{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,6]],"date-time":"2026-04-06T22:16:54Z","timestamp":1775513814559,"version":"3.50.1"},"reference-count":11,"publisher":"Cambridge University Press (CUP)","issue":"2","license":[{"start":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T00:00:00Z","timestamp":1394582400000},"content-version":"unspecified","delay-in-days":11607,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1982,6]]},"abstract":"<jats:p>A recent result of J.P. Burgess [1] states:<\/jats:p><jats:p>Theorem 0. <jats:italic>Let F be a multifunction from an analytic subset T of a Polish space to a Polish space X. If F is Borel measurable<\/jats:italic>, Graph(<jats:italic>F<\/jats:italic>) <jats:italic>is coanalytic in T \u00d7 X and F(t) is nonmeager in its closure <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200044303_inline01\"\/> for each t \u0404 T, then F admits a Borel measurable selector<\/jats:italic>.<\/jats:p><jats:p>The above result unifies and significantly extends earlier results of H. Sarbadhikari [8], S.M. Srivastava [9] and G. Debs (unpublished). The reader is referred to [1] for details.<\/jats:p><jats:p>The aim of this article is to give an effective version of Theorem 0. We do this by proving a basis theorem for \u03a0<jats:sub arrange=\"stack\">1<\/jats:sub><jats:sub arrange=\"stack\">1<\/jats:sub> sets which are nonmeager in their closure and satisfy a local version of the measurability condition in Theorem 0. Our basis theorem generalizes a well-known result of P.G. Hinman [4] and S.K. Thomason [10] (see also [5] and [7, 4F.20]). Our methods are similar to those used by A. Louveau to prove that a <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200044303_inline02\"\/>, \u03c3-compact set is contained in a <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200044303_inline03\"\/>, \u03c3-compact set (see [7, 4F.18]).<\/jats:p><jats:p>The paper is organized as follows. \u00a72 is devoted to preliminaries. In \u00a73, we prove the basis theorem and deduce as a consequence an effective version of Theorem 0. We show in \u00a74 how our methods can be used to give alternative proofs of some known results.<\/jats:p><jats:p>Discussions with R. Barua, B.V. Rao and V.V. Srivatsa are gratefully acknowledged. I am indebted to J.P. Burgess for drawing my attention to an error in an earlier draft of this paper.<\/jats:p>","DOI":"10.2307\/2273148","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T21:59:42Z","timestamp":1146952782000},"page":"388-394","source":"Crossref","is-referenced-by-count":2,"title":["An effective selection theorem"],"prefix":"10.1017","volume":"47","author":[{"given":"Ashok","family":"Maitra","sequence":"first","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200044303_ref011","doi-asserted-by":"publisher","DOI":"10.4064\/fm-82-3-269-294"},{"key":"S0022481200044303_ref010","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1967-0219421-0"},{"key":"S0022481200044303_ref009","first-page":"283","article-title":"Selection theorems for G\u2202-valued multifunctions","volume":"254","author":"Srivastava","year":"1979","journal-title":"Transactions of the American Mathematical Society"},{"key":"S0022481200044303_ref005","doi-asserted-by":"publisher","DOI":"10.1016\/0003-4843(73)90012-0"},{"key":"S0022481200044303_ref004","doi-asserted-by":"publisher","DOI":"10.1002\/malq.19690152004"},{"key":"S0022481200044303_ref002","doi-asserted-by":"publisher","DOI":"10.1016\/0001-8708(80)90057-2"},{"key":"S0022481200044303_ref001","unstructured":"Burgess J. P. , Careful choices: A last word on Borel selectors, preprint, 1979."},{"key":"S0022481200044303_ref006","volume-title":"Proceedings of the Oberwolf ach Conference, April 1977","author":"Louveau","year":"1978"},{"key":"S0022481200044303_ref007","volume-title":"Descriptive set theory","author":"Moschovakis","year":"1980"},{"key":"S0022481200044303_ref008","doi-asserted-by":"publisher","DOI":"10.4064\/fm-97-3-209-214"},{"key":"S0022481200044303_ref003","first-page":"749","volume-title":"Comptes Rendues Hebdomadaires des S\u00e9ances de l'Acad\u00e9mie des Sciences. S\u00e9ries A. (Paris)","author":"Hillard","year":"1979"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200044303","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,24]],"date-time":"2019-05-24T21:16:01Z","timestamp":1558732561000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200044303\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1982,6]]},"references-count":11,"journal-issue":{"issue":"2","published-print":{"date-parts":[[1982,6]]}},"alternative-id":["S0022481200044303"],"URL":"https:\/\/doi.org\/10.2307\/2273148","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1982,6]]}}}