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Uniqueness and ergodic properties of attractive g-measures

Published online by Cambridge University Press:  19 September 2008

Paul Hulse
Paul Hulse
Affiliation:
Tufts University, Dept. of Mathematics, Medford MA 02155, USA
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Abstract

We consider g-measures for the shift on where S is a finite set. For a certain class of continuous g, two g-measures are identified; they are equal if and only if there is a unique g-measure. We prove that the natural extensions of these measures are Bernoulli. With a further restriction on g when S is a two-point set, we show that there is a unique g-measure. We also consider extensions of these results to the non-continuous case.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 11 , Issue 1 , March 1991 , pp. 65 - 77
Copyright
Copyright © Cambridge University Press 1991

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References

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