The Connections Between Consistent Maps and Measures

Lucas Aberg, Charles L. Samuels
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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.
一致的地图与措施之间的联系
让 Y 表示阿科克和瓦勒 2009 年的一篇文章中所定义的有理代数闭包的位置空间。 作为某些对偶空间分类工作的一部分,第二作者定义了一个称为一致映射的对象。Y 上的每一个有符号伯勒度量都可以用来构造一致映射,然而,我们未经证明就断言,并非所有一致映射都是这样产生的。在本文中,我们通过构建一个反例,证明了并非所有一致映射都是由度量产生的,从而证实了第二位作者早期工作中的说法。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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