{"paper":{"title":"Cardinal invariants of Haar null and Haar meager sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GN"],"primary_cat":"math.LO","authors_text":"M\\'ark Po\\'or, M\\'arton Elekes","submitted_at":"2019-08-15T21:40:41Z","abstract_excerpt":"A subset $X$ of a Polish group $G$ is \\emph{Haar null} if there exists a Borel probability measure $\\mu$ and a Borel set $B$ containing $X$ such that $\\mu(gBh)=0$ for every $g,h \\in G$. A set $X$ is \\emph{Haar meager} if there exists a compact metric space $K$, a continuous function $f : K \\to G$ and a Borel set $B$ containing $X$ such that $f^{-1}(gBh)$ is meager in $K$ for every $g,h \\in G$. We calculate (in $ZFC$) the four cardinal invariants ($\\rm add$, $\\rm cov$, $\\rm non$, $\\rm cof$) of these two $\\sigma$-ideals for the simplest non-locally compact Polish group, namely in the case $G = \\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.05776","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1908.05776/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}