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International Journal of Mathematics and Mathematical Sciences
Volume 31 (2002), Issue 1, Pages 11-21
http://dx.doi.org/10.1155/S0161171202110337

The Hausdorff dimension and exact Hausdorff measure of random recursive sets with overlapping

College of Mathematics and Statistics, Wuhan University, Wuhan 430072, China

Received 15 October 2001

Copyright © 2002 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We weaken the open set condition and define a finite intersection property in the construction of the random recursive sets. We prove that this larger class of random sets are fractals in the sense of Taylor, and give conditions when these sets have positive and finite Hausdorff measures, which in certain extent generalize some of the known results, about random recursive fractals.