{"paper":{"title":"Mean Equicontinuity and Related Properties in Hyperspace and Measure Dynamics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Chunlin Liu, Till Hauser","submitted_at":"2026-06-21T20:24:03Z","abstract_excerpt":"For a dynamical system $(X,T)$ we consider the induced dynamical systems $(\\myper(X),T)$ and $(\\hyper(X),T)$, consisting of Borel probability measures and closed non-empty subsets, respectively. We show that diam-mean equicontinuity of $(X,T)$ is equivalent to the diam-mean equicontinuity of $(\\myper(X),T)$.\n  Furthermore, we establish that $(X,T)$ is mean equicontinuous, iff $(\\myper(X),T)$ is mean equicontinuous, iff $(\\myper(X),T)$ is weakly-mean equicontinuous.\n  For $(\\hyper(X),T)$ the situation is different.\n  It is not hard to see that the diam-mean equicontinuity of $(\\hyper(X),T)$ imp"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.22658","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.22658/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}