{"paper":{"title":"Th\\'eorie de la mesure dans les lieux r\\'eguliers. ou : Les intersections cach\\'ees dans le paradoxe de Banach-Tarski","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"Olivier Leroy","submitted_at":"2013-03-22T14:47:17Z","abstract_excerpt":"It is well known that axiom of choice implies the existence of non-measurable sets for Lebesgue's measure on R as well as the existence of \"paradoxical\" decompositions of the unit ball of R^3 (Banach-Tarski). This is generally interpreted as the price to be paid for the numerous services provided by this axiom. The theory proposed by Olivier Leroy shows that we can have simultaneously axiom of choice and \" everything is measurable \" it takes place within the framework of \"locales\" which are particular cases of Grothendieck's toposes : a \"locale\" is just a poset which has the formal properties "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.5631","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"}