{"title":"关于Stieltjes型Henstock积分的注释","authors":"Y. Kubota","doi":"10.5036/BFSIU1968.17.25","DOIUrl":null,"url":null,"abstract":"Let f:[a, b]→ R be bounded and g:[a, b]→ R be of bounded variation.It is shown that f is Henstock integrable with respect to g on [a, b] if and only if f is Young refinement integrable with respect g on [a, b], and both integrals have the same value.Some relations to the mean Stieltjes integral will also be given.","PeriodicalId":141145,"journal":{"name":"Bulletin of The Faculty of Science, Ibaraki University. Series A, Mathematics","volume":"47 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1985-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Remarks on the Henstock Integral of Stieltjes Type\",\"authors\":\"Y. Kubota\",\"doi\":\"10.5036/BFSIU1968.17.25\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Let f:[a, b]→ R be bounded and g:[a, b]→ R be of bounded variation.It is shown that f is Henstock integrable with respect to g on [a, b] if and only if f is Young refinement integrable with respect g on [a, b], and both integrals have the same value.Some relations to the mean Stieltjes integral will also be given.\",\"PeriodicalId\":141145,\"journal\":{\"name\":\"Bulletin of The Faculty of Science, Ibaraki University. Series A, Mathematics\",\"volume\":\"47 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1985-05-31\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Bulletin of The Faculty of Science, Ibaraki University. Series A, Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.5036/BFSIU1968.17.25\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Bulletin of The Faculty of Science, Ibaraki University. Series A, Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.5036/BFSIU1968.17.25","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Remarks on the Henstock Integral of Stieltjes Type
Let f:[a, b]→ R be bounded and g:[a, b]→ R be of bounded variation.It is shown that f is Henstock integrable with respect to g on [a, b] if and only if f is Young refinement integrable with respect g on [a, b], and both integrals have the same value.Some relations to the mean Stieltjes integral will also be given.
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