Measure density for set decompositions and uniform distribution

  • Maria Rita Iacò
  • Milan Paštéka
  • Robert F. Tichy


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.


Uniform distribution Measure theory 

Mathematics Subject Classification

11K06 11J71 11A67 28A05 28C10 



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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Copyright information

© Springer-Verlag Italia 2015

Authors and Affiliations

  • Maria Rita Iacò
    • 1
  • Milan Paštéka
    • 2
  • Robert F. Tichy
    • 1
  1. 1.Institute of Mathematics AGraz University of TechnologyGrazAustria
  2. 2.Pedagogická fakulta TU v TrnavaTrnavaSlovakia

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