Self-Similar Measures in Quasi-Metric Spaces

Abstract

We prove the existence and uniqueness of invariant selfsimilar measures for given families of contractions in locally compact complete quasi-metric spaces. We also show that the invariant measure is an attractor in the space of measures, both for the weak topology as well as for a suitable metric on measures, defined in terms of Holder continuous functions. Our results apply to complete quasi-metric spaces of homogeneous type.