{"paper":{"title":"On Borel maps, calibrated $\\sigma$-ideals and homogeneity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GN"],"primary_cat":"math.LO","authors_text":"Piotr Zakrzewski, Roman Pol","submitted_at":"2017-06-15T08:19:03Z","abstract_excerpt":"Let $\\mu$ be a Borel measure on a compactum $X$. The main objects in this paper are $\\sigma$-ideals $I(dim)$, $J_0(\\mu)$, $J_f(\\mu)$ of Borel sets in $X$ that can be covered by countably many compacta which are finite-dimensional, or of $\\mu$-measure null, or of finite $\\mu$-measure, respectively. Answering a question of J. Zapletal, we shall show that for the Hilbert cube, the $\\sigma$-ideal $I(dim)$ is not homogeneous in a strong way. We shall also show that in some natural instances of measures $\\mu$ with non-homogeneous $\\sigma$-ideals $J_0(\\mu)$ or $J_f(\\mu)$, the completions of the quoti"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.04773","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"}