Hausdorff dimension, Mean quadratic variation of infinite self-similar measures

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Under weaker condition than that of Riedi & Mandelbrot, the Hausdorff (and Hausdorff-Besicovitch) dimension of infinite self-similar set K which is the invariant compact set of infinite contractive similarities {S_j(x)} satisfying open set condition is obtained. It is proved (under some additional hypotheses) that the mean quadratic variation of infinite self-similar measure is of asymptotic property.
8 pages with no figures

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Classical Analysis and ODEs, 28A80 (Primary) 00A73 (Secondary)

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http://salesiana.dossiersoluciones.com/handle/123456789/77890

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/9812138
 http://arxiv.org/abs/math/9812138
 Bull. of Hong Kong Math. Soc., II(2) (1998) 161-169

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arXiv