Thin and fat sets for doubling measures in metric spaces

Volume 208 / 2012

Tuomo Ojala, Tapio Rajala, Ville Suomala Studia Mathematica 208 (2012), 195-211 MSC: Primary 28A12; Secondary 30L10. DOI: 10.4064/sm208-3-1


We consider sets in uniformly perfect metric spaces which are null for every doubling measure of the space or which have positive measure for all doubling measures. These sets are called thin and fat, respectively. In our main results, we give sufficient conditions for certain cut-out sets being thin or fat.


  • Tuomo OjalaDepartment of Mathematics and Statistics
    P.O. Box 35 (MaD)
    FI-40014 University of Jyväskylä, Finland
  • Tapio RajalaScuola Normale Superiore
    Piazza dei Cavalieri 7
    I-56127 Pisa, Italy
  • Ville SuomalaDepartment of Mathematical Sciences
    P.O. Box 3000
    FI-90014 University of Oulu, Finland

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