{"id":"https://openalex.org/W2580431628","doi":"https://doi.org/10.1007/s00224-017-9822-5","title":"On Effective Birkhoff\u2019s Ergodic Theorem for Computable Actions of Amenable Groups","display_name":"On Effective Birkhoff\u2019s Ergodic Theorem for Computable Actions of Amenable Groups","publication_year":2017,"publication_date":"2017-11-19","ids":{"openalex":"https://openalex.org/W2580431628","doi":"https://doi.org/10.1007/s00224-017-9822-5","mag":"2580431628"},"language":"en","primary_location":{"id":"doi:10.1007/s00224-017-9822-5","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00224-017-9822-5","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00224-017-9822-5.pdf","source":{"id":"https://openalex.org/S4210177266","display_name":"Theory of Computing Systems","issn_l":"1432-4350","issn":["1432-4350","1433-0490"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Theory of Computing Systems","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s00224-017-9822-5.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5069109153","display_name":"Nikita Moriakov","orcid":"https://orcid.org/0000-0002-7127-1006"},"institutions":[{"id":"https://openalex.org/I98358874","display_name":"Delft University of Technology","ror":"https://ror.org/02e2c7k09","country_code":"NL","type":"education","lineage":["https://openalex.org/I98358874"]}],"countries":["NL"],"is_corresponding":true,"raw_author_name":"Nikita Moriakov","raw_affiliation_strings":["Technische Universiteit Delft, Delft, Netherlands","ABN AMRO, Amsterdam, Netherlands"],"affiliations":[{"raw_affiliation_string":"Technische Universiteit Delft, Delft, Netherlands","institution_ids":["https://openalex.org/I98358874"]},{"raw_affiliation_string":"ABN AMRO, Amsterdam, Netherlands","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5069109153"],"corresponding_institution_ids":["https://openalex.org/I98358874"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":{"value":2290,"currency":"EUR","value_usd":2890},"fwci":0.2364,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":{"value":0.52698238,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"62","issue":"5","first_page":"1269","last_page":"1287"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9990000128746033,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9990000128746033,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10304","display_name":"Geometric and Algebraic Topology","score":0.9505000114440918,"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/T11567","display_name":"semigroups and automata theory","score":0.9498000144958496,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/ergodic-theory","display_name":"Ergodic theory","score":0.7960351705551147},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7314748167991638},{"id":"https://openalex.org/keywords/computable-number","display_name":"Computable number","score":0.6626029014587402},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6496304869651794},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5645484328269958},{"id":"https://openalex.org/keywords/omega","display_name":"Omega","score":0.5435788631439209},{"id":"https://openalex.org/keywords/computable-function","display_name":"Computable function","score":0.5400894284248352},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.4947464168071747},{"id":"https://openalex.org/keywords/computable-analysis","display_name":"Computable analysis","score":0.46243298053741455},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4159841239452362},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.1629261076450348},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.06525689363479614},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.064415842294693}],"concepts":[{"id":"https://openalex.org/C122044880","wikidata":"https://www.wikidata.org/wiki/Q5498822","display_name":"Ergodic theory","level":2,"score":0.7960351705551147},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7314748167991638},{"id":"https://openalex.org/C156382255","wikidata":"https://www.wikidata.org/wiki/Q818895","display_name":"Computable number","level":4,"score":0.6626029014587402},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6496304869651794},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5645484328269958},{"id":"https://openalex.org/C2779557605","wikidata":"https://www.wikidata.org/wiki/Q9890","display_name":"Omega","level":2,"score":0.5435788631439209},{"id":"https://openalex.org/C54271186","wikidata":"https://www.wikidata.org/wiki/Q1148456","display_name":"Computable function","level":2,"score":0.5400894284248352},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.4947464168071747},{"id":"https://openalex.org/C27318111","wikidata":"https://www.wikidata.org/wiki/Q5157264","display_name":"Computable