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Measures and Charges on the Places of $\bar{\mathbb Q}$
- Publication Year :
- 2024
-
Abstract
- Recent work of the author established dual representation theorems for certain vector spaces that arise in an important article of Allcock and Vaaler. These results constructed an object called a consistent map which acts like a measure on the set of places of $\bar{\mathbb Q}$, but is not a Borel measure on this space. We describe the appropriate ring of sets $\mathcal R$ for which every consistent map arises from a measure on $\mathcal R$. We further obtain the conditions under which a consistent map may be extended to a measure on the smallest algebra containing $\mathcal R$.
- Subjects :
- Mathematics - Number Theory
11G50, 11R04, 28A05, 46B10
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2405.06519
- Document Type :
- Working Paper