Geodesic
On uniqueness of G-measures and g-measures
Studia Mathematica, Tome 119 (1996) no. 3, pp. 255-269

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

We give a simple proof of the sufficiency of a log-lipschitzian condition for the uniqueness of G-measures and g-measures which were studied by G. Brown, A. H. Dooley and M. Keane. In the opposite direction, we show that the lipschitzian condition together with positivity is not sufficient. In the special case where the defining function depends only upon two coordinates, we find a necessary and sufficient condition. The special case of Riesz products is discussed and the Hausdorff dimension of Riesz products is calculated.
DOI : 10.4064/sm-119-3-255-269
Keywords: G-measures, g-measures, ergodic measures, Riesz products, quasi-invariance, dimension of measures

Ai Hua Fan 1

1 
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Ai Hua Fan. On uniqueness of G-measures and g-measures. Studia Mathematica, Tome 119 (1996) no. 3, pp. 255-269. doi: 10.4064/sm-119-3-255-269

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