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A random map is a discrete-time dynamical system in which one of a number of transformations is randomly selected and applied on each iteration of the process. We study random maps with position dependent probabilities on the interval and on a bounded domain of ℝⁿ. Sufficient conditions for the existence of an absolutely continuous invariant measure for a random map with position dependent probabilities on the interval and on a bounded domain of ℝⁿ are the main results.
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