{"paper":{"title":"Rate distortion theory, metric mean dimension and measure theoretic entropy","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Anibal Velozo, Renato Velozo","submitted_at":"2017-07-18T17:45:09Z","abstract_excerpt":"We prove a variational principle for the metric mean dimension analog to the one in [LT]. Instead of using the rate distortion function we use the function $h_\\mu(\\epsilon,T,\\delta)$ that is closely related to the entropy $h_\\mu(T)$ of $\\mu$. Our formulation has the advantage of being, in the authors opinion, more natural when doing computations. As a corollary we obtain a proof of the standard variational principle. We also obtain some relations between the rate distortion function with our function $\\tilde{h}_\\mu(\\epsilon,T,\\delta)$, a modification of $h_\\mu(\\epsilon,T,\\delta)$ when replacin"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.05762","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"}