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2.1 Minimization approach

For affine IFS there exist a simple and useful relation between the moments of probability measures on M(X). Given an N-maps IFS(w, p) with associated Markov operator M, and given a measure

then, for any continuous function

(2)

where

In our case

so we readly have a relation involving the

moments of

Let

be the moments of the two measures, with g_{0} = h_{0} = 1. Then, by (2), with f(x) = x^{k}, we have

Recursive relations for the moments and more details on polynomial IFSs can be found in Forte and Vrscay (1995). The following theorem is due to Vrscay and can be found in Forte and Vrscay (1995) as well.

Stefano M. Iacus, Davide La Torre

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