{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T15:38:14Z","timestamp":1753889894001,"version":"3.41.2"},"reference-count":1,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","license":[{"start":{"date-parts":[[2014,12,24]],"date-time":"2014-12-24T00:00:00Z","timestamp":1419379200000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/arxiv.org\/licenses\/nonexclusive-distrib\/1.0"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"abstract":"<jats:p>We analyze the strength of Helly's selection theorem HST, which is the most\nimportant compactness theorem on the space of functions of bounded variation.\nFor this we utilize a new representation of this space intermediate between\n$L_1$ and the Sobolev space W1,1, compatible with the, so called, weak*\ntopology. We obtain that HST is instance-wise equivalent to the\nBolzano-Weierstra\\ss\\ principle over RCA0. With this HST is equivalent to ACA0\nover RCA0. A similar classification is obtained in the Weihrauch lattice.<\/jats:p>","DOI":"10.2168\/lmcs-10(4:16)2014","type":"journal-article","created":{"date-parts":[[2015,5,18]],"date-time":"2015-05-18T07:32:47Z","timestamp":1431934367000},"source":"Crossref","is-referenced-by-count":6,"title":["Bounded variation and the strength of Helly's selection theorem"],"prefix":"10.46298","volume":"Volume 10, Issue 4","author":[{"given":"Alexander P.","family":"Kreuzer","sequence":"first","affiliation":[]}],"member":"25203","published-online":{"date-parts":[[2014,12,24]]},"reference":[{"key":"928:not-found"}],"container-title":["Logical Methods in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/lmcs.episciences.org\/980\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/lmcs.episciences.org\/980\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,4,11]],"date-time":"2023-04-11T20:00:39Z","timestamp":1681243239000},"score":1,"resource":{"primary":{"URL":"https:\/\/lmcs.episciences.org\/980"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,12,24]]},"references-count":1,"URL":"https:\/\/doi.org\/10.2168\/lmcs-10(4:16)2014","relation":{"is-same-as":[{"id-type":"arxiv","id":"1308.3881","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arXiv.1308.3881","asserted-by":"subject"}]},"ISSN":["1860-5974"],"issn-type":[{"type":"electronic","value":"1860-5974"}],"subject":[],"published":{"date-parts":[[2014,12,24]]},"article-number":"980"}}