{"title":"论概率措施的投影极限的 $$L^{p}$$ 空间","authors":"Juan Carlos Sampedro","doi":"10.1007/s10959-024-01329-1","DOIUrl":null,"url":null,"abstract":"<p>The present article describes the precise structure of the <span>\\(L^{p}\\)</span>-spaces of projective limit measures by introducing a category-theoretical perspective. This analysis is applied to measures on vector spaces and in particular to Gaussian measures on nuclear topological vector spaces. A simple application to constructive quantum field theory (QFT) is given through the Osterwalder–Schrader axioms.</p>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-04-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On the $$L^{p}$$ -Spaces of Projective Limits of Probability Measures\",\"authors\":\"Juan Carlos Sampedro\",\"doi\":\"10.1007/s10959-024-01329-1\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>The present article describes the precise structure of the <span>\\\\(L^{p}\\\\)</span>-spaces of projective limit measures by introducing a category-theoretical perspective. This analysis is applied to measures on vector spaces and in particular to Gaussian measures on nuclear topological vector spaces. A simple application to constructive quantum field theory (QFT) is given through the Osterwalder–Schrader axioms.</p>\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2024-04-20\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s10959-024-01329-1\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s10959-024-01329-1","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
On the $$L^{p}$$ -Spaces of Projective Limits of Probability Measures
The present article describes the precise structure of the \(L^{p}\)-spaces of projective limit measures by introducing a category-theoretical perspective. This analysis is applied to measures on vector spaces and in particular to Gaussian measures on nuclear topological vector spaces. A simple application to constructive quantum field theory (QFT) is given through the Osterwalder–Schrader axioms.
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