Geodesic
Discrete Copies of Rings of Sets in Groups and Orlicz-Pettis Theorems
Canadian journal of mathematics, Tome 30 (1978) no. 4, pp. 748-755

Voir la notice de l'article provenant de la source Cambridge University Press

The Orlicz-Pettis type theorems are essentially statements about the equivalence of strong and weak subseries convergence of series in topological groups. The corresponding problem of the equivalence of subfamily summability for summable families was examined for instance in [2] and (16). We give here another uncountable generalization of the Orlicz-Pettis theorem in the sense that we assume less than subfamily summability and obtain straightforward generalizations of the classical case, which include or imply in a trivial manner—at least for polar topologies on groups—all known theorems “from weak to strong σ-additivity”. 
Labuda, Iwo. Discrete Copies of Rings of Sets in Groups and Orlicz-Pettis Theorems. Canadian journal of mathematics, Tome 30 (1978) no. 4, pp. 748-755. doi: 10.4153/CJM-1978-064-0
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