{"id":"https://openalex.org/W4390479453","doi":"https://doi.org/10.2478/forma-2023-0017","title":"Multidimensional Measure Space and Integration","display_name":"Multidimensional Measure Space and Integration","publication_year":2023,"publication_date":"2023-09-01","ids":{"openalex":"https://openalex.org/W4390479453","doi":"https://doi.org/10.2478/forma-2023-0017"},"language":"en","primary_location":{"id":"doi:10.2478/forma-2023-0017","is_oa":true,"landing_page_url":"https://doi.org/10.2478/forma-2023-0017","pdf_url":"https://sciendo.com/pdf/10.2478/forma-2023-0017","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"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://sciendo.com/pdf/10.2478/forma-2023-0017","any_repository_has_fulltext":true},"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":false,"raw_author_name":"Noboru Endou","raw_affiliation_strings":["National Institute of Technology, Gifu College , 2236-2 Kamimakuwa, Motosu , Gifu , Japan"],"raw_orcid":"https://orcid.org/0000-0002-5922-2332","affiliations":[{"raw_affiliation_string":"National Institute of Technology, Gifu College , 2236-2 Kamimakuwa, Motosu , Gifu , Japan","institution_ids":["https://openalex.org/I4210113483"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5055549852","display_name":"Yasunari Shidama","orcid":"https://orcid.org/0000-0001-5634-0838"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yasunari Shidama","raw_affiliation_strings":["Karuizawa Hotch 244-1 , Nagano , Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Karuizawa Hotch 244-1 , Nagano , Japan","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.8158,"has_fulltext":true,"cited_by_count":5,"citation_normalized_percentile":{"value":0.79197789,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":95,"max":97},"biblio":{"volume":"31","issue":"1","first_page":"181","last_page":"192"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.9968000054359436,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T10126","display_name":"Logic, programming, and type systems","score":0.9968000054359436,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9922999739646912,"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/T12504","display_name":"Mathematics and Applications","score":0.9646000266075134,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/measure","display_name":"Measure (data warehouse)","score":0.823207676410675},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6791337728500366},{"id":"https://openalex.org/keywords/cartesian-product","display_name":"Cartesian product","score":0.6204516291618347},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.604241132736206},{"id":"https://openalex.org/keywords/product-measure","display_name":"Product measure","score":0.6001725792884827},{"id":"https://openalex.org/keywords/product","display_name":"Product (mathematics)","score":0.48929402232170105},{"id":"https://openalex.org/keywords/product-topology","display_name":"Product topology","score":0.4380439221858978},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.4253900647163391},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.34306809306144714},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.3246329724788666},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.27833282947540283},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2755761742591858},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.23751652240753174},{"id":"https://openalex.org/keywords/data-mining","display_name":"Data mining","score":0.1276666522026062},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.08517596125602722}],"concepts":[{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.823207676410675},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6791337728500366},{"id":"https://openalex.org/C65236422","wikidata":"https://www.wikidata.org/wiki/Q173740","display_name":"Cartesian product","level":2,"score":0.6204516291618347},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.604241132736206},{"id":"https://openalex.org/C55606962","wikidata":"https://www.wikidata.org/wiki/Q1572094","display_name":"Product measure","level":3,"score":0.6001725792884827},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.48929402232170105},{"id":"https://openalex.org/C123222754","wikidata":"https://www.wikidata.org/wiki/Q1070472","display_name":"Product topology","level":2,"score":0.4380439221858978},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.4253900647163391},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.34306809306144714},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3246329724788666},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.27833282947540283},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2755761742591858},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.23751652240753174},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.1276666522026062},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.08517596125602722},{"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/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.2478/forma-2023-0017","is_oa":true,"landing_page_url":"https://doi.org/10.2478/forma-2023-0017","pdf_url":"https://sciendo.com/pdf/10.2478/forma-2023-0017","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:repozytorium.uwb.edu.pl:11320/15855","is_oa":true,"landing_page_url":"http://hdl.handle.net/11320/15855","pdf_url":"https://repozytorium.uwb.edu.pl/jspui/bitstream/11320/15855/1/Multidimensional-Measure-Space-and-Integration.pdf","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":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"}],"best_oa_location":{"id":"doi:10.2478/forma-2023-0017","is_oa":true,"landing_page_url":"https://doi.org/10.2478/forma-2023-0017","pdf_url":"https://sciendo.com/pdf/10.2478/forma-2023-0017","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":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4390479453.pdf"},"referenced_works_count":12,"referenced_works":["https://openalex.org/W36540068","https://openalex.org/W112168304","https://openalex.org/W166580360","https://openalex.org/W1526346179","https://openalex.org/W1591577758","https://openalex.org/W2044555352","https://openalex.org/W2143235494","https://openalex.org/W2295728669","https://openalex.org/W2615765359","https://openalex.org/W2945905363","https://openalex.org/W4285324967","https://openalex.org/W4312947013"],"related_works":["https://openalex.org/W2515736565","https://openalex.org/W1504600961","https://openalex.org/W3092588299","https://openalex.org/W4389247778","https://openalex.org/W2890133966","https://openalex.org/W2319753075","https://openalex.org/W1999996981","https://openalex.org/W4394669524","https://openalex.org/W4234344577","https://openalex.org/W2389748081"],"abstract_inverted_index":{"Summary":[0],"This":[1],"paper":[2],"introduces":[3],"multidimensional":[4,20],"measure":[5,23],"spaces":[6,14],"and":[7,27],"the":[8,19],"integration":[9],"of":[10],"functions":[11],"on":[12,18],"these":[13],"in":[15],"Mizar.":[16],"Integrals":[17],"Cartesian":[21],"product":[22],"space":[24],"are":[25],"defined":[26],"appropriate":[28],"formal":[29],"apparatus":[30],"to":[31],"deal":[32],"with":[33],"this":[34],"notion":[35],"is":[36],"provided":[37],"as":[38],"well.":[39]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":3}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
