A NOTE ON THE INTERSECTIONS OF THE BESICOVITCH SETS AND ERD&x150;S-ReNYI SETS

摘要

For x 2 (0; 1] and a positive integer n; let Sn(x) denote the summation of the first n digits in the dyadic expansion of x and let rn(x) denote the run-length function. In this paper, we obtain the Hausdor ff dimensions of the following sets: x 2 (0; 1] : lim inf n!1 Sn(x) n = ff; lim sup n !1 Sn(x) n = fi; lim n!1 rn(x) log2 n = ; where 0 <=alpha <=beta <= 1,0 <=gamma <=+infinity.

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