{"id":"https://openalex.org/W2005641361","doi":"https://doi.org/10.2478/v10037-011-0031-4","title":"Borel-Cantelli Lemma","display_name":"Borel-Cantelli Lemma","publication_year":2011,"publication_date":"2011-01-01","ids":{"openalex":"https://openalex.org/W2005641361","doi":"https://doi.org/10.2478/v10037-011-0031-4","mag":"2005641361"},"language":"en","primary_location":{"id":"doi:10.2478/v10037-011-0031-4","is_oa":true,"landing_page_url":"https://doi.org/10.2478/v10037-011-0031-4","pdf_url":"https://sciendo.com/pdf/10.2478/v10037-011-0031-4","source":{"id":"https://openalex.org/S179241345","display_name":"Formalized Mathematics","issn_l":"1426-2630","issn":["1426-2630","1898-9934"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320322","host_organization_name":"De Gruyter Open","host_organization_lineage":["https://openalex.org/P4310320322","https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter Open","De Gruyter"],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Formalized Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://sciendo.com/pdf/10.2478/v10037-011-0031-4","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5004607775","display_name":"Peter De Jaeger","orcid":"https://orcid.org/0000-0003-3398-6833"},"institutions":[{"id":"https://openalex.org/I8204097","display_name":"Ludwig-Maximilians-Universit\u00e4t M\u00fcnchen","ror":"https://ror.org/05591te55","country_code":"DE","type":"education","lineage":["https://openalex.org/I8204097"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Peter Jaeger","raw_affiliation_strings":["Ludwig Maximilians University of Munich Germany","Ludwig-Maximilians-Univ. of Munich (Germany)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Ludwig Maximilians University of Munich Germany","institution_ids":["https://openalex.org/I8204097"]},{"raw_affiliation_string":"Ludwig-Maximilians-Univ. of Munich (Germany)","institution_ids":["https://openalex.org/I8204097"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5004607775"],"corresponding_institution_ids":["https://openalex.org/I8204097"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.12985316,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"19","issue":"4","first_page":"227","last_page":"232"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11720","display_name":"Probability and Risk Models","score":0.9726999998092651,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T11720","display_name":"Probability and Risk Models","score":0.9726999998092651,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T12135","display_name":"Fuzzy Systems and Optimization","score":0.9448000192642212,"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"}},{"id":"https://openalex.org/T10067","display_name":"Stochastic processes and financial applications","score":0.9172000288963318,"subfield":{"id":"https://openalex.org/subfields/2003","display_name":"Finance"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/lemma","display_name":"Lemma (botany)","score":0.9027200937271118},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8364666700363159},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4907175302505493}],"concepts":[{"id":"https://openalex.org/C2777759810","wikidata":"https://www.wikidata.org/wiki/Q149316","display_name":"Lemma (botany)","level":3,"score":0.9027200937271118},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8364666700363159},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4907175302505493},{"id":"https://openalex.org/C46757340","wikidata":"https://www.wikidata.org/wiki/Q43238","display_name":"Poaceae","level":2,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","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}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.2478/v10037-011-0031-4","is_oa":true,"landing_page_url":"https://doi.org/10.2478/v10037-011-0031-4","pdf_url":"https://sciendo.com/pdf/10.2478/v10037-011-0031-4","source":{"id":"https://openalex.org/S179241345","display_name":"Formalized Mathematics","issn_l":"1426-2630","issn":["1426-2630","1898-9934"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320322","host_organization_name":"De Gruyter Open","host_organization_lineage":["https://openalex.org/P4310320322","https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter Open","De Gruyter"],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Formalized Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:4cc1f4a0071840729b9abae3e964e48a","is_oa":false,"landing_page_url":"https://doaj.org/article/4cc1f4a0071840729b9abae3e964e48a","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Formalized Mathematics, Vol 19, Iss 4, Pp 227-232 (2011)","raw_type":"article"},{"id":"pmh:oai:repozytorium.uwb.edu.pl:11320/3618","is_oa":false,"landing_page_url":"http://hdl.handle.net/11320/3618","pdf_url":null,"source":{"id":"https://openalex.org/S4306400933","display_name":"The Repository of University in Bialystok (University in Bialystok)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210094198","host_organization_name":"University Clinical Hospital In Bialystok","host_organization_lineage":["https://openalex.org/I4210094198"],"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":"Article"}],"best_oa_location":{"id":"doi:10.2478/v10037-011-0031-4","is_oa":true,"landing_page_url":"https://doi.org/10.2478/v10037-011-0031-4","pdf_url":"https://sciendo.com/pdf/10.2478/v10037-011-0031-4","source":{"id":"https://openalex.org/S179241345","display_name":"Formalized Mathematics","issn_l":"1426-2630","issn":["1426-2630","1898-9934"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320322","host_organization_name":"De Gruyter Open","host_organization_lineage":["https://openalex.org/P4310320322","https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter Open","De Gruyter"],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Formalized Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2005641361.pdf","grobid_xml":"https://content.openalex.org/works/W2005641361.grobid-xml"},"referenced_works_count":17,"referenced_works":["https://openalex.org/W66860599","https://openalex.org/W68895216","https://openalex.org/W144386393","https://openalex.org/W260340778","https://openalex.org/W1619732349","https://openalex.org/W2059412369","https://openalex.org/W2060337820","https://openalex.org/W2082647537","https://openalex.org/W2105559527","https://openalex.org/W2106853651","https://openalex.org/W2112770788","https://openalex.org/W2121880107","https://openalex.org/W2262237570","https://openalex.org/W2296232473","https://openalex.org/W2552817710","https://openalex.org/W4242800525","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W3006682748","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W1097487277","https://openalex.org/W2061531152","https://openalex.org/W2735923117","https://openalex.org/W2159703794","https://openalex.org/W2089427484","https://openalex.org/W2115913661"],"abstract_inverted_index":{"Borel-Cantelli":[0,7],"Lemma":[1,8],"This":[2],"article":[3],"is":[4],"about":[5],"the":[6],"in":[9,18],"probability":[10],"theory.":[11],"Necessary":[12],"definitions":[13],"and":[14,20],"theorems":[15],"are":[16],"given":[17],"[10]":[19],"[7].":[21]},"counts_by_year":[{"year":2019,"cited_by_count":1},{"year":2015,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2016-06-24T00:00:00"}