It is well known that every locally compact group admits a (one sided) translation invariant Haar measure. Applications of the Haar measure in algebraic number theory to local fields and adelic groups appear in [Cassels-Fröhlich, Chap. II] and [Weil6]. Here we use it to investigate absolute Galois groups of fields. Since these groups are compact, the Haar measure is a two sided invariant. We provide a simple direct proof of the existence and uniqueness of the Haar measure of profinite groups (Sections 18.1 and 18.2).
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
(2008). The Haar Measure. In: Field Arithmetic. Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics, vol 11. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-77270-5_18
Download citation
DOI: https://doi.org/10.1007/978-3-540-77270-5_18
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-77269-9
Online ISBN: 978-3-540-77270-5
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)