{"paper":{"title":"Range of density measures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.NT","authors_text":"Martin Sleziak, Milo\\v{s} Ziman","submitted_at":"2013-05-30T19:30:22Z","abstract_excerpt":"We investigate some properties of density measures -- finitely additive measures on the set of natural numbers $\\N$ extending asymptotic density. We introduce a class of density measures, which is defined using cluster points of the sequence $\\big(\\frac{A(n)}{n}\\big)$ as well as cluster points of some other similar sequences.\n  We obtain range of possible values of density measures for any subset of $\\N$. Our description of this range simplifies the description of Bhashkara Rao and Bhashkara Rao \\cite{brbr} for general finitely additive measures. Also the values which can be attained by the me"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.7213","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"}