On uniqueness of G-measures and g-measures

Volume 119 / 1996

Ai Hua Fan Studia Mathematica 119 (1996), 255-269 DOI: 10.4064/sm-119-3-255-269


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.


  • Ai Hua Fan

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