{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T14:25:26Z","timestamp":1740147926106,"version":"3.37.3"},"reference-count":13,"publisher":"Wiley","issue":"4-5","license":[{"start":{"date-parts":[[2018,10,23]],"date-time":"2018-10-23T00:00:00Z","timestamp":1540252800000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"funder":[{"DOI":"10.13039\/501100001824","name":"GA\u010cR","doi-asserted-by":"crossref","award":["15-08218S"],"award-info":[{"award-number":["15-08218S"]}],"id":[{"id":"10.13039\/501100001824","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Mathematical Logic Qtrly"],"published-print":{"date-parts":[[2018,11]]},"abstract":"Abstract<\/jats:title>The Doob convergence theorem implies that the set of divergence of any martingale has measure zero. We prove that, conversely, any subset of the Cantor space with Lebesgue\u2010measure zero can be represented as the set of divergence of some martingale. In fact, this is effective and uniform. A consequence of this is that the set of everywhere converging martingales is \u2010complete, in a uniform way. We derive from this some universal and complete sets for the whole projective hierarchy, via a general method. We provide some other complete sets for the classes and in the theory of martingales.<\/jats:p>","DOI":"10.1002\/malq.201500094","type":"journal-article","created":{"date-parts":[[2018,10,24]],"date-time":"2018-10-24T07:01:21Z","timestamp":1540364481000},"page":"312-335","update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Universal and complete sets in martingale theory"],"prefix":"10.1002","volume":"64","author":[{"given":"Dominique","family":"Lecomte","sequence":"first","affiliation":[{"name":"Projet Analyse Fonctionnelle Institut de Math\u00e9matiques de Jussieu Universit\u00e9 Paris 6, Couloir 16\u201026, 4\u00e8me \u00e9tage, Case 247, 4, place Jussieu 75 252 Paris Cedex 05 France"},{"name":"Universit\u00e9 de Picardie I.U.T. de l'Oise site de Creil, 13, all\u00e9e de la fa\u00efencerie 60 107 Creil France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Miroslav","family":"Zelen\u00fd","sequence":"additional","affiliation":[{"name":"Department of Mathematical Analysis, Faculty of Mathematics and Physics Charles University Sokolovsk\u00e1 83 186 75 Prague Czech Republic"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2018,10,23]]},"reference":[{"key":"e_1_2_8_2_1","first-page":"323","article-title":"Some complete sets in harmonic analysis","volume":"339","author":"Becker H.","year":"1993","journal-title":"Trans. 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