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Singularity of self-similar measures with respect to Hausdorff measures

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Morán Cabré, Manuel and Rey Simo, José Manuel (1995) Singularity of self-similar measures with respect to Hausdorff measures. [ Documentos de trabajo de la Facultad de Ciencias Económicas y Empresariales; nº 03, 1995, ]

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Official URL: http://eprints.ucm.es/26380/




Abstract

Besicoviteh (1941) and Egglestone (1949) analyzed subsets of points of the unit interval with given frequencies in the figures of their base-p expansions. We extend this analysis to self-similar sets, by replacing the frequencies of figures with the frequencies of the generating similitudes. We focus on the interplay among such sets, self-similar measures, and Hausdorff measures. We give a fine-tuned classification of the Hausdorff measures according to the singularity of the self-similar measures with respect to those measures. We show that the self-similar measures are concentrated on sets whose frequencies of similitudes obey the law of the iterated logarithm


Item Type:Working Paper or Technical Report
Uncontrolled Keywords:Self-similar measures, Hausdorff measures
Subjects:Social sciences > Economics > Econometrics
Series Name:Documentos de trabajo de la Facultad de Ciencias Económicas y Empresariales
Volume:1995
Number:03
ID Code:26380
Deposited On:29 Jul 2014 08:38
Last Modified:20 May 2019 08:06

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