{"id":"https://openalex.org/W2962711276","doi":"https://doi.org/10.1002/malq.201500094","title":"Universal and complete sets in martingale theory","display_name":"Universal and complete sets in martingale theory","publication_year":2018,"publication_date":"2018-10-23","ids":{"openalex":"https://openalex.org/W2962711276","doi":"https://doi.org/10.1002/malq.201500094","mag":"2962711276"},"language":"en","primary_location":{"id":"doi:10.1002/malq.201500094","is_oa":false,"landing_page_url":"https://doi.org/10.1002/malq.201500094","pdf_url":null,"source":{"id":"https://openalex.org/S172351290","display_name":"Mathematical logic quarterly","issn_l":"0044-3050","issn":["0044-3050","0942-5616","1521-3870"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Logic Quarterly","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5063083696","display_name":"Dominique Lecomte","orcid":"https://orcid.org/0000-0001-5410-767X"},"institutions":[{"id":"https://openalex.org/I3017942884","display_name":"Institut de Math\u00e9matiques de Jussieu-Paris Rive Gauche","ror":"https://ror.org/03fk87k11","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I204730241","https://openalex.org/I3017942884","https://openalex.org/I39804081","https://openalex.org/I4210141950"]},{"id":"https://openalex.org/I39804081","display_name":"Sorbonne Universit\u00e9","ror":"https://ror.org/02en5vm52","country_code":"FR","type":"education","lineage":["https://openalex.org/I39804081"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Dominique Lecomte","raw_affiliation_strings":["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","Universit\u00e9 de Picardie I.U.T. de l'Oise  site de Creil, 13, all\u00e9e de la fa\u00efencerie 60 107 Creil France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"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","institution_ids":["https://openalex.org/I3017942884","https://openalex.org/I39804081"]},{"raw_affiliation_string":"Universit\u00e9 de Picardie I.U.T. de l'Oise  site de Creil, 13, all\u00e9e de la fa\u00efencerie 60 107 Creil France","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5006615993","display_name":"Miroslav Zelen\u00fd","orcid":"https://orcid.org/0000-0001-5242-2203"},"institutions":[{"id":"https://openalex.org/I21250087","display_name":"Charles University","ror":"https://ror.org/024d6js02","country_code":"CZ","type":"education","lineage":["https://openalex.org/I21250087"]}],"countries":["CZ"],"is_corresponding":false,"raw_author_name":"Miroslav Zelen\u00fd","raw_affiliation_strings":["Department of Mathematical Analysis, Faculty of Mathematics and Physics Charles University Sokolovsk\u00e1 83 186 75 Prague Czech Republic"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematical Analysis, Faculty of Mathematics and Physics Charles University Sokolovsk\u00e1 83 186 75 Prague Czech Republic","institution_ids":["https://openalex.org/I21250087"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5063083696"],"corresponding_institution_ids":["https://openalex.org/I3017942884","https://openalex.org/I39804081"],"apc_list":{"value":2630,"currency":"USD","value_usd":2630},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.27901135,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"64","issue":"4-5","first_page":"312","last_page":"335"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory","score":0.9980000257492065,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory","score":0.9980000257492065,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11545","display_name":"Advanced Banach Space Theory","score":0.9925000071525574,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11049","display_name":"Advanced Harmonic Analysis Research","score":0.9846000075340271,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8741844892501831},{"id":"https://openalex.org/keywords/martingale","display_name":"Martingale (probability theory)","score":0.6101499795913696},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4284512996673584},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.414470374584198},{"id":"https://openalex.org/keywords/martingale-pricing","display_name":"Martingale pricing","score":0.41216689348220825},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.3746371865272522},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.33200472593307495},{"id":"https://openalex.org/keywords/local-martingale","display_name":"Local