Kodai Mathematical Journal

A note on Patterson measures

Kurt Falk and Pekka Tukia

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Conformal measures are measures satisfying a certain transformation rule for elements of a Kleinian group G and are normally supported by the limit set of G. They are usually constructed by a method due to S. J. Patterson as weak limits of measures supported by a fixed orbit of G in the hyperbolic space, often identified with the unit ball Bn. We call such limit measures Patterson measures. This has been the predominant way to obtain conformal measures and one may get the impression that all conformal measures are Patterson measures. We show in this note that this is not the case and two concrete examples are given in the last section.

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Kodai Math. J. Volume 29, Number 2 (2006), 227-236.

First available in Project Euclid: 3 July 2006

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Falk, Kurt; Tukia, Pekka. A note on Patterson measures. Kodai Math. J. 29 (2006), no. 2, 227--236. doi:10.2996/kmj/1151936437. http://projecteuclid.org/euclid.kmj/1151936437.

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