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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Fine asymptotic densities for sets of natural numbers


Author: Mauro Di Nasso
Journal: Proc. Amer. Math. Soc. 138 (2010), 2657-2665
MSC (2010): Primary 11B05, 03E05; Secondary 11R21
Published electronically: April 1, 2010
MathSciNet review: 2644882
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Abstract: By allowing values in non-Archimedean extensions of the unit interval, we consider finitely additive measures that generalize the asymptotic density. The existence of a natural class of such ``fine densities'' is independent of ZFC.


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Additional Information

Mauro Di Nasso
Affiliation: Dipartimento di Matematica, Università di Pisa, Pisa, Italy
Email: dinasso@dm.unipi.it

DOI: http://dx.doi.org/10.1090/S0002-9939-10-10351-7
PII: S 0002-9939(10)10351-7
Keywords: Asymptotic density, ultrafilter, non-Archimedean group
Received by editor(s): August 21, 2009
Received by editor(s) in revised form: October 10, 2009
Published electronically: April 1, 2010
Communicated by: Julia Knight
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.