We prove that in separable, complete, quasi-metric spaces there exists exactly one probability measure with bounded support, invariant with respect to given families of contractions and weights. The invariant measure has compact support and is an attractor in the space of probability measures with bounded support equipped with a metric defined in term of Hölder continuous functions.
Cite this article
Maria Vittoria Marchi, Invariant Measures in Quasi-Metric Spaces. Z. Anal. Anwend. 22 (2003), no. 1, pp. 17–32DOI 10.4171/ZAA/1129