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
In our case
so we readly have a relation involving the
be the moments of the two measures, with g0 = h0 = 1. Then, by (2), with f(x) = xk, 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
Next: Theorem 1.