{"paper":{"title":"Classifying invariant $\\sigma$-ideals with analytic base on good Cantor measure spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.LO"],"primary_cat":"math.GN","authors_text":"Robert Ralowski, Szymon Zeberski, Taras Banakh","submitted_at":"2014-09-13T07:31:38Z","abstract_excerpt":"Let $X$ be a zero-dimensional compact metrizable space endowed with a strictly positive continuous Borel $\\sigma$-additive measure $\\mu$ which is good in the sense that for any clopen subsets $U,V\\subset X$ with $\\mu(U)<\\mu(V)$ there is a clopen set $W\\subset V$ with $\\mu(W)=\\mu(U)$. We study $\\sigma$-ideals with Borel base on $X$ which are invariant under the action of the group $H_\\mu(X)$ of measure-preserving homeomorphisms of $(X,\\mu)$, and show that any such $\\sigma$-ideal $\\mathcal I$ is equal to one of seven $\\sigma$-ideals: $\\{\\emptyset\\}$, $[X]^{\\le\\omega}$, $\\mathcal E$, $\\mathcal M\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.3922","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"}