The necessary and sufficient conditions for various self-similar sets and their dimension

[摘要] We have given several necessary and sufficient conditions for statistically self-similar sets and a.s. self-similar sets and have got the Hausdorff dimension and exact Hausdorff measure function of any a.s. self-similar set in this paper. It is useful in the study of probability properties and fractal properties and structure of statistically recursive sets. (C) 2000 Elsevier Science B.V. All rights reserved. MSC: 60G10.

[发布日期] 2000-12-01

[关键词] statistically self-similar sets;a.s. self-similar sets;Hausdorff dimension;statistically recursive sets;statistical contraction operators