{"paper":{"title":"Generalized Hausdorff measure for generic compact sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Andr\\'as M\\'ath\\'e, Rich\\'ard Balka","submitted_at":"2012-04-05T00:58:03Z","abstract_excerpt":"Let $X$ be a Polish space. We prove that the generic compact set $K\\subseteq X$ (in the sense of Baire category) is either finite or there is a continuous gauge function $h$ such that $0<\\mathcal{H}^{h}(K)<\\infty$, where $\\mathcal{H}^h$ denotes the $h$-Hausdorff measure. This answers a question of C. Cabrelli, U. B. Darji, and U. M. Molter. Moreover, for every weak contraction $f\\colon K\\to X$ we have $\\mathcal{H}^{h} (K\\cap f(K))=0$. This is a measure theoretic analogue of a result of M. Elekes."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.1100","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"}