{"paper":{"title":"Infinite measures on Cantor spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Olena Karpel","submitted_at":"2011-02-05T14:14:59Z","abstract_excerpt":"We study the set $M_\\infty(X)$ of all infinite full non-atomic Borel measures on a Cantor space X. For a measure $\\mu$ from $M_\\infty(X)$ we define a defective set $M_\\mu = \\{x \\in X : for any clopen set U which contains x we have \\mu(U) = \\infty \\}$. We call a measure $\\mu$ from $M_\\infty(X)$ non-defective ($\\mu \\in M_\\infty^0(X)$) if $\\mu(M_\\mu) = 0$. The paper is devoted to the classification of measures $\\mu$ from $M_\\infty^0(X)$ with respect to a homeomorphism. The notions of goodness and clopen values set $S(\\mu)$ are defined for a non-defective measure $\\mu$. We give a criterion when tw"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.1072","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"}