Template-Type: ReDIF-Paper 1.0
Author-Name: Manuel Morán Cabré
Author-Workplace-Name: Departamento de Análisis Económico y Economía Cuantitativa. Universidad Complutense de Madrid.
Author-Workplace-Homepage: https://www.ucm.es/fundamentos-analisis-economico2
Author-Name: Jose María Rey Simó
Author-Workplace-Name: Departamento de Análisis Económico y Economía Cuantitativa. Universidad Complutense de Madrid.
Author-Workplace-Homepage: https://www.ucm.es/fundamentos-analisis-economico2
Title: Singularity of self-similar measures with respect to Hausdorff measures
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.
Keywords: Self-similar measures, Hausdorff measures.
Length: 16 pages
Creation-Date: 1995
Number: 95-03
X-File-Ref: http://america.sim.ucm.es/repec/ucm/ref/doctra95-03.txt
File-URL: https://eprints.ucm.es/id/eprint/26380/1/9503.pdf
File-Format: Application/pdf
Handle: RePEc:ucm:doctra:95-03