{"id":"https://openalex.org/W2333722679","doi":"https://doi.org/10.1515/forma-2015-0025","title":"Construction of Measure from Semialgebra of Sets1","display_name":"Construction of Measure from Semialgebra of Sets1","publication_year":2015,"publication_date":"2015-12-01","ids":{"openalex":"https://openalex.org/W2333722679","doi":"https://doi.org/10.1515/forma-2015-0025","mag":"2333722679"},"language":"en","primary_location":{"id":"doi:10.1515/forma-2015-0025","is_oa":true,"landing_page_url":"https://doi.org/10.1515/forma-2015-0025","pdf_url":"https://sciendo.com/pdf/10.1515/forma-2015-0025","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/10.1515/forma-2015-0025","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5015450295","display_name":"Noboru Endou","orcid":"https://orcid.org/0000-0002-5922-2332"},"institutions":[{"id":"https://openalex.org/I4210113483","display_name":"National Institute of Technology, Gifu College","ror":"https://ror.org/025b2hx26","country_code":"JP","type":"education","lineage":["https://openalex.org/I4210113483","https://openalex.org/I4210120810"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"Noboru Endou","raw_affiliation_strings":["Gifu National College of Technology, Gifu, Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Gifu National College of Technology, Gifu, Japan","institution_ids":["https://openalex.org/I4210113483"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5015450295"],"corresponding_institution_ids":["https://openalex.org/I4210113483"],"apc_list":null,"apc_paid":null,"fwci":0.3364,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.68234264,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"23","issue":"4","first_page":"309","last_page":"323"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11727","display_name":"Advanced Algebra and Logic","score":0.9269000291824341,"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/T11727","display_name":"Advanced Algebra and Logic","score":0.9269000291824341,"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/T11703","display_name":"Rings, Modules, and Algebras","score":0.9190999865531921,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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/measure","display_name":"Measure (data warehouse)","score":0.9456005096435547},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7294115424156189},{"id":"https://openalex.org/keywords/\u03c3-finite-measure","display_name":"\u03c3-finite measure","score":0.6719298362731934},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.6640053987503052},{"id":"https://openalex.org/keywords/discrete-measure","display_name":"Discrete measure","score":0.6221831440925598},{"id":"https://openalex.org/keywords/extension","display_name":"Extension (predicate logic)","score":0.5233494639396667},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3514021337032318},{"id":"https://openalex.org/keywords/probability-measure","display_name":"Probability measure","score":0.19773536920547485},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.18880248069763184},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.17553091049194336},{"id":"https://openalex.org/keywords/borel-measure","display_name":"Borel measure","score":0.1557157337665558},{"id":"https://openalex.org/keywords/data-mining","display_name":"Data mining","score":0.129924476146698}],"concepts":[{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.9456005096435547},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7294115424156189},{"id":"https://openalex.org/C102065156","wikidata":"https://www.wikidata.org/wiki/Q291430","display_name":"\u03c3-finite measure","level":4,"score":0.6719298362731934},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.6640053987503052},{"id":"https://openalex.org/C204154756","wikidata":"https://www.wikidata.org/wiki/Q3859392","display_name":"Discrete measure","level":3,"score":0.6221831440925598},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.5233494639396667},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3514021337032318},{"id":"https://openalex.org/C21031990","wikidata":"https://www.wikidata.org/wiki/Q355020","display_name":"Probability measure","level":2,"score":0.19773536920547485},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.18880248069763184},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.17553091049194336},{"id":"https://openalex.org/C166758865","wikidata":"https://www.wikidata.org/wiki/Q892585","display_name":"Borel measure","level":3,"score":0.1557157337665558},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.129924476146698},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1515/forma-2015-0025","is_oa":true,"landing_page_url":"https://doi.org/10.1515/forma-2015-0025","pdf_url":"https://sciendo.com/pdf/10.1515/forma-2015-0025","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:b99185d425a7429c883013523ce47a36","is_oa":false,"landing_page_url":"https://doaj.org/article/b99185d425a7429c883013523ce47a36","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 23, Iss 4, Pp 309-323 (2015)","raw_type":"article"},{"id":"pmh:oai:repozytorium.uwb.edu.pl:11320/4905","is_oa":false,"landing_page_url":"http://hdl.handle.net/11320/4905","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:10.1515/forma-2015-0025","is_oa":true,"landing_page_url":"https://doi.org/10.1515/forma-2015-0025","pdf_url":"https://sciendo.com/pdf/10.1515/forma-2015-0025","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":[{"score":0.44999998807907104,"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities"}],"awards":[{"id":"https://openalex.org/G7250689446","display_name":"Construction of reasoning library for realization of computer verification system","funder_award_id":"23500029","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"}],"funders":[{"id":"https://openalex.org/F4320334764","display_name":"Japan Society for the Promotion of Science","ror":"https://ror.org/00hhkn466"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2333722679.pdf","grobid_xml":"https://content.openalex.org/works/W2333722679.grobid-xml"},"referenced_works_count":16,"referenced_works":["https://openalex.org/W39299451","https://openalex.org/W180239714","https://openalex.org/W192809544","https://openalex.org/W210666191","https://openalex.org/W260340778","https://openalex.org/W1176327680","https://openalex.org/W1574047977","https://openalex.org/W2104238184","https://openalex.org/W2105559527","https://openalex.org/W2117575167","https://openalex.org/W2145706675","https://openalex.org/W2148011644","https://openalex.org/W2150348213","https://openalex.org/W2163011897","https://openalex.org/W2163641194","https://openalex.org/W2490390969"],"related_works":["https://openalex.org/W2333722679","https://openalex.org/W2097081898","https://openalex.org/W4245121557","https://openalex.org/W2315835829","https://openalex.org/W1977114845","https://openalex.org/W2339347544","https://openalex.org/W2389551393","https://openalex.org/W1999179650","https://openalex.org/W4386563502","https://openalex.org/W2280435155"],"abstract_inverted_index":{"Summary":[0],"In":[1,32],"our":[2],"previous":[3],"article":[4,70],"[22],":[5],"we":[6,71,89],"showed":[7],"complete":[8],"additivity":[9],"as":[10,93],"a":[11,16,25,53,56,65,73,77,83,86,91,100],"condition":[12,20],"for":[13],"extension":[14,95],"of":[15,24,36,50,52,64,96],"measure.":[17],"However,":[18],"this":[19,69],"premised":[21],"the":[22,28,34,37,45,48,62,97],"existence":[23,35,51],"\u03c3-field":[26,40],"and":[27,79,106],"measure":[29,38,54,74,84,98],"on":[30,39,55,76,85,99],"it.":[31],"general,":[33],"is":[41,58],"not":[42],"obvious.":[43],"On":[44],"other":[46],"hand,":[47],"proof":[49],"semialgebra":[57,78],"easier":[59],"than":[60],"in":[61,68],"case":[63],"\u03c3-field.":[66,87,101],"Therefore,":[67],"define":[72],"(pre-measure)":[75],"extend":[80],"it":[81],"to":[82],"Furthermore,":[88],"give":[90],"\u03c3-measure":[92],"an":[94],"We":[102],"follow":[103],"[24],":[104],"[10],":[105],"[31].":[107]},"counts_by_year":[{"year":2016,"cited_by_count":1}],"updated_date":"2026-08-21T09:56:20.448147","created_date":"2016-06-24T00:00:00"}