The correlation dimensions of loosely self-similar sets (Q2718048)

The notion of loosely self-similar sets was introduced in 1995 by \textit{S. Ikeda} [Hiroshima Math. J. 25, No. 3, 527-540 (1995; Zbl 0921.28005)]. The main difference to the usual (Hutchinson) notion of self-similarity is that the similarities used in the construction may vary from step to step in a certain way, while the contraction rates are kept constant (and overlap is excluded). In the present paper, the authors prove that the Hausdorff dimension of a loosely self-similar set coincides with its correlation dimension with respect to the push-down measure. It was known before that the former is always an upper bound for the latter; the result that they are in fact equal seems to be new.