{"title":"序贯Henstock积分与序贯拓扑Henstock积分的等价性","authors":"V. O. Iluebe, Adesanmi Alao Mogbademu","doi":"10.48185/jmam.v3i1.332","DOIUrl":null,"url":null,"abstract":"Let $X$ be a topological space and $\\Omega \\subset X$. Suppose $f:\\Omega\\rightarrow X$ is a function defined in a complete space $ \\Omega $ and $ \\tau $ is a vector in $ \\mathbb{R} $ taking values in $X$. Suppose $ f $ is ap-Sequential Henstock integrable with respect to $\\tau$, is $ f $ ap-Sequential Topological Henstock integrable with respect to $\\tau$? It is the purpose of this paper to proffer affirmative answer to this question.","PeriodicalId":393347,"journal":{"name":"Journal of Mathematical Analysis and Modeling","volume":"79 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2022-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Equivalence of the ap-Sequential Henstock and ap-Sequential Topological Henstock Integrals\",\"authors\":\"V. O. Iluebe, Adesanmi Alao Mogbademu\",\"doi\":\"10.48185/jmam.v3i1.332\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Let $X$ be a topological space and $\\\\Omega \\\\subset X$. Suppose $f:\\\\Omega\\\\rightarrow X$ is a function defined in a complete space $ \\\\Omega $ and $ \\\\tau $ is a vector in $ \\\\mathbb{R} $ taking values in $X$. Suppose $ f $ is ap-Sequential Henstock integrable with respect to $\\\\tau$, is $ f $ ap-Sequential Topological Henstock integrable with respect to $\\\\tau$? It is the purpose of this paper to proffer affirmative answer to this question.\",\"PeriodicalId\":393347,\"journal\":{\"name\":\"Journal of Mathematical Analysis and Modeling\",\"volume\":\"79 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2022-06-15\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Mathematical Analysis and Modeling\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.48185/jmam.v3i1.332\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Mathematical Analysis and Modeling","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.48185/jmam.v3i1.332","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
摘要
设$X$为拓扑空间,$\Omega \subset X$。假设$f:\Omega\rightarrow X$是在完整空间$ \Omega $中定义的函数,$ \tau $是$ \mathbb{R} $中的矢量,其值在$X$中。假设$ f $是ap-顺序Henstock对$\tau$可积,$ f $ ap-顺序Henstock对$\tau$可积吗?本文的目的是为这个问题提供肯定的答案。
Equivalence of the ap-Sequential Henstock and ap-Sequential Topological Henstock Integrals
Let $X$ be a topological space and $\Omega \subset X$. Suppose $f:\Omega\rightarrow X$ is a function defined in a complete space $ \Omega $ and $ \tau $ is a vector in $ \mathbb{R} $ taking values in $X$. Suppose $ f $ is ap-Sequential Henstock integrable with respect to $\tau$, is $ f $ ap-Sequential Topological Henstock integrable with respect to $\tau$? It is the purpose of this paper to proffer affirmative answer to this question.