The Connections Between Consistent Maps and Measures

Keywords: consistent maps; measures; Weil height

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.

Published
2024-02-09
How to Cite
Aberg, L., & Samuels, C. L. (2024). The Connections Between Consistent Maps and Measures. The PUMP Journal of Undergraduate Research, 7, 60-78. https://doi.org/10.46787/pump.v7i0.4030