{"title":"从下收敛就足够了","authors":"J. Feinstein","doi":"10.33232/bims.0059.65.70","DOIUrl":null,"url":null,"abstract":"An elementary application of Fatou's lemma gives a strengthened version of the monotone convergence theorem. We call this the convergence from below theorem. We make the case that this result should be better known, and deserves a place in any introductory course on measure and integration.","PeriodicalId":103198,"journal":{"name":"Irish Mathematical Society Bulletin","volume":"8 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2014-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Convergence from Below Suffices\",\"authors\":\"J. Feinstein\",\"doi\":\"10.33232/bims.0059.65.70\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"An elementary application of Fatou's lemma gives a strengthened version of the monotone convergence theorem. We call this the convergence from below theorem. We make the case that this result should be better known, and deserves a place in any introductory course on measure and integration.\",\"PeriodicalId\":103198,\"journal\":{\"name\":\"Irish Mathematical Society Bulletin\",\"volume\":\"8 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2014-12-24\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Irish Mathematical Society Bulletin\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.33232/bims.0059.65.70\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Irish Mathematical Society Bulletin","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.33232/bims.0059.65.70","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
An elementary application of Fatou's lemma gives a strengthened version of the monotone convergence theorem. We call this the convergence from below theorem. We make the case that this result should be better known, and deserves a place in any introductory course on measure and integration.
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