{"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":1761611214275},"reference-count":15,"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>In a recent paper, probabilistic processes are used to generate Borel probability measures on topological spaces<jats:italic>X<\/jats:italic>that are equipped with a representation in the sense of type\u20102 theory of effectivity. This gives rise to a natural representation of the set of Borel probability measures on<jats:italic>X<\/jats:italic>. We compare this representation to a canonically constructed representation which encodes a Borel probability measure as a lower semicontinuous function from the open sets to the unit interval. We show that this canonical representation is admissible with respect to the weak topology on Borel probability measures. Moreover, we prove that for countably\u2010based topological spaces the representation via probabilistic processes is equivalent to the canonical representation and thus admissible with respect to the weak topology. (\u00a9 2007 WILEY\u2010VCH Verlag GmbH &amp; Co. KGaA, Weinheim)<\/jats:p>","DOI":"10.1002\/malq.200710010","type":"journal-article","created":{"date-parts":[[2007,7,26]],"date-time":"2007-07-26T08:47:32Z","timestamp":1185439652000},"page":"431-445","source":"Crossref","is-referenced-by-count":19,"title":["Admissible representations for probability measures"],"prefix":"10.1002","volume":"53","author":[{"given":"Matthias","family":"Schr\u00f6der","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2007,7,26]]},"reference":[{"key":"e_1_2_1_2_2","unstructured":"D. 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J.Taylor Introduction to Measure and Probability (Cambridge University Press 1966).","DOI":"10.1017\/CBO9780511897214"},{"key":"e_1_2_1_9_2","unstructured":"E. L.Lawler Combinatorial Optimization: Networks and Matroids (Holt Rinehart and Winston 1976)."},{"key":"e_1_2_1_10_2","doi-asserted-by":"publisher","DOI":"10.1017\/S0960129504004372"},{"key":"e_1_2_1_11_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0304-3975(01)00109-8"},{"key":"e_1_2_1_12_2","unstructured":"M.Schr\u00f6der Admissible representations for continuous computations. Ph. D. Thesis Informatik\u2010Berichte299 Fern\u2010Universit\u00e4t Hagen (2003)."},{"key":"e_1_2_1_13_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.jco.2006.05.003"},{"key":"e_1_2_1_14_2","doi-asserted-by":"crossref","unstructured":"M. B.Smyth Topology. In: Handbook of Logic in Computer Science Vol. 1 pp. 641\u2013761 (Oxford Science Publications 1992).","DOI":"10.1093\/oso\/9780198537359.003.0005"},{"key":"e_1_2_1_15_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0304-3975(98)00298-9"},{"key":"e_1_2_1_16_2","doi-asserted-by":"crossref","unstructured":"K.Weihrauch Computable Analysis (Springer 2000).","DOI":"10.1007\/978-3-642-56999-9"}],"container-title":["Mathematical Logic Quarterly"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fmalq.200710010","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/malq.200710010","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,2,17]],"date-time":"2024-02-17T02:11:33Z","timestamp":1708135893000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/malq.200710010"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2007,7,26]]},"references-count":15,"journal-issue":{"issue":"4-5","published-print":{"date-parts":[[2007,9]]}},"alternative-id":["10.1002\/malq.200710010"],"URL":"https:\/\/doi.org\/10.1002\/malq.200710010","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]]}}}