analysis","level":3,"score":0.46243298053741455},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4159841239452362},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.1629261076450348},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.06525689363479614},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.064415842294693},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s00224-017-9822-5","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00224-017-9822-5","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00224-017-9822-5.pdf","source":{"id":"https://openalex.org/S4210177266","display_name":"Theory of Computing Systems","issn_l":"1432-4350","issn":["1432-4350","1433-0490"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Theory of Computing Systems","raw_type":"journal-article"},{"id":"pmh:oai:tudelft.nl:uuid:234e191f-ac11-402d-99e2-0b2b93e26577","is_oa":true,"landing_page_url":"http://resolver.tudelft.nl/uuid:234e191f-ac11-402d-99e2-0b2b93e26577","pdf_url":null,"source":{"id":"https://openalex.org/S4306400906","display_name":"Research Repository (Delft University of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I98358874","host_organization_name":"Delft University of Technology","host_organization_lineage":["https://openalex.org/I98358874"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"journal article"}],"best_oa_location":{"id":"doi:10.1007/s00224-017-9822-5","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00224-017-9822-5","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00224-017-9822-5.pdf","source":{"id":"https://openalex.org/S4210177266","display_name":"Theory of Computing Systems","issn_l":"1432-4350","issn":["1432-4350","1433-0490"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Theory of Computing Systems","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320321012","display_name":"Technische Universiteit Delft","ror":"https://ror.org/02e2c7k09"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2580431628.pdf","grobid_xml":"https://content.openalex.org/works/W2580431628.grobid-xml"},"referenced_works_count":16,"referenced_works":["https://openalex.org/W1483336251","https://openalex.org/W1483888214","https://openalex.org/W1593512589","https://openalex.org/W1978783671","https://openalex.org/W2027896280","https://openalex.org/W2032868343","https://openalex.org/W2059568104","https://openalex.org/W2074864316","https://openalex.org/W2101900964","https://openalex.org/W2107892052","https://openalex.org/W2139647880","https://openalex.org/W2313402717","https://openalex.org/W2320887888","https://openalex.org/W2324802422","https://openalex.org/W3042328837","https://openalex.org/W4292512159"],"related_works":["https://openalex.org/W2150482238","https://openalex.org/W197714092","https://openalex.org/W1577501449","https://openalex.org/W2527631632","https://openalex.org/W1994403863","https://openalex.org/W2108904240","https://openalex.org/W1987175852","https://openalex.org/W1498085647","https://openalex.org/W153068418","https://openalex.org/W2080359559"],"abstract_inverted_index":{"We":[0,126],"introduce":[1],"computable":[2,5,21,30,60,116,145],"actions":[3],"of":[4,12,48,147,159],"groups":[6],"and":[7,78,150],"prove":[8,128],"the":[9,87,107,129,138,156,162],"following":[10],"versions":[11],"effective":[13],"Birkhoff\u2019s":[14],"ergodic":[15,46],"theorem.":[16],"Let":[17],"\u0393":[18,49,142],"be":[19],"a":[20,28,43,51,59,114,144],"amenable":[22],"group,":[23],"then":[24],"there":[25],"always":[26],"exists":[27],"canonically":[29,115],"tempered":[31,117],"two-sided":[32,118],"F\u00f8lner":[33,119,157],"sequence":[34,120,158],"(F":[35,121],"n":[36,122,152],")":[37,123],"n\u2265":[38,124],"1":[39],"in":[40,137],"\u0393.":[41,164],"For":[42],"computable,":[44],"measure-preserving,":[45],"action":[47],"on":[50,75],"Cantor":[52],"space":[53],"$\\{":[54],"0,1\\}^{\\mathbb":[55],"N}$":[56],"endowed":[57],"with":[58,111],"probability":[61],"measure":[62],"\u03bc,":[63],"it":[64],"is":[65,143,155],"shown":[66],"that":[67],"for":[68,79,132],"every":[69,80],"bounded":[70],"lower":[71,134],"semicomputable":[72,135],"function":[73],"f":[74,101],"$\\{0,1\\}^{\\mathbb":[76],"{N}}$":[77,86],"Martin-L\u00f6f":[81],"random":[82],"$\\omega":[83],"\\in":[84,94],"\\{0,1\\}^{\\mathbb":[85],"equality":[88],"$$\\underset{n":[89],"\\to":[90],"\\infty}{\\lim}":[91],"\\frac{1}{|F_{n}|}":[92],"\\sum\\limits_{g":[93],"F_{n}}":[95],"f(g":[96],"\\cdot":[97],"\\omega)":[98],"=":[99],"\\int\\limits":[100],"d":[102],"\\mu":[103],"$$":[104],"holds,":[105],"where":[106],"averages":[108],"are":[109],"taken":[110],"respect":[112],"to":[113],"1.":[125],"also":[127],"same":[130],"identity":[131],"all":[133],"f\u2019s":[136],"special":[139],"case":[140],"when":[141],"group":[146],"polynomial":[148],"growth":[149],"F":[151],":=":[153],"B(n)":[154],"balls":[160],"around":[161],"neutral":[163]},"counts_by_year":[{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":1}],"updated_date":"2026-03-17T17:19:04.345684","created_date":"2025-10-10T00:00:00"}
