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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

REFERENCES

[1]Berbee, H.. Chains with infinite connections: uniqueness and Markov representation. Probab. Th. Rel. Fields 76 (1987), 243–253.CrossRefGoogle Scholar
[2]Doeblin, W. & Fortet, R.. Sur les chaînes a liaisons complètes. Bull. Soc. Math. France 65 (1937), 132–148.Google Scholar
[3]Keane, M., Strongly mixing g-measures. Invent. Math. 16 (1972), 309–324.CrossRefGoogle Scholar
[4]Ledrappier, F., Principe variationnel et systèmes dynamiques symboliques. Z. Wahrscheinlichkeitstheorie verw. Gebiete 30 (1974), 185–202.CrossRefGoogle Scholar
[5]Ornstein, D. S.. Ergodic Theory, Randomness and Dynamical Systems. Yale University Press, New Haven, 1974.Google Scholar
[6]Preston, C.. Random Fields, Lecture Notes in Mathematics 534. Springer-Verlag, Berlin, 1976.Google Scholar
[7]Walters, P.. Ruelle's operator theorem and g-measures. Trans. Amer. Math. Soc. 214 (1975), 375–387.Google Scholar