{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,3,29]],"date-time":"2022-03-29T15:55:17Z","timestamp":1648569317856},"reference-count":3,"publisher":"Cambridge University Press (CUP)","issue":"4","license":[{"start":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T00:00:00Z","timestamp":1394582400000},"content-version":"unspecified","delay-in-days":2658,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[2006,12]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Jeremy Avigad kindly pointed out to me that the proof of Theorem 2 in [3] is incomplete. At the very end it assumes that when <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200005855_inline1\" \/> is located, so is <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200005855_inline2\" \/>. This is not correct. In fact, Avigad explained that the construction in the proof of Theorem 15.3 in [1] can be read as a recursive counterexample to the statement: \u2018If <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200005855_inline3\" \/>, then <jats:italic>A<jats:sub>n<\/jats:sub>x<\/jats:italic> converges for every x\u2019. As a result the conclusion of Theorem 2 should be that <jats:italic>A<jats:sub>n<\/jats:sub><\/jats:italic> converges if and only if <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200005855_inline2\" \/> is located. Similar changes have to be made in the abstract, Lemma 4, and Theorem 16. Finally, the paragraph on ergodic measure preserving transformations should be removed.<\/jats:p><jats:p>As an unrelated point we would like to mention that in the last two displayed equations of the proof of theorem 1 the term <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200005855_inline4\" \/> should be replaced by <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200005855_inline5\" \/>.<\/jats:p>","DOI":"10.2178\/jsl\/1164060464","type":"journal-article","created":{"date-parts":[[2007,12,19]],"date-time":"2007-12-19T16:24:03Z","timestamp":1198081443000},"page":"1431-1432","source":"Crossref","is-referenced-by-count":0,"title":["Corrigendum to: \u2018A constructive view on ergodic theorems\u2019"],"prefix":"10.1017","volume":"71","author":[{"given":"Bas","family":"Spitters","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200005855_ref003","first-page":"611","volume":"71","author":"Spitters","year":"2006","journal-title":"A constructive view on ergodic theorems"},{"key":"S0022481200005855_ref001","doi-asserted-by":"publisher","DOI":"10.1016\/j.apal.2005.03.004"},{"key":"S0022481200005855_ref002","unstructured":"Spitters Bas , Constructive and intuitionistic integration theory and function al analysis, Ph.D. thesis , University of Nijmegen, 2002."}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200005855","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,2]],"date-time":"2019-05-02T19:29:46Z","timestamp":1556825386000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200005855\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006,12]]},"references-count":3,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2006,12]]}},"alternative-id":["S0022481200005855"],"URL":"https:\/\/doi.org\/10.2178\/jsl\/1164060464","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[2006,12]]}}}