{"id":"https://openalex.org/W2115770784","doi":"https://doi.org/10.2178/jsl/1146620162","title":"A constructive view on ergodic theorems","display_name":"A constructive view on ergodic theorems","publication_year":2006,"publication_date":"2006-06-01","ids":{"openalex":"https://openalex.org/W2115770784","doi":"https://doi.org/10.2178/jsl/1146620162","mag":"2115770784"},"language":"en","primary_location":{"id":"doi:10.2178/jsl/1146620162","is_oa":false,"landing_page_url":"https://doi.org/10.2178/jsl/1146620162","pdf_url":null,"source":{"id":"https://openalex.org/S177675236","display_name":"Journal of Symbolic Logic","issn_l":"0022-4812","issn":["0022-4812","1943-5886"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Symbolic Logic","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/A5043123968","display_name":"Bas Spitters","orcid":"https://orcid.org/0000-0002-2802-0973"},"institutions":[{"id":"https://openalex.org/I145872427","display_name":"Radboud University Nijmegen","ror":"https://ror.org/016xsfp80","country_code":"NL","type":"education","lineage":["https://openalex.org/I145872427"]}],"countries":["NL"],"is_corresponding":true,"raw_author_name":"Bas Spitters","raw_affiliation_strings":["Radboud University, Nijmegen, The Netherlands. E-mail:","RADBOUD UNIVERSITY"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Radboud University, Nijmegen, The Netherlands. E-mail:","institution_ids":["https://openalex.org/I145872427"]},{"raw_affiliation_string":"RADBOUD UNIVERSITY","institution_ids":["https://openalex.org/I145872427"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5043123968"],"corresponding_institution_ids":["https://openalex.org/I145872427"],"apc_list":null,"apc_paid":null,"fwci":1.2381,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.77406226,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"71","issue":"2","first_page":"611","last_page":"623"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9995999932289124,"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"}},"topics":[{"id":"https://openalex.org/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9995999932289124,"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/T13234","display_name":"advanced mathematical theories","score":0.9843999743461609,"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/T13400","display_name":"Mathematical and Theoretical Analysis","score":0.9503999948501587,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/ergodic-theory","display_name":"Ergodic theory","score":0.9241000413894653},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8136892318725586},{"id":"https://openalex.org/keywords/constructive","display_name":"Constructive","score":0.7409801483154297},{"id":"https://openalex.org/keywords/almost-everywhere","display_name":"Almost everywhere","score":0.694333016872406},{"id":"https://openalex.org/keywords/invariant-measure","display_name":"Invariant measure","score":0.6333646178245544},{"id":"https://openalex.org/keywords/pointwise","display_name":"Pointwise","score":0.6228173971176147},{"id":"https://openalex.org/keywords/corollary","display_name":"Corollary","score":0.5993626117706299},{"id":"https://openalex.org/keywords/stationary-ergodic-process","display_name":"Stationary ergodic process","score":0.554735004901886},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.5020356178283691},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.4912063479423523},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.4790707528591156},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.47538650035858154},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4601912796497345},{"id":"https://openalex.org/keywords/contraction","display_name":"Contraction (grammar)","score":0.4329086244106293},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.19334676861763},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.06236237287521362},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.0619235634803772}],"concepts":[{"id":"https://openalex.org/C122044880","wikidata":"https://www.wikidata.org/wiki/Q5498822","display_name":"Ergodic theory","level":2,"score":0.9241000413894653},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8136892318725586},{"id":"https://openalex.org/C2778701210","wikidata":"https://www.wikidata.org/wiki/Q28130034","display_name":"Constructive","level":3,"score":0.7409801483154297},{"id":"https://openalex.org/C27142425","wikidata":"https://www.wikidata.org/wiki/Q1139334","display_name":"Almost everywhere","level":2,"score":0.694333016872406},{"id":"https://openalex.org/C115667082","wikidata":"https://www.wikidata.org/wiki/Q4200518","display_name":"Invariant measure","level":3,"score":0.6333646178245544},{"id":"https://openalex.org/C2777984123","wikidata":"https://www.wikidata.org/wiki/Q9248237","display_name":"Pointwise","level":2,"score":0.6228173971176147},{"id":"https://openalex.org/C2780012671","wikidata":"https://www.wikidata.org/wiki/Q1343870","display_name":"Corollary","level":2,"score":0.5993626117706299},{"id":"https://openalex.org/C151424130","wikidata":"https://www.wikidata.org/wiki/Q17123911","display_name":"Stationary ergodic process","level":4,"score":0.554735004901886},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5020356178283691},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.4912063479423523},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.4790707528591156},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.47538650035858154},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4601912796497345},{"id":"https://openalex.org/C163415756","wikidata":"https://www.wikidata.org/wiki/Q126473","display_name":"Contraction (grammar)","level":2,"score":0.4329086244106293},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.19334676861763},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.06236237287521362},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0619235634803772},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.0},{"id":"https://openalex.org/C126322002","wikidata":"https://www.wikidata.org/wiki/Q11180","display_name":"Internal medicine","level":1,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.2178/jsl/1146620162","is_oa":false,"landing_page_url":"https://doi.org/10.2178/jsl/1146620162","pdf_url":null,"source":{"id":"https://openalex.org/S177675236","display_name":"Journal of Symbolic Logic","issn_l":"0022-4812","issn":["0022-4812","1943-5886"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Symbolic Logic","raw_type":"journal-article"},{"id":"pmh:oai:pure.tue.nl:openaire_cris_publications/1be2186e-0f6f-457b-9600-8db7e7b82f97","is_oa":false,"landing_page_url":"https://research.tue.nl/en/publications/1be2186e-0f6f-457b-9600-8db7e7b82f97","pdf_url":null,"source":{"id":"https://openalex.org/S4406922641","display_name":"TU/e Research Portal","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Spitters, B A W 2006, 'A constructive view on ergodic theorems', Journal of Symbolic Logic, vol. 71, no. 2, pp. 611-623. https://doi.org/10.2178/jsl/1146620162","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:CULeuclid:euclid.jsl/1146620162","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jsl/1146620162","pdf_url":null,"source":{"id":"https://openalex.org/S4306400787","display_name":"Project Euclid (Cornell University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"},{"id":"pmh:oai:repository.ubn.ru.nl:2066/112753","is_oa":false,"landing_page_url":"http://hdl.handle.net/2066/112753","pdf_url":null,"source":{"id":"https://openalex.org/S4306401067","display_name":"Radboud Repository (Radboud University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I145872427","host_organization_name":"Radboud University Nijmegen","host_organization_lineage":["https://openalex.org/I145872427"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Journal of Symbolic Logic, 71, 2, pp. 611-623","raw_type":"Article / Letter to editor"},{"id":"pmh:tue:oai:pure.tue.nl:publications/1be2186e-0f6f-457b-9600-8db7e7b82f97","is_oa":false,"landing_page_url":"https://research.tue.nl/nl/publications/1be2186e-0f6f-457b-9600-8db7e7b82f97","pdf_url":null,"source":{"id":"https://openalex.org/S4306401843","display_name":"Data Archiving and Networked Services (DANS)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1322597698","host_organization_name":"Royal Netherlands Academy of Arts and Sciences","host_organization_lineage":["https://openalex.org/I1322597698"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Journal of Symbolic Logic, 71(2), 611 - 623. Association for Symbolic Logic","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":20,"referenced_works":["https://openalex.org/W649907824","https://openalex.org/W1537034681","https://openalex.org/W1540066904","https://openalex.org/W2003008253","https://openalex.org/W2021556472","https://openalex.org/W2047115383","https://openalex.org/W2067914884","https://openalex.org/W2073658032","https://openalex.org/W2127217337","https://openalex.org/W2132932239","https://openalex.org/W2335062971","https://openalex.org/W2551720480","https://openalex.org/W2575695474","https://openalex.org/W3109381375","https://openalex.org/W3152478022","https://openalex.org/W4205976284","https://openalex.org/W4230278731","https://openalex.org/W4231009334","https://openalex.org/W4239316923","https://openalex.org/W6655621478"],"related_works":["https://openalex.org/W3048177030","https://openalex.org/W613715564","https://openalex.org/W1779535197","https://openalex.org/W4301461899","https://openalex.org/W2289299723","https://openalex.org/W2624948617","https://openalex.org/W2794147199","https://openalex.org/W2094015173","https://openalex.org/W2962834376","https://openalex.org/W2022180792"],"abstract_inverted_index":{"Abstract":[0],"Let":[1],"T":[2,41,56],"be":[3],"a":[4,83,87,97],"positive":[5],"L":[6,9,27,49],"1":[7],"-":[8],"\u221e":[10],"contraction.":[11],"We":[12],"prove":[13],"that":[14],"the":[15,31,48,72,77],"following":[16],"statements":[17],"are":[18],"equivalent":[19],"in":[20,26,47],"constructive":[21,88],"mathematics.":[22],"(1)":[23],"The":[24,38,53],"projection":[25],"2":[28,50],",":[29],"on":[30],"space":[32],"of":[33],"invariant":[34],"functions":[35],"exists:":[36],"(2)":[37],"sequence":[39,54],"(":[40,55],"n":[42,44,57,59],")":[43,58],"\u2208N":[45,60],"Ces\u00e1ro-converges":[46,61],"norm:":[51],"(3)":[52],"almost":[62],"everywhere.":[63],"Thus,":[64],"we":[65,85],"find":[66],"necessary":[67],"and":[68,76],"sufficient":[69],"conditions":[70],"for":[71,91],"Mean":[73],"Ergodic":[74,80],"Theorem":[75],"Dunford-Schwartz":[78],"Pointwise":[79],"Theorem.":[81],"As":[82],"corollary":[84],"obtain":[86],"ergodic":[89,92],"theorem":[90],"measure-preserving":[93],"transformations.":[94],"This":[95],"answers":[96],"question":[98],"posed":[99],"by":[100],"Bishop.":[101]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}