A family of measures associated with iterated function systems
نویسنده
چکیده
Let (X, d) be a compact metric space, and let an iterated function system (IFS) be given on X, i.e., a finite set of continuous maps σi: X → X, i = 0, 1, · · · , N − 1. The maps σi transform the measures μ on X into new measures μ i . If the diameter of σi1 ◦ · · · ◦ σik (X) tends to zero as k → ∞, and if pi > 0 satisfies ∑ i pi = 1, then it is known that there is a unique Borel probability measure μ on X such that
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