Hostname: page-component-cd9895bd7-8ctnn Total loading time: 0 Render date: 2024-12-22T20:04:12.575Z Has data issue: false hasContentIssue false

Invariant measures on groups satisfying various chain conditions

Published online by Cambridge University Press:  12 March 2014

Lou van den Dries
Affiliation:
University of Illinois at Urbana-Champaign, 1409 West Green Street, Urbana, Il 61801, USA, E-mail: [email protected]
Vinicius Cifú Lopes
Affiliation:
University of Illinois at Urbana-Champaign, 1409 West Green Street, Urbana, Il 61801, USA, E-mail: [email protected]

Abstract

For any group satisfying a suitable chain condition, we construct a finitely additive measure on it that is invariant under certain actions.

Type
Research Article
Copyright
Copyright © Association for Symbolic Logic 2011

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1]van den Dries, L. and Vinicius, C. L., Division rings whose vector spaces are pseudofinite, this Journal, vol. 75 (2010), no. 2, pp. 10871090.Google Scholar
[2]Groemer, H., On the extension of additive functionals on classes of convex sets, Pacific Journal of Mathematics, vol. 75 (1978), pp. 397410.CrossRefGoogle Scholar
[3]Hodges, W., Model theory, Encyclopedia of Mathematics and its Applications, vol. 42, Cambridge University Press, Cambridge, 1993, xiv + 772 pp.CrossRefGoogle Scholar
[4]Vinicius, C. L., Grothendieck semirings and definable endofunctions, Ph.D. thesis, University of Illinois at Urbana-Champaign, 2009.Google Scholar
[5]Vinicius, C. L., Euler characteristics for strongly minimal groups and the eq-expansions of vector spaces, this Journal, vol. 76 (2011), no. 1, pp. 235242.Google Scholar
[6]Ziegler, M., Model theory of modules, Annals of Pure and Applied Logic, vol. 26 (1984), pp. 149213.CrossRefGoogle Scholar