Geodesic
Probability distributions with
Teoriâ slučajnyh processov, Tome 13 (2007) no. 2, pp. 281-293

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The paper is devoted to the study of connections between fractal properties of one-dimensional singularly continuous probability measures and the preservation of the Hausdorff dimension of any subset of the unit interval under the corresponding distribution function. Conditions for the distribution function of a random variable with independent $Q$-digits to be a transformation preserving the Hausdorff dimension (DP-transformation) are studied in details. It is shown that for a large class of probability measures the distribution function is a DP-transformation if and only if the corresponding probability measure is of full Hausdorff dimension.
Keywords: Singularly continuous probability distributions, Hausdorff dimension of probability measures, Hausdorff-Billingsley dimension, fractals
Mots-clés : DP-transformations. 
@article{THSP_2007_13_2_a11,
     author = {Grygoriy Torbin},
     title = {Probability distributions with},
     journal = {Teori\^a slu\v{c}ajnyh processov},
     pages = {281--293},
     publisher = {mathdoc},
     volume = {13},
     number = {2},
     year = {2007},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/THSP_2007_13_2_a11/}
}
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Grygoriy Torbin. Probability distributions with. Teoriâ slučajnyh processov, Tome 13 (2007) no. 2, pp. 281-293. http://geodesic.mathdoc.fr/item/THSP_2007_13_2_a11/