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Measure density for set decompositions and uniform distribution

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Abstract

The aim of this paper is to extend the concept of measure density introduced by Buck for finite unions of arithmetic progressions, to arbitrary subsets of \({\mathbb {N}}\) defined by a given system of decompositions. This leads to a variety of new examples and to applications to uniform distribution theory.

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Acknowledgments

M. R. Iacò and R. F. Tichy would like to acknowledge the support of the Austrian Science Fund (FWF) Project F5510. They are also grateful to Professor O. Strauch from the Slovak Academy of Science and Professor V. Baláž from Comenius University in Bratislava for the fruitful discussions they had during their visit in Bratislava in November 2014. The authors would like to thank the referee for careful reading of the manuscript and valuable comments which helped improving the quality of the paper.

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Authors and Affiliations

  1. Institute of Mathematics A, Graz University of Technology, Steyrergasse 30, 8010, Graz, Austria

    Maria Rita Iacò & Robert F. Tichy

  2. Pedagogická fakulta TU v Trnava, Priemyselná 4, P.O. Box 9, 918 43, Trnava, Slovakia

    Milan Paštéka

Authors
  1. Maria Rita Iacò
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  2. Milan Paštéka
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  3. Robert F. Tichy
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Corresponding author

Correspondence to Robert F. Tichy.

Additional information

Dedicated to W. G. Nowak on the occasion of his 60th birthday.

M. R. Iacò and R. F. Tichy are participants in the ANR/FWF project FAN Fractals and Numeration (ANR-12-IS01-0002, FWF grant I1136) and they are supported by the Austrian Science Fund (FWF): Project F5510, which is a part of the Special Research Program “Quasi-Monte Carlo Methods: Theory and Applications”.

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Iacò, M.R., Paštéka, M. & Tichy, R.F. Measure density for set decompositions and uniform distribution. Rend. Circ. Mat. Palermo 64, 323–339 (2015). https://doi.org/10.1007/s12215-015-0202-1

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  • DOI: https://doi.org/10.1007/s12215-015-0202-1

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