FRACTAL VECTOR MEASURES

In this paper we extend the concept of the fractal measure (the Hutchinson measure, which is the unique fixed point of a contraction on the set of normalized Borel measures on a compact metric space) associated to an iterated function system. An important property of this measure is that its support is the atractor of the iterated function system. Here, an extension of this result is given for the case of vector measures taking their values in a finite dimensional space or in an arbitrary Banach space..