{"paper":{"title":"Measure doubling in unimodular locally compact groups and quotients","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CO","math.LO"],"primary_cat":"math.GR","authors_text":"Chieu-Minh Tran, Fei Peng, Zuxiang Kong","submitted_at":"2024-11-26T09:25:28Z","abstract_excerpt":"We consider a (possibly discrete) unimodular locally compact group $G$ with Haar measure $\\mu_G$, and a compact $A\\subseteq G$ of positive measure with $\\mu_G(A^2)\\leq K\\mu_G(A)$. Let $H$ be a closed normal subgroup of G and $\\pi: G \\rightarrow G/H$ be the quotient map. With the further assumption that $A= A^{-1}$, we show $$\\mu_{G/H}(\\pi A ^2) \\leq K^2 \\mu_{G/H}(\\pi A).$$ We also demonstrate that $K^2$ cannot be replaced by $(1-\\epsilon)K^2$ for any $\\epsilon>0$.\n  In the general case (without $A=A^{-1}$), we show $\\mu_{G/H}(\\pi A ^2) \\leq K^3 \\mu_{G/H}(\\pi A)$, improving an earlier result by"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.17246","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2411.17246/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"}