Separation conditions on controlled Moran constructions

Volume 200 / 2008

Antti Käenmäki, Markku Vilppolainen Fundamenta Mathematicae 200 (2008), 69-100 MSC: Primary 28A80; Secondary 37C45. DOI: 10.4064/fm200-1-2

Abstract

It is well known that the open set condition and the positivity of the $t$-dimensional Hausdorff measure are equivalent on self-similar sets, where $t$ is the zero of the topological pressure. We prove an analogous result for a class of Moran constructions and we study different kinds of Moran constructions in this respect.

Authors

  • Antti KäenmäkiDepartment of Mathematics and Statistics
    P.O. Box 35 (MaD)
    FI-40014 University of Jyväskylä, Finland
    e-mail
  • Markku VilppolainenDepartment of Mathematics and Statistics
    P.O. Box 35 (MaD)
    FI-40014 University of Jyväskylä, Finland
    e-mail

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