{"paper":{"title":"Radon-Nikod\\'ym property and thick families of geodesics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.FA","authors_text":"Mikhail I. Ostrovskii","submitted_at":"2013-06-24T23:26:10Z","abstract_excerpt":"Banach spaces without the Radon-Nikod\\'ym property are characterized as spaces containing bilipschitz images of thick families of geodesics defined as follows. A family $T$ of geodesics joining points $u$ and $v$ in a metric space is called {\\it thick} if there is $\\alpha>0$ such that for every $g\\in T$ and for any finite collection of points $r_1,...,r_n$ in the image of $g$, there is another $uv$-geodesic $\\widetilde g\\in T$ satisfying the conditions: $\\widetilde g$ also passes through $r_1,...,r_n$, and, possibly, has some more common points with $g$. On the other hand, there is a finite co"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.5807","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"}