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

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

1998-12-24

arxiv.org/abs/math/9812138v1

Bull. of Hong Kong Math. Soc., II(2) (1998) 161-169

Mathematics

Classical Analysis and ODEs

8 pages with no figures

Scientific paper

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.

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