Hausdorff dimension, Mean quadratic variation of infinite self-similar measures
Classical Analysis and ODEs
2007-05-23 v1
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 {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.
Keywords
Cite
@article{arxiv.math/9812138,
title = {Hausdorff dimension, Mean quadratic variation of infinite self-similar measures},
author = {Zu-Guo Yu and Fu-Yao Ren and Jin-Rong Liang},
journal= {arXiv preprint arXiv:math/9812138},
year = {2007}
}
Comments
8 pages with no figures