Jon Aaronson, Tom Meyerovitch (2008)
Colloquium Mathematicae
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We show that a dissipative, ergodic measure preserving transformation of a σ-finite, non-atomic measure space always has many non-proportional, absolutely continuous, invariant measures and is ergodic with respect to each one of these.
Ai Fan (1996)
Studia Mathematica
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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...
F. Schweiger (1989)
Banach Center Publications
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Jon Aaronson (1977)
Publications mathématiques et informatique de Rennes
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M. Keane (1970-1971)
Publications mathématiques et informatique de Rennes
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J. Aaronson, H. Nakada, O. Sarig (2006)
Annales de l'I.H.P. Probabilités et statistiques
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S. G. Dani, M. Keane (1979)
Annales de l'I.H.P. Probabilités et statistiques
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Bezhaeva, Z.I., Oseledets, V.I. (2005)
Zapiski Nauchnykh Seminarov POMI
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Ethan Akin, Randall Dougherty, R. Daniel Mauldin, Andrew Yingst (2008)
Colloquium Mathematicae
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For measures on a Cantor space, the demand that the measure be "good" is a useful homogeneity condition. We examine the question of when a Bernoulli measure on the sequence space for an alphabet of size n is good. Complete answers are given for the n = 2 cases and the rational cases. Partial results are obtained for the general cases.
Wolfgang Krieger (1971)
Inventiones mathematicae
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Franz Hofbauer, Gerhard Keller (1982)
Mathematische Zeitschrift
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Dalibor Volný (1989)
Aplikace matematiky
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The author investigates non ergodic versions of several well known limit theorems for strictly stationary processes. In some cases, the assumptions which are given with respect to general invariant measure, guarantee the validity of the theorem with respect to ergodic components of the measure. In other cases, the limit theorem can fail for all ergodic components, while for the original invariant measure it holds.