{"paper":{"title":"Mean dimension and rate-distortion function revisited","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.IT"],"primary_cat":"math.DS","authors_text":"Rui Yang","submitted_at":"2025-10-09T10:37:23Z","abstract_excerpt":"Around the mean dimensions and rate-distortion functions, using some tools from local entropy theory this paper establishes the following main results:\n  $(1)$ We prove that for non-ergodic measures associated with almost sure processes, the mean R\\'enyi information dimension coincides with the information dimension rate. This answers a question posed by Gutman and \\'Spiewak (in Around the variational principle for metric mean dimension, \\emph{Studia Math.} \\textbf{261}(2021) 345-360).\n  $(2)$ We introduce four types of rate-distortion entropies and establish their relation with Kolmogorov-Sin"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2510.08051","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2510.08051/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"}