## A note on extensions of asymptotic density

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- by A. Blass, R. Frankiewicz, G. Plebanek and C. Ryll–Nardzewski PDF
- Proc. Amer. Math. Soc.
**129**(2001), 3313-3320 Request permission

## 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.## References

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## Additional Information

**A. Blass**- Affiliation: Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109-1109
- MR Author ID: 37805
- 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
- MR Author ID: 239421
- 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
- 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
- © Copyright 2001 American Mathematical Society
- 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
- MathSciNet review: 1845008