Probabilistic Iterated Function Systems and Probabilistic Systems

Le Xuan Son and Nguyen Ngoc Phan


    We study the relation between probabilistic iterated function systems introduced in [1] and probabilistic systems introduced in [4]. We prove that the probabilistic iterated function system $\{f_i(x)=\rho x +r_i:\ i=0,1,\ldots ,m\}$ with probabilities $p_i\ge 0,\ \sum_{i=0}^m p_i =1$ and the probabilistic system in the sense of [4] induce the same measure and therefore these systems are equivalent to each other.