{"paper":{"title":"On uniform continuity of convex bodies with respect to measures in Banach spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Anatolij Plichko","submitted_at":"2012-08-31T06:54:43Z","abstract_excerpt":"Let $\\mu$ be a probability measure on a separable Banach space $X$. A subset $U\\subset X$ is $\\mu$-continuous if $\\mu(\\partial U)=0$. In the paper the $\\mu$-continuity and uniform $\\mu$-continuity of convex bodies in $X$, especially of balls and half-spaces, is considered. The $\\mu$-continuity is interesting for study of the Glivenko-Cantelli theorem in Banach spaces. Answer to a question of F. Tops{\\o}e is given."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.6407","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"}