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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The Orlicz-Pettis theorem
for topological Riesz spaces


Authors: Lech Drewnowski and Iwo Labuda
Journal: Proc. Amer. Math. Soc. 126 (1998), 823-825
MSC (1991): Primary 40A99, 46A40
MathSciNet review: 1422864
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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.


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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

DOI: http://dx.doi.org/10.1090/S0002-9939-98-04107-0
PII: S 0002-9939(98)04107-0
Keywords: Subseries convergence, countably additive vector measure, exhaustive vector measure, topological Riesz space, Lebesgue topology
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
Article copyright: © Copyright 1998 American Mathematical Society