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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

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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