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A note on extensions of asymptotic density

Author(s): A. Blass; R. Frankiewicz; G. Plebanek; C. Ryll-Nardzewski
Journal: Proc. Amer. Math. Soc. 129 (2001), 3313-3320.
MSC (2000): Primary 28A12; Secondary 03E05, 03E35, 11B05
Posted: April 9, 2001
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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 Wroclaw, pl. Grunwaldzki 2/4, 50--218 Wroclaw, Poland
Email: grzes@math.uni.wroc.pl

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

DOI: 10.1090/S0002-9939-01-05941-X
PII: S 0002-9939(01)05941-X
Received by editor(s): June 29, 1999
Received by editor(s) in revised form: March 17, 2000
Posted: 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
Copyright of article: Copyright 2001, American Mathematical Society

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