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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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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The Orlicz-Pettis theorem for topological Riesz spaces
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by Lech Drewnowski and Iwo Labuda PDF
Proc. Amer. Math. Soc. 126 (1998), 823-825 Request permission

Abstract:

A finitely additive vector measure from a $\sigma$-ring to a Riesz space is countably additive (exhaustive) for all Hausdorff Lebesgue topologies on the range space, or for none of them. In particular, subseries convergent series are the same for all Hausdorff Lebesgue topologies on a Riesz space.
References
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Additional Information
  • Lech Drewnowski
  • Affiliation: Faculty of Mathematics and Computer Science, A.  Mickiewicz University, Matejki 48/49, 60–769 Poznań, Poland
  • Email: drewlech@math.amu.edu.pl
  • Iwo Labuda
  • Affiliation: Department of Mathematics, University of Mississippi, University, Mississippi 38677
  • Email: mmlabuda@vm.cc.olemiss.edu
  • Received by editor(s): April 16, 1996
  • Received by editor(s) in revised form: September 9, 1996
  • Additional Notes: The paper was written while the first author held a visiting position in the Department of Mathematics, University of Mississippi, in the Spring Semester of 1996. He was also partially supported by the State Committee for Scientific Research (Poland), grant no 2 P301 003 07
  • Communicated by: Dale Alspach
  • © Copyright 1998 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 126 (1998), 823-825
  • MSC (1991): Primary 40A99, 46A40
  • DOI: https://doi.org/10.1090/S0002-9939-98-04107-0
  • MathSciNet review: 1422864