{"id":"https://openalex.org/W4312947013","doi":"https://doi.org/10.2478/forma-2022-0004","title":"Absolutely Integrable Functions","display_name":"Absolutely Integrable Functions","publication_year":2022,"publication_date":"2022-04-01","ids":{"openalex":"https://openalex.org/W4312947013","doi":"https://doi.org/10.2478/forma-2022-0004"},"language":"en","primary_location":{"id":"doi:10.2478/forma-2022-0004","is_oa":true,"landing_page_url":"https://doi.org/10.2478/forma-2022-0004","pdf_url":"https://sciendo.com/pdf/10.2478/forma-2022-0004","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-2022-0004","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":["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"]}]}],"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":0.2873,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.56509551,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":96},"biblio":{"volume":"30","issue":"1","first_page":"31","last_page":"52"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10622","display_name":"Quantum Mechanics and Applications","score":0.993399977684021,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10622","display_name":"Quantum Mechanics and Applications","score":0.993399977684021,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"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/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9305999875068665,"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/T12516","display_name":"Advanced Mathematical Theories and Applications","score":0.9132999777793884,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/lebesgue-integration","display_name":"Lebesgue integration","score":0.8872756958007812},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7845859527587891},{"id":"https://openalex.org/keywords/riemann-integral","display_name":"Riemann integral","score":0.7289765477180481},{"id":"https://openalex.org/keywords/integrable-system","display_name":"Integrable system","score":0.6321930289268494},{"id":"https://openalex.org/keywords/riemann-hypothesis","display_name":"Riemann hypothesis","score":0.5472001433372498},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.47526615858078003},{"id":"https://openalex.org/keywords/formalism","display_name":"Formalism (music)","score":0.4724231958389282},{"id":"https://openalex.org/keywords/riemann\u2013stieltjes-integral","display_name":"Riemann\u2013Stieltjes integral","score":0.4601721167564392},{"id":"https://openalex.org/keywords/lebesgues-number-lemma","display_name":"Lebesgue's number lemma","score":0.45064646005630493},{"id":"https://openalex.org/keywords/darboux-integral","display_name":"Darboux integral","score":0.4442511200904846},{"id":"https://openalex.org/keywords/daniell-integral","display_name":"Daniell integral","score":0.4240637421607971},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.359516978263855},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3336215019226074},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3299403190612793},{"id":"https://openalex.org/keywords/integral-equation","display_name":"Integral equation","score":0.1279946267604828},{"id":"https://openalex.org/keywords/singular-integral","display_name":"Singular integral","score":0.1198117733001709},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.04470992088317871}],"concepts":[{"id":"https://openalex.org/C14158598","wikidata":"https://www.wikidata.org/wiki/Q853831","display_name":"Lebesgue integration","level":2,"score":0.8872756958007812},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7845859527587891},{"id":"https://openalex.org/C41833934","wikidata":"https://www.wikidata.org/wiki/Q697181","display_name":"Riemann integral","level":4,"score":0.7289765477180481},{"id":"https://openalex.org/C200741047","wikidata":"https://www.wikidata.org/wiki/Q1957758","display_name":"Integrable system","level":2,"score":0.6321930289268494},{"id":"https://openalex.org/C199479865","wikidata":"https://www.wikidata.org/wiki/Q205966","display_name":"Riemann hypothesis","level":2,"score":0.5472001433372498},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.47526615858078003},{"id":"https://openalex.org/C73301696","wikidata":"https://www.wikidata.org/wiki/Q5469984","display_name":"Formalism (music)","level":3,"score":0.4724231958389282},{"id":"https://openalex.org/C167211080","wikidata":"https://www.wikidata.org/wiki/Q285771","display_name":"Riemann\u2013Stieltjes integral","level":3,"score":0.4601721167564392},{"id":"https://openalex.org/C100094221","wikidata":"https://www.wikidata.org/wiki/Q1049869","display_name":"Lebesgue's number lemma","level":5,"score":0.45064646005630493},{"id":"https://openalex.org/C133389509","wikidata":"https://www.wikidata.org/wiki/Q2294564","display_name":"Darboux integral","level":3,"score":0.4442511200904846},{"id":"https://openalex.org/C134810832","wikidata":"https://www.wikidata.org/wiki/Q2996956","display_name":"Daniell integral","level":4,"score":0.4240637421607971},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.359516978263855},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3336215019226074},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3299403190612793},{"id":"https://openalex.org/C27016315","wikidata":"https://www.wikidata.org/wiki/Q580101","display_name":"Integral equation","level":2,"score":0.1279946267604828},{"id":"https://openalex.org/C92571104","wikidata":"https://www.wikidata.org/wiki/Q888122","display_name":"Singular integral","level":3,"score":0.1198117733001709},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.04470992088317871},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0},{"id":"https://openalex.org/C558565934","wikidata":"https://www.wikidata.org/wiki/Q2743","display_name":"Musical","level":2,"score":0.0},{"id":"https://openalex.org/C153349607","wikidata":"https://www.wikidata.org/wiki/Q36649","display_name":"Visual arts","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/C195065555","wikidata":"https://www.wikidata.org/wiki/Q214881","display_name":"Curvature","level":2,"score":0.0},{"id":"https://openalex.org/C142362112","wikidata":"https://www.wikidata.org/wiki/Q735","display_name":"Art","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.2478/forma-2022-0004","is_oa":true,"landing_page_url":"https://doi.org/10.2478/forma-2022-0004","pdf_url":"https://sciendo.com/pdf/10.2478/forma-2022-0004","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:11320/14245","is_oa":false,"landing_page_url":"http://hdl.handle.net/11320/14245","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/forma-2022-0004","is_oa":true,"landing_page_url":"https://doi.org/10.2478/forma-2022-0004","pdf_url":"https://sciendo.com/pdf/10.2478/forma-2022-0004","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":[{"display_name":"Reduced inequalities","score":0.44999998807907104,"id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4312947013.pdf","grobid_xml":"https://content.openalex.org/works/W4312947013.grobid-xml"},"referenced_works_count":8,"referenced_works":["https://openalex.org/W1582706191","https://openalex.org/W2146235261","https://openalex.org/W2295560716","https://openalex.org/W2295728669","https://openalex.org/W2770430340","https://openalex.org/W4285324967","https://openalex.org/W4285325472","https://openalex.org/W4285326779"],"related_works":["https://openalex.org/W2784778011","https://openalex.org/W1970788826","https://openalex.org/W4248085762","https://openalex.org/W2372686356","https://openalex.org/W2135004407","https://openalex.org/W1550832881","https://openalex.org/W2392926382","https://openalex.org/W4205964675","https://openalex.org/W628624666","https://openalex.org/W3148119979"],"abstract_inverted_index":{"Summary":[0],"The":[1],"goal":[2],"of":[3],"this":[4,37],"article":[5],"is":[6],"to":[7,42],"clarify":[8,43],"the":[9,44,54],"relationship":[10,45],"between":[11,46],"Riemann\u2019s":[12,25],"improper":[13,26,47],"integrals":[14,27,48,51],"and":[15,30,49],"Lebesgue":[16,50],"integrals.":[17],"In":[18],"previous":[19],"articles":[20],"[6],":[21],"[7],":[22],"we":[23,39],"treated":[24],"[1],":[28],"[11]":[29],"[4]":[31],"on":[32],"arbitrary":[33],"intervals.":[34],"Therefore,":[35],"in":[36],"article,":[38],"will":[40],"continue":[41],"[8],":[52],"using":[53],"Mizar":[55],"[3],":[56],"[2]":[57],"formalism.":[58]},"counts_by_year":[{"year":2023,"cited_by_count":2}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}