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A note on extensions of asymptotic density


Authors: A. Blass, R. Frankiewicz, G. Plebanek and C. Ryll-Nardzewski
Journal: Proc. Amer. Math. Soc. 129 (2001), 3313-3320
MSC (2000): Primary 28A12; Secondary 03E05, 03E35, 11B05
DOI: https://doi.org/10.1090/S0002-9939-01-05941-X
Published electronically: April 9, 2001
MathSciNet review: 1845008
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Abstract | References | Similar Articles | Additional Information

Abstract:

By a density we mean any extension of the asymptotic density to a finitely additive measure defined on all sets of natural numbers. We consider densities associated to ultrafilters on $\omega$ and investigate two additivity properties of such densities. In particular, we show that there is a density $\nu$ for which $L_{1}(\nu)$ is complete.


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Additional Information

A. Blass
Affiliation: Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109-1109
Email: ablass@math.lsa.umich.edu

R. Frankiewicz
Affiliation: Institute of Mathematics, Polish Academy of Sciences, 00-950 Warsaw, Poland
Email: rf@impan.gov.pl

G. Plebanek
Affiliation: Institute of Mathematics, University of Wrocław, pl. Grunwaldzki 2/4, 50–218 Wrocław, Poland
Email: grzes@math.uni.wroc.pl

C. Ryll-Nardzewski
Affiliation: Institute of Mathematics, Wrocław Technical University and Institute of Mathematics, Polish Academy of Sciences, 51-617 Wrocław, Poland
Email: crn@graf.im.pwr.wroc.pl

DOI: https://doi.org/10.1090/S0002-9939-01-05941-X
Received by editor(s): June 29, 1999
Received by editor(s) in revised form: March 17, 2000
Published electronically: April 9, 2001
Additional Notes: The first-named author was partially supported by NSF grant DMS–9505118
The other authors were partially supported by KBN grant 2P03A 018 13.
Communicated by: Dale Alspach
Article copyright: © Copyright 2001 American Mathematical Society

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