{"paper":{"title":"Good measures on locally compact Cantor sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"O. Karpel","submitted_at":"2012-03-30T21:25:40Z","abstract_excerpt":"We study the set M(X) of full non-atomic Borel (finite or infinite) measures on a non-compact locally compact Cantor set X. For an infinite measure $\\mu$ in M(X), the set $\\mathfrak{M}_\\mu = \\{x \\in X : {for any compact open set} U \\ni x {we have} \\mu(U) = \\infty \\}$ is called defective. We call $\\mu$ non-defective if $\\mu(\\mathfrak{M}_\\mu) = 0$. The class $M^0(X) \\subset M(X)$ consists of probability measures and infinite non-defective measures. We classify measures $\\mu$ from $M^0(X)$ with respect to a homeomorphism. The notions of goodness and compact open values set $S(\\mu)$ are defined. A"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.0027","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"}