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Upper estimate of concentration and thin dimensions of measures

Gacki H., Lasota A., Myjak J.

Bulletin of the Polish Academy of Sciences. Mathematics

2009

Vol. 57, no 2

149-162

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.