FRACTAL VECTOR MEASURES IN THE CASE OF AN UNCOUNTABLE ITERATED FUNCTION SYSTEM

Abstract

In this paper we obtain an extension of the concept of Hutchinson measure (which is the unique fi xed point of a contraction on the set of normalized Borel measures on a compact metric space) related to an iterated function system. Our extension means that we consider vector measures (instead of normalized Borel measures) and, also, an uncountable iterated function system instead of a fi nite one, as in the case of Hutchinson measure.

Keywords

• uncountable iterated function system
• Monge-Kantorovich norm
• variation of a vector measure
• fractal measure