{"paper":{"title":"Extreme points of the set of density measures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.NT","authors_text":"Ladislav Mi\\v{s}\\'ik, Martin Sleziak, Peter Letavaj","submitted_at":"2014-06-10T15:40:40Z","abstract_excerpt":"We study finitely additive measures on the set $\\mathbb N$ which extend the asymptotic density (density measures). We show that there is a one-to-one correspondence between density measures and positive functionals in $\\ell_\\infty^*$, which extend Ces\\`{a}ro mean. Then we study maximal possible value attained by a density measure for a given set $A$ and the corresponding question for the positive functionals extending Ces\\`{a}ro mean. Using the obtained results, we can find a set of functionals such that their closed convex hull in $\\ell_\\infty^*$ with weak${}^*$ topology is precisely the set "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.2597","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"}