On permutational invariance of the metric discrepancy results

Author:

Fukuyama Katusi1,Noda Yutaro1

Affiliation:

1. Department of Mathematics , Graduate School of Science, Kobe University , Kobe 657-8501 Japan

Abstract

Abstract Let {nk } be a sequence of non-zero real numbers. We prove that the law of the iterated logarithm for discrepancies of the sequence {nkx} is permutational invariant if |n k +1/nk | → ∞ is satisfied.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

Reference16 articles.

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2. Aistleitner, C.—Berkes, I.—Tichy, R.: On the asymptotic behaviour of weakly lacunary series, Proc. Amer. Math. Soc. 139 (2011), 2505–2517.

3. Aistleitner, C.—Berkes, I.—Tichy, R.: On the law of the iterated logarithm for permuted lacunary sequences, Proc. Steklov Inst. Math. 276 (2012), 3–20.

4. Berkes, I.: On Strassen’s version of the log log law for multiplicative systems, Studia Sci. Math. Hungar. 8 (1973), 425–431.

5. Dhompongsa, S.: Almost sure invariance principles for the empirical process of lacunary sequences, Acta Math. Hungar. 49 (1987), 83–102.

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