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International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 52, Pages 3299-3313
http://dx.doi.org/10.1155/S0161171203301048

Self-similar random fractal measures using contraction method in probabilistic metric spaces

Faculty of Mathematics and Computer Science, Babes-Bolyai University, Cluj-Napoca 3400, Romania

Received 2 January 2003

Copyright © 2003 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

Self-similar random fractal measures were studied by Hutchinson and Rüschendorf. Working with probability metric in complete metric spaces, they need the first moment condition for the existence and uniqueness of these measures. In this paper, we use contraction method in probabilistic metric spaces to prove the existence and uniqueness of self-similar random fractal measures replacing the first moment condition.