{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,28]],"date-time":"2025-10-28T00:26:54Z","timestamp":1761611214343},"reference-count":11,"publisher":"Wiley","issue":"4-5","license":[{"start":{"date-parts":[[2007,7,26]],"date-time":"2007-07-26T00:00:00Z","timestamp":1185408000000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematical Logic Qtrly"],"published-print":{"date-parts":[[2007,9]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>By the Riesz representation theorem for the dual of <jats:italic>C<\/jats:italic> [0; 1], if <jats:italic>F<\/jats:italic>: <jats:italic>C<\/jats:italic> [0; 1] \u2192 \u211d is a continuous linear operator, then there is a function <jats:italic>g<\/jats:italic>: [0;1] \u2192 \u211d of bounded variation such that <jats:italic>F<\/jats:italic> (<jats:italic>f<\/jats:italic>) = \u222b <jats:italic>f<\/jats:italic> d<jats:italic>g<\/jats:italic> (<jats:italic>f<\/jats:italic> \u2208 <jats:italic>C<\/jats:italic> [0; 1]). The function <jats:italic>g<\/jats:italic> can be normalized such that <jats:italic>V<\/jats:italic> (<jats:italic>g<\/jats:italic>) = \u2016<jats:italic>F<\/jats:italic> \u2016. In this paper we prove a computable version of this theorem. We use the framework of TTE, the representation approach to computable analysis, which allows to define natural computability for a variety of operators. We show that there are a computable operator <jats:italic>S<\/jats:italic> mapping <jats:italic>g<\/jats:italic> and an upper bound of its variation to <jats:italic>F<\/jats:italic> and a computable operator <jats:italic>S<\/jats:italic> \u2032 mapping <jats:italic>F<\/jats:italic> and its norm to some appropriate <jats:italic>g<\/jats:italic>. (\u00a9 2007 WILEY\u2010VCH Verlag GmbH &amp; Co. KGaA, Weinheim)<\/jats:p>","DOI":"10.1002\/malq.200710008","type":"journal-article","created":{"date-parts":[[2007,7,26]],"date-time":"2007-07-26T08:47:08Z","timestamp":1185439628000},"page":"415-430","source":"Crossref","is-referenced-by-count":1,"title":["Computable Riesz representation for the dual of <i>C<\/i> [0; 1]"],"prefix":"10.1002","volume":"53","author":[{"given":"Hong","family":"Lu","sequence":"first","affiliation":[]},{"given":"Klaus","family":"Weihrauch","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2007,7,26]]},"reference":[{"key":"e_1_2_1_2_2","unstructured":"V.Brattka Computable versions of the uniform boundedness theorem. In: Logic Colloquium 2002 (Z. Chatzidakis P. Koepke and W. Pohlers eds.). 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Informatik Berichte 326 pp. 267\u2013300 (FernUniversit\u00e4t Hagen 2005)."},{"key":"e_1_2_1_12_2","doi-asserted-by":"publisher","DOI":"10.1007\/s00224-004-1193-z"}],"container-title":["Mathematical Logic Quarterly"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fmalq.200710008","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/malq.200710008","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,8,31]],"date-time":"2023-08-31T03:16:34Z","timestamp":1693451794000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/malq.200710008"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2007,7,26]]},"references-count":11,"journal-issue":{"issue":"4-5","published-print":{"date-parts":[[2007,9]]}},"alternative-id":["10.1002\/malq.200710008"],"URL":"https:\/\/doi.org\/10.1002\/malq.200710008","archive":["Portico"],"relation":{},"ISSN":["0942-5616","1521-3870"],"issn-type":[{"value":"0942-5616","type":"print"},{"value":"1521-3870","type":"electronic"}],"subject":[],"published":{"date-parts":[[2007,7,26]]}}}