{"title":"Theory of Riemann-Stieltjes integration","authors":"","doi":"10.1142/9789811224492_0010","DOIUrl":"https://doi.org/10.1142/9789811224492_0010","url":null,"abstract":"","PeriodicalId":377607,"journal":{"name":"Analysis and Beyond","volume":"37 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-01-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117095826","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Limit values and summability","authors":"","doi":"10.1142/9789811224492_0012","DOIUrl":"https://doi.org/10.1142/9789811224492_0012","url":null,"abstract":"","PeriodicalId":377607,"journal":{"name":"Analysis and Beyond","volume":"35 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-01-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131793441","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Limits and continuity","authors":"Walter Noll","doi":"10.4135/9781544307770.n2","DOIUrl":"https://doi.org/10.4135/9781544307770.n2","url":null,"abstract":"(ξa)i := ξai for all ξ ∈ R and i ∈ I. (1.2) We are here interested in the case when I := N× or I := N, in which case the elements of R are called real sequences. We deal explicitly only with the case I := N×, but all the definitions and results below apply also to the case I := N. Definition 1: We say that the sequence b ∈ RN is a subsequence of a given sequence a ∈ RN if b = a ◦ σ for some strictly isotone σ : N× → N×, so that","PeriodicalId":377607,"journal":{"name":"Analysis and Beyond","volume":"112 50","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-04-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141216294","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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