martingale","score":0.32057905197143555},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.2096012830734253},{"id":"https://openalex.org/keywords/medicine","display_name":"Medicine","score":0.05163565278053284}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8741844892501831},{"id":"https://openalex.org/C48406656","wikidata":"https://www.wikidata.org/wiki/Q534112","display_name":"Martingale (probability theory)","level":2,"score":0.6101499795913696},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4284512996673584},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.414470374584198},{"id":"https://openalex.org/C76374431","wikidata":"https://www.wikidata.org/wiki/Q6777132","display_name":"Martingale pricing","level":4,"score":0.41216689348220825},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.3746371865272522},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.33200472593307495},{"id":"https://openalex.org/C58435881","wikidata":"https://www.wikidata.org/wiki/Q1868500","display_name":"Local martingale","level":3,"score":0.32057905197143555},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.2096012830734253},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.05163565278053284},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1002/malq.201500094","is_oa":false,"landing_page_url":"https://doi.org/10.1002/malq.201500094","pdf_url":null,"source":{"id":"https://openalex.org/S172351290","display_name":"Mathematical logic quarterly","issn_l":"0044-3050","issn":["0044-3050","0942-5616","1521-3870"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Logic Quarterly","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.5099999904632568,"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10"}],"awards":[{"id":"https://openalex.org/G3010065771","display_name":"Theory of real functions and its applications in geometry","funder_award_id":"GA15-08218S","funder_id":"https://openalex.org/F4320321006","funder_display_name":"Grantov\u00e1 Agentura \u010cesk\u00e9 Republiky"}],"funders":[{"id":"https://openalex.org/F4320321006","display_name":"Grantov\u00e1 Agentura \u010cesk\u00e9 Republiky","ror":"https://ror.org/01pv73b02"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W569741787","https://openalex.org/W1539382740","https://openalex.org/W1827192160","https://openalex.org/W1973944900","https://openalex.org/W2018919209","https://openalex.org/W2033288360","https://openalex.org/W2081278058","https://openalex.org/W2088959087","https://openalex.org/W2095083440","https://openalex.org/W2243808376","https://openalex.org/W2325673722","https://openalex.org/W2585308301","https://openalex.org/W4205518192","https://openalex.org/W4233662453","https://openalex.org/W4241736549","https://openalex.org/W6824235028"],"related_works":["https://openalex.org/W1978561097","https://openalex.org/W1537069888","https://openalex.org/W3123844941","https://openalex.org/W3123900559","https://openalex.org/W2006323275","https://openalex.org/W2358946586","https://openalex.org/W4289784528","https://openalex.org/W2941875586","https://openalex.org/W2433301815","https://openalex.org/W2040425860"],"abstract_inverted_index":{"Abstract":[0],"The":[1],"Doob":[2],"convergence":[3],"theorem":[4],"implies":[5],"that":[6,53],"the":[7,24,34,54,76,91,95],"set":[8,35,55],"of":[9,11,23,36,38,50,56,97],"divergence":[10,37],"any":[12,21],"martingale":[13],"has":[14],"measure":[15],"zero.":[16],"We":[17,66,84],"prove":[18],"that,":[19],"conversely,":[20],"subset":[22],"Cantor":[25],"space":[26],"with":[27],"Lebesgue\u2010measure":[28],"zero":[29],"can":[30],"be":[31],"represented":[32],"as":[33],"some":[39,70,86],"martingale.":[40],"In":[41],"fact,":[42],"this":[43,51,69],"is":[44,52,60],"effective":[45],"and":[46,72,93],"uniform.":[47],"A":[48],"consequence":[49],"everywhere":[57],"converging":[58],"martingales":[59],"\u2010complete,":[61],"in":[62,94],"a":[63,81],"uniform":[64],"way.":[65],"derive":[67],"from":[68],"universal":[71],"complete":[73,88],"sets":[74,89],"for":[75,90],"whole":[77],"projective":[78],"hierarchy,":[79],"via":[80],"general":[82],"method.":[83],"provide":[85],"other":[87],"classes":[92],"theory":[96],"martingales.":[98]},"counts_by_year":[],"updated_date":"2026-08-08T01:25:22.217667","created_date":"2025-10-10T00:00:00"}
