{"paper":{"title":"The type and stable type of the boundary of a Gromov hyperbolic group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.DS","authors_text":"Lewis Bowen","submitted_at":"2012-09-10T23:44:30Z","abstract_excerpt":"Consider an ergodic non-singular action $\\Gamma \\cc B$ of a countable group on a probability space. The type of this action codes the asymptotic range of the Radon-Nikodym derivative, also called the {\\em ratio set}. If $\\Gamma \\cc X$ is a pmp (probability-measure-preserving) action, then the ratio set of the product action $\\Gamma \\cc B\\times X$ is contained in the ratio set of $\\Gamma \\cc B$. So we define the {\\em stable ratio set} of $\\Gamma \\cc B$ to be the intersection over all pmp actions $\\Gamma \\cc X$ of the ratio sets of $\\Gamma \\cc B\\times X$. By analogy, there is a notion of {\\em st"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.2181","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"}