A Generalization of Ifs with Probabilities to Innnitely Many Maps
نویسنده
چکیده
This paper considers the problem of extending the notion of an IFS with probabilities from the case of nitely many maps in the IFS to the case of innnitely many maps. We prove that under an average contractiv-ity condition the IFS is contractive in the Monge-Kantorovich metric. We also show that the invariant distribution is continuous with respect to the parameters of the IFS. Furthermore, using results of Lewellen , we obtain a result relating the support of the invariant measure to the attractor of the "geometric" IFS. Finally, we discuss the issue of the convergence of integrals with respect to the invariant measure and estimates on the error of these integrals.
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