Zeitschrift für Analysis und ihre Anwendungen
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Published online: 2003-03-31
Invariant Measures in Quasi-Metric SpacesMaria Vittoria Marchi (1) Università di Roma La Sapienza, Italy
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.
Keywords: Quasi-metric spaces, invariant self-similar measures, Hölder continuous functions, fractals, multifractals
Marchi Maria Vittoria: Invariant Measures in Quasi-Metric Spaces. Z. Anal. Anwend. 22 (2003), 17-32. doi: 10.4171/ZAA/1129