{"title":"lctvs值函数的sl积分","authors":"Rodolfo Erodias Maza, Sergio Rosales Canoy","doi":"10.14321/REALANALEXCH.46.2.0505","DOIUrl":null,"url":null,"abstract":"A function F:[a,b]→X is said to be an SL function if it satisfies the Strong Lusin (SL) condition given as follows: for every θ-nbd U and a set E⊂[a,b] of measure zero, there exists a gauge δ such that for every δ-fine partial partition D={([xi-1,xi],ti):1≤i≤n} of [a,b] with ti∈E, there exist θ-nbds U1,U2,…,Un such that ∑i=1nUi⊆V and F(xi)-F(xi-1)∈Ui for each i=1,2,…,n. In this paper, we introduce the SL integral of a function taking values on a locally convex topological vector space (LCTVS). Further, we show that this integral is equivalent to a stronger version of the Henstock integral.","PeriodicalId":44674,"journal":{"name":"Real Analysis Exchange","volume":" ","pages":""},"PeriodicalIF":0.1000,"publicationDate":"2021-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"ON THE SL-INTEGRAL OF LCTVS-VALUED FUNCTIONS\",\"authors\":\"Rodolfo Erodias Maza, Sergio Rosales Canoy\",\"doi\":\"10.14321/REALANALEXCH.46.2.0505\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"A function F:[a,b]→X is said to be an SL function if it satisfies the Strong Lusin (SL) condition given as follows: for every θ-nbd U and a set E⊂[a,b] of measure zero, there exists a gauge δ such that for every δ-fine partial partition D={([xi-1,xi],ti):1≤i≤n} of [a,b] with ti∈E, there exist θ-nbds U1,U2,…,Un such that ∑i=1nUi⊆V and F(xi)-F(xi-1)∈Ui for each i=1,2,…,n. In this paper, we introduce the SL integral of a function taking values on a locally convex topological vector space (LCTVS). Further, we show that this integral is equivalent to a stronger version of the Henstock integral.\",\"PeriodicalId\":44674,\"journal\":{\"name\":\"Real Analysis Exchange\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":0.1000,\"publicationDate\":\"2021-11-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Real Analysis Exchange\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.14321/REALANALEXCH.46.2.0505\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Real Analysis Exchange","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.14321/REALANALEXCH.46.2.0505","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
A function F:[a,b]→X is said to be an SL function if it satisfies the Strong Lusin (SL) condition given as follows: for every θ-nbd U and a set E⊂[a,b] of measure zero, there exists a gauge δ such that for every δ-fine partial partition D={([xi-1,xi],ti):1≤i≤n} of [a,b] with ti∈E, there exist θ-nbds U1,U2,…,Un such that ∑i=1nUi⊆V and F(xi)-F(xi-1)∈Ui for each i=1,2,…,n. In this paper, we introduce the SL integral of a function taking values on a locally convex topological vector space (LCTVS). Further, we show that this integral is equivalent to a stronger version of the Henstock integral.
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