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Proceedings of the American Mathematical Society

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ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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.
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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