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

Voir la notice de l'article dans European Digital Mathematics Library

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.
Classification : 28D05, 43A05
Mots-clés : G-measures, g-measures, ergodic measures, Riesz products, quasi-invariance, dimension of measures, -measures, log-Lipschitzian condition, uniqueness, measures 
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     author = {Ai Fan},
     title = {On uniqueness of {G-measures} and g-measures},
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     url = {https://geodesic-test.mathdoc.fr/item/STUMA_1996__119_3_216299/}
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Ai Fan. On uniqueness of G-measures and g-measures. Studia Mathematica, Tome 119 (1996) no. 3, p. 255. https://geodesic-test.mathdoc.fr/item/STUMA_1996__119_3_216299/