{"id":"https://openalex.org/W3024182785","doi":"https://doi.org/10.32408/compositionality-2-3","title":"Infinite products and zero-one laws in categorical probability","display_name":"Infinite products and zero-one laws in categorical probability","publication_year":2020,"publication_date":"2020-08-11","ids":{"openalex":"https://openalex.org/W3024182785","doi":"https://doi.org/10.32408/compositionality-2-3","mag":"3024182785"},"language":"en","primary_location":{"id":"doi:10.32408/compositionality-2-3","is_oa":true,"landing_page_url":"https://doi.org/10.32408/compositionality-2-3","pdf_url":"https://compositionality-journal.org/papers/compositionality-2-3/pdf/","source":{"id":"https://openalex.org/S4210182901","display_name":"Compositionality","issn_l":"2631-4444","issn":["2631-4444"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Compositionality","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://compositionality-journal.org/papers/compositionality-2-3/pdf/","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Tobias Fritz","orcid":null},"institutions":[{"id":"https://openalex.org/I124055696","display_name":"University of Copenhagen","ror":"https://ror.org/035b05819","country_code":"DK","type":"education","lineage":["https://openalex.org/I124055696"]}],"countries":["DK"],"is_corresponding":false,"raw_author_name":"Tobias Fritz","raw_affiliation_strings":["Deparment of Mathematical Sciences, University of Copenhagen, 2100 Denmark"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Deparment of Mathematical Sciences, University of Copenhagen, 2100 Denmark","institution_ids":["https://openalex.org/I124055696"]}]},{"author_position":"last","author":{"id":null,"display_name":"Eigil Fjeldgren Rischel","orcid":null},"institutions":[{"id":"https://openalex.org/I183974707","display_name":"Perimeter Institute","ror":"https://ror.org/013m0ej23","country_code":"CA","type":"facility","lineage":["https://openalex.org/I183974707"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Eigil Fjeldgren Rischel","raw_affiliation_strings":["Perimeter Institute for Theoretical Physics, N2L 2Y5, Waterloo, Ontario, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Perimeter Institute for Theoretical Physics, N2L 2Y5, Waterloo, Ontario, Canada","institution_ids":["https://openalex.org/I183974707"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":0,"currency":"USD","value_usd":0},"apc_paid":null,"fwci":1.2677,"has_fulltext":true,"cited_by_count":20,"citation_normalized_percentile":{"value":0.842077,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"2","issue":null,"first_page":"3","last_page":"3"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.35109999775886536,"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":0.35109999775886536,"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/T12261","display_name":"Statistical Mechanics and Entropy","score":0.15569999814033508,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11716","display_name":"Random Matrices and Applications","score":0.10300000011920929,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/extension","display_name":"Extension (predicate logic)","score":0.5443000197410583},{"id":"https://openalex.org/keywords/categorical-variable","display_name":"Categorical variable","score":0.542900025844574},{"id":"https://openalex.org/keywords/markov-chain","display_name":"Markov chain","score":0.5058000087738037},{"id":"https://openalex.org/keywords/probability-measure","display_name":"Probability measure","score":0.47920000553131104},{"id":"https://openalex.org/keywords/imprecise-probability","display_name":"Imprecise probability","score":0.44920000433921814},{"id":"https://openalex.org/keywords/markov-process","display_name":"Markov process","score":0.4250999987125397},{"id":"https://openalex.org/keywords/probability-theory","display_name":"Probability theory","score":0.4169999957084656},{"id":"https://openalex.org/keywords/random-variable","display_name":"Random variable","score":0.40119999647140503}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7537999749183655},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.5443000197410583},{"id":"https://openalex.org/C5274069","wikidata":"https://www.wikidata.org/wiki/Q2285707","display_name":"Categorical variable","level":2,"score":0.542900025844574},{"id":"https://openalex.org/C98763669","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov chain","level":2,"score":0.5058000087738037},{"id":"https://openalex.org/C21031990","wikidata":"https://www.wikidata.org/wiki/Q355020","display_name":"Probability measure","level":2,"score":0.47920000553131104},{"id":"https://openalex.org/C130648207","wikidata":"https://www.wikidata.org/wiki/Q6007562","display_name":"Imprecise probability","level":3,"score":0.44920000433921814},{"id":"https://openalex.org/C159886148","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov process","level":2,"score":0.4250999987125397},{"id":"https://openalex.org/C122203268","wikidata":"https://www.wikidata.org/wiki/Q5862903","display_name":"Probability theory","level":2,"score":0.4169999957084656},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.40119999647140503},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.39739999175071716},{"id":"https://openalex.org/C189973286","wikidata":"https://www.wikidata.org/wiki/Q176695","display_name":"Markov