{"title":"The Connections Between Consistent Maps and Measures","authors":"Lucas Aberg, Charles L. Samuels","doi":"10.46787/pump.v7i0.4030","DOIUrl":null,"url":null,"abstract":"Let Y denote the space of places of the algebraic closure of the rationals as defined in a 2009 article of Allcock and Vaaler. As part of an effort to classify certain dual spaces, the second author defined an object called a consistent map. Every signed Borel measure on Y can be used to construct a consistent map, however, we asserted without proof that not all consistent maps arise in this way. By constructing a counterexample, we show in the present article that not all consistent maps arise from measures, confirming claims made in the second author's earlier work.","PeriodicalId":518794,"journal":{"name":"The PUMP Journal of Undergraduate Research","volume":"340 ","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-02-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"The PUMP Journal of Undergraduate Research","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.46787/pump.v7i0.4030","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
Let Y denote the space of places of the algebraic closure of the rationals as defined in a 2009 article of Allcock and Vaaler. As part of an effort to classify certain dual spaces, the second author defined an object called a consistent map. Every signed Borel measure on Y can be used to construct a consistent map, however, we asserted without proof that not all consistent maps arise in this way. By constructing a counterexample, we show in the present article that not all consistent maps arise from measures, confirming claims made in the second author's earlier work.