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Countable state shifts and uniqueness of g -measures
- American Journal of Mathematics
- Johns Hopkins University Press
- Volume 129, Number 6, December 2007
- pp. 1501-1511
- 10.1353/ajm.2007.0044
- Article
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In this paper we present a new approach to studying g-measures which is based upon local absolute continuity. We extend an earlier result that square summability of variations of g ensures uniqueness of g-measures. The first extension is to the case of countably many symbols. The second extension is to some cases where g ≥ 0, relaxing the earlier requirement that inf g > 0.