for discrepancies of subsequences of {θ k x}. We prove that the set coincides with the interval [ 1/2, Σ θ ], where Σ θ is the constant for {θ k x}. It implies that the discrepancies decrease if we take a subsequence of {θ k x}.