Xingni Jiang, Jan Harm van der Walt, Marten Wortel
{"title":"L 值积分","authors":"Xingni Jiang, Jan Harm van der Walt, Marten Wortel","doi":"arxiv-2408.17306","DOIUrl":null,"url":null,"abstract":"We develop integration theory for integrating functions taking values into a\nDedekind complete unital $f$-algebra $\\mathbb{L}$ with respect to\n$\\mathbb{L}$-valued measures. We then discuss and prove completeness results of\n$\\mathbb{L}$-valued $L^p$-spaces.","PeriodicalId":501036,"journal":{"name":"arXiv - MATH - Functional Analysis","volume":"6 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"L-valued integration\",\"authors\":\"Xingni Jiang, Jan Harm van der Walt, Marten Wortel\",\"doi\":\"arxiv-2408.17306\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We develop integration theory for integrating functions taking values into a\\nDedekind complete unital $f$-algebra $\\\\mathbb{L}$ with respect to\\n$\\\\mathbb{L}$-valued measures. We then discuss and prove completeness results of\\n$\\\\mathbb{L}$-valued $L^p$-spaces.\",\"PeriodicalId\":501036,\"journal\":{\"name\":\"arXiv - MATH - Functional Analysis\",\"volume\":\"6 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-08-30\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - MATH - Functional Analysis\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2408.17306\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Functional Analysis","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2408.17306","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
We develop integration theory for integrating functions taking values into a
Dedekind complete unital $f$-algebra $\mathbb{L}$ with respect to
$\mathbb{L}$-valued measures. We then discuss and prove completeness results of
$\mathbb{L}$-valued $L^p$-spaces.
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