{"title":"高维局部场上GL<i><sub>d </sub></i>","authors":"Masaoki MORI","doi":"10.2206/kyushujm.77.271","DOIUrl":null,"url":null,"abstract":"The aims of this paper are expansions of the measure theory in Fesenko (Amer. Math. Soc, Transl. Ser. 2 219 (2006)) and Waller (New York J. Math. 25 (2019), 396-442). We define countably additive translation-invariant measures and integrals on product spaces of F and of GLd(F), and on a parabolic subgroup of GLd(F). Moreover, we will prove that measurable functions on these product spaces are repeatedly integrable.","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"MEASURE THEORY ON GL<i><sub>d </sub></i>OVER A HIGHER-DIMENSIONAL LOCAL FIELD\",\"authors\":\"Masaoki MORI\",\"doi\":\"10.2206/kyushujm.77.271\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The aims of this paper are expansions of the measure theory in Fesenko (Amer. Math. Soc, Transl. Ser. 2 219 (2006)) and Waller (New York J. Math. 25 (2019), 396-442). We define countably additive translation-invariant measures and integrals on product spaces of F and of GLd(F), and on a parabolic subgroup of GLd(F). Moreover, we will prove that measurable functions on these product spaces are repeatedly integrable.\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2023-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.2206/kyushujm.77.271\",\"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":"1085","ListUrlMain":"https://doi.org/10.2206/kyushujm.77.271","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
本文的目的是对Fesenko (Amer)的测量理论进行扩展。数学。Soc, Transl。Ser. 2 219(2006))和Waller (New York J. Math. 25(2019)， 396-442)。定义了F和GLd(F)的积空间以及GLd(F)的抛物子群上的可数可加平移不变测度和积分。此外，我们将证明这些积空间上的可测函数是重复可积的。
MEASURE THEORY ON GL<i><sub>d </sub></i>OVER A HIGHER-DIMENSIONAL LOCAL FIELD
The aims of this paper are expansions of the measure theory in Fesenko (Amer. Math. Soc, Transl. Ser. 2 219 (2006)) and Waller (New York J. Math. 25 (2019), 396-442). We define countably additive translation-invariant measures and integrals on product spaces of F and of GLd(F), and on a parabolic subgroup of GLd(F). Moreover, we will prove that measurable functions on these product spaces are repeatedly integrable.
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