{"title":"论丹乔伊-欣钦因与 $ \\operatorname{HK}_{r} $ - 积分的关系","authors":"","doi":"10.1134/s0037446624020162","DOIUrl":null,"url":null,"abstract":"<h3>Abstract</h3> <p>We locate Musial and Sagher’s concept of <span> <span>\\( \\operatorname{HK}_{r} \\)</span> </span>-integration within the approximate Henstock–Kurzweil integral theory. If we restrict the <span> <span>\\( \\operatorname{HK}_{r} \\)</span> </span>-integral by the requirement that the indefinite <span> <span>\\( \\operatorname{HK}_{r} \\)</span> </span>-integral is continuous, then it becomes included in the classical Denjoy–Khintchine integral. We provide a direct argument demonstrating that this inclusion is proper.</p>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On the Relation between Denjoy–Khintchine and $ \\\\operatorname{HK}_{r} $ -Integrals\",\"authors\":\"\",\"doi\":\"10.1134/s0037446624020162\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<h3>Abstract</h3> <p>We locate Musial and Sagher’s concept of <span> <span>\\\\( \\\\operatorname{HK}_{r} \\\\)</span> </span>-integration within the approximate Henstock–Kurzweil integral theory. If we restrict the <span> <span>\\\\( \\\\operatorname{HK}_{r} \\\\)</span> </span>-integral by the requirement that the indefinite <span> <span>\\\\( \\\\operatorname{HK}_{r} \\\\)</span> </span>-integral is continuous, then it becomes included in the classical Denjoy–Khintchine integral. We provide a direct argument demonstrating that this inclusion is proper.</p>\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2024-03-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1134/s0037446624020162\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1134/s0037446624020162","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
On the Relation between Denjoy–Khintchine and $ \operatorname{HK}_{r} $ -Integrals
Abstract
We locate Musial and Sagher’s concept of \( \operatorname{HK}_{r} \)-integration within the approximate Henstock–Kurzweil integral theory. If we restrict the \( \operatorname{HK}_{r} \)-integral by the requirement that the indefinite \( \operatorname{HK}_{r} \)-integral is continuous, then it becomes included in the classical Denjoy–Khintchine integral. We provide a direct argument demonstrating that this inclusion is proper.
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