Hausdorff dimension, Mean quadratic variation of infinite self-similar measures
Zu-Guo Yu, Fu-Yao Ren, Jin-Rong Liang
Abstract
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 Sj(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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