Upper Estimate of Concentration and Thin Dimensions of Measures

Tom 57 / 2009

H. Gacki, A. Lasota, J. Myjak Bulletin Polish Acad. Sci. Math. 57 (2009), 149-162 MSC: Primary 37C45; Secondary 28A80, 11K55, 37C40. DOI: 10.4064/ba57-2-8


We show upper estimates of the concentration and thin dimensions of measures invariant with respect to families of transformations. These estimates are proved under the assumption that the transformations have a squeezing property which is more general than the Lipschitz condition. These results are in the spirit of a paper by A. Lasota and J. Traple [Chaos Solitons Fractals 28 (2006)] and generalize the classical Moran formula.


  • H. GackiInstitute of Mathematics
    Silesian University
    Bankowa 14
    40-007 Katowice, Poland
  • A. Lasota[deceased]
  • J. MyjakDipartimento di Matematica Pura ed Applicata
    Università di L'Aquila
    Via Vetoio
    67100 L'Aquila, Italy
    Al. Mickiewicza 30
    30-059 Kraków, Poland

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