Summary
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.
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Mosco, U. (2000). Self-Similar Measures in Quasi-Metric Spaces. In: Appell, J. (eds) Recent Trends in Nonlinear Analysis. Progress in Nonlinear Differential Equations and Their Applications, vol 40. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8411-2_21
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DOI: https://doi.org/10.1007/978-3-0348-8411-2_21
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9556-9
Online ISBN: 978-3-0348-8411-2
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