{"paper":{"title":"On s-sets in spaces of homogeneous type","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Marilina Carena, Marisa Toschi","submitted_at":"2013-12-10T21:30:05Z","abstract_excerpt":"Let $(X,d,\\mu)$ be a space of homogeneous type. In this note we study the relationship between two types of $s$-sets: relative to a distance and relative to a measure. We find a condition on a closed subset $F$ of $X$ under which we have that $F$ is $s$-set relative to the measure $\\mu$ if and only if $F$ is $s$-set relative to $\\delta$. Here $\\delta$ denotes the quasi-distance defined by Mac\\'ias and Segovia such that $(X,\\delta,\\mu)$ is a normal space. In order to prove this result, we show a covering type lemma and a type of Hausdorff measure based criteria for the $s$-set condition relativ"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.2971","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"}