{"paper":{"title":"Unique Bernoulli g-measures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.DS","authors_text":"Anders Johansson, Anders \\\"Oberg, Mark Pollicott","submitted_at":"2010-04-05T15:27:11Z","abstract_excerpt":"We improve and subsume the conditions of Johansson and \\\"Oberg [18] and Berbee [2] for uniqueness of a g-measure, i.e., a stationary distribution for chains with complete connections.  In addition, we prove that these unique g-measures have Bernoulli natural extensions. In particular, we obtain a unique g-measure that has the Bernoulli property for the full shift on finitely many states under any one of the following additional assumptions. (1) $$\\sum_{n=1}^\\infty (\\var_n \\log g)^2<\\infty,$$ (2) For any fixed $\\epsilon>0$, $$\\sum_{n=1}^\\infty e^{-(\\{1}{2}+\\epsilon) (\\var_1 \\log g+...+\\var_n \\l"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.0650","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}