{"paper":{"title":"On \\mu-Compatible Metrics and Measurable Sensitivity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Amos Lubin, Cesar E. Silva, Ilya Grigoriev, Marius Catalin Iordan, Nathaniel Ince","submitted_at":"2009-10-10T23:41:30Z","abstract_excerpt":"We introduce the notion of W-measurable sensitivity, which extends and strictly implies canonical measurable sensitivity, a measure- theoretic version of sensitive dependence on initial conditions. This notion also implies pairwise sensitivity with respect to a large class of metrics. We show that nonsingular ergodic and conservative dynamical systems on standard spaces must be either W-measurably sensitive, or isomorphic mod 0 to a minimal uniformly rigid isometry. In the finite measure-preserving case they are W-measurably sensitive or measurably isomorphic to an ergodic isometry on a compac"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0910.1958","kind":"arxiv","version":2},"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"}