Common Contracts
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SEMIGROUPS ON SPACES OF MEASURESJune 16th, 2010
Iterating, Pnµ0 is the probability measure that describes the distribution after n times of switching. If Ω is a complete separable metric space and the Φi are strict contractions, then there exists in fact a unique invariant probability measure µ∗ (Pµ∗ = µ∗), and for every probability measure µ the iterates Pnµ converge, in some sense, to µ∗. The support of this invariant measure is exactly the fractal associated to the iterated function system [66].