property","level":4,"score":0.3878999948501587},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.3871000111103058},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.357699990272522},{"id":"https://openalex.org/C149441793","wikidata":"https://www.wikidata.org/wiki/Q200726","display_name":"Probability distribution","level":2,"score":0.3255000114440918},{"id":"https://openalex.org/C51255310","wikidata":"https://www.wikidata.org/wiki/Q1163016","display_name":"Tensor product","level":2,"score":0.3199999928474426},{"id":"https://openalex.org/C155281189","wikidata":"https://www.wikidata.org/wiki/Q3518150","display_name":"Tensor (intrinsic definition)","level":2,"score":0.29600000381469727},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.2946000099182129},{"id":"https://openalex.org/C106666656","wikidata":"https://www.wikidata.org/wiki/Q6771323","display_name":"Markov kernel","level":5,"score":0.2822999954223633},{"id":"https://openalex.org/C59465623","wikidata":"https://www.wikidata.org/wiki/Q6427428","display_name":"Kolmogorov equations (Markov jump process)","level":5,"score":0.26600000262260437},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.26179999113082886},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.26159998774528503},{"id":"https://openalex.org/C185767445","wikidata":"https://www.wikidata.org/wiki/Q207952","display_name":"Law of large numbers","level":3,"score":0.2614000141620636}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.32408/compositionality-2-3","is_oa":true,"landing_page_url":"https://doi.org/10.32408/compositionality-2-3","pdf_url":"https://compositionality-journal.org/papers/compositionality-2-3/pdf/","source":{"id":"https://openalex.org/S4210182901","display_name":"Compositionality","issn_l":"2631-4444","issn":["2631-4444"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Compositionality","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1912.02769","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1912.02769","pdf_url":"https://arxiv.org/pdf/1912.02769","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"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":null,"raw_type":"text"}],"best_oa_location":{"id":"doi:10.32408/compositionality-2-3","is_oa":true,"landing_page_url":"https://doi.org/10.32408/compositionality-2-3","pdf_url":"https://compositionality-journal.org/papers/compositionality-2-3/pdf/","source":{"id":"https://openalex.org/S4210182901","display_name":"Compositionality","issn_l":"2631-4444","issn":["2631-4444"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Compositionality","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3024182785.pdf","grobid_xml":"https://content.openalex.org/works/W3024182785.grobid-xml"},"referenced_works_count":11,"referenced_works":["https://openalex.org/W342302233","https://openalex.org/W1547322272","https://openalex.org/W1995503922","https://openalex.org/W2054673836","https://openalex.org/W2087931010","https://openalex.org/W2949602009","https://openalex.org/W2953849352","https://openalex.org/W2969875089","https://openalex.org/W4226021988","https://openalex.org/W4232171345","https://openalex.org/W4294791947"],"related_works":[],"abstract_inverted_index":{"Markov":[0,91,110],"categories":[1],"are":[2],"a":[3,46,59,80,93],"recent":[4],"category-theoretic":[5],"approach":[6,18],"to":[7,131],"the":[8,25,102,132,136],"foundations":[9],"of":[10,35,67,88,101,105,116,138],"probability":[11,36],"and":[12,24,79,98,107],"statistics.":[13],"Here":[14],"we":[15,96],"develop":[16],"this":[17],"further":[19],"by":[20],"treating":[21],"infinite":[22,49],"products":[23,51],"Kolmogorov":[26,106],"extension":[27],"theorem.":[28],"This":[29,112],"is":[30],"relevant":[31],"for":[32,65,86,109],"all":[33],"aspects":[34],"theory":[37],"in":[38,56,74,90,125,135,144],"which":[39,119],"infinitely":[40],"many":[41],"random":[42],"variables":[43],"appear":[44],"at":[45],"time.":[47],"These":[48],"tensor":[50],"<mml:math":[52,69],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:munder><mml:mo>\u2a02</mml:mo><mml:mrow":[53],"class=\"MJX-TeXAtom-ORD\"><mml:mi>i</mml:mi><mml:mo>\u2208</mml:mo><mml:mi>J</mml:mi></mml:mrow></mml:munder><mml:msub><mml:mi>X</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:math>":[54],"come":[55],"two":[57],"versions:":[58],"weaker":[60],"but":[61,82,142],"more":[62,83],"general":[63,114],"one":[64,85],"families":[66,87],"objects":[68,89],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mo":[70],"stretchy=\"false\">(</mml:mo><mml:msub><mml:mi>X</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:msub><mml:mo":[71],"stretchy=\"false\">)</mml:mo><mml:mrow":[72],"class=\"MJX-TeXAtom-ORD\"><mml:mi>i</mml:mi><mml:mo>\u2208</mml:mo><mml:mi>J</mml:mi></mml:mrow></mml:msub></mml:math>":[73],"semicartesian":[75],"symmetric":[76],"monoidal":[77],"categories,":[78],"stronger":[81],"specific":[84],"categories.As":[92],"first":[94],"application,":[95],"state":[97],"prove":[99],"versions":[100,115],"zero--one":[103],"laws":[104],"Hewitt--Savage":[108],"categories.":[111],"gives":[113],"these":[117],"results":[118],"can":[120],"be":[121],"instantiated":[122],"not":[123],"only":[124],"measure-theoretic":[126],"probability,":[127],"where":[128],"they":[129],"specialize":[130],"standard":[133,139],"ones":[134],"setting":[137],"Borel":[140],"spaces,":[141],"also":[143],"other":[145],"contexts.":[146]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":9},{"year":2023,"cited_by_count":8},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1}],"updated_date":"2026-08-05T07:39:15.569665","created_date":"2020-05-21T00:00:00"}