Invariant (fractal) vector measures as fixed points of Markov-type operators (Q2108943)

The authors present a generalization of the theory of fractal invariant measures in the context of the Barnsley-Hutchinson setting of iterated function systems (IFSs). The discrete index in the definition of an IFS is replaced by a measurable function from a general measure space. The associated Markov operator is then seen to act on vector measures. Employing such concepts as sequilinear integrals, a Kantorovich-type metric and the Bochner integral, the authors derive the fixed points for this Markov operator which are vector-valued measures. Examples are also given.