2 4 D ec 1 99 8 Hausdorff dimension , Mean quadratic variation of infinite self - similar measures ∗
نویسنده
چکیده
Under weaker condition than that of Riedi & Mandelbrot, the Hausdorff (and Hausdorff-Besicovitch) dimension of infinite self-similar set K ⊂ R which is the invariant compact set of infinite contractive similarities {Sj(x) = ρjRjx + bj}j∈N (0 < ρj < 1, bj ∈ R , Rj orthogonal) satisfying open set condition is obtained. It is proved (under some additional hypotheses) that the β-mean quadratic variation of infinite selfsimilar measure is of asymptotic property (as t −→ 0).
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