{"paper":{"title":"A dimension gap for continued fractions with independent digits - the non stationary case","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Ariel Rapaport","submitted_at":"2017-03-09T07:25:35Z","abstract_excerpt":"We show there exists a constant $0<c_{0}<1$ such that the dimension of every measure on $[0,1]$, which makes the digits in the continued fraction expansion independent, is at most $1-c_{0}$. This extends a result of Kifer, Peres and Weiss from 2001, which established this under the additional assumption of stationarity. For $k\\ge1$ we prove an analogues statement for measures under which the digits form a $*$-mixing $k$-step Markov chain. This is also generalized to the case of $f$-expansions. In addition, we construct for each $k$ a measure, which makes the continued fraction digits a station"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.03164","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"}