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The Orlicz-Pettis theorem for topological Riesz spaces |
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| Authors: | Lech Drewnowski Iwo Labuda |
| Affiliation: | Faculty of Mathematics and Computer Science, A.~ Mickiewicz University, Matejki 48/49, 60--769 Poznan, Poland ; Department of Mathematics, University of Mississippi, University, Mississippi 38677 |
| Abstract: | A finitely additive vector measure from a  -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. |
| Keywords: | Subseries convergence countably additive vector measure exhaustive vector measure topological Riesz space Lebesgue topology |
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