  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.
