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Proceedings of the American Mathematical Society

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

 

 

Regular and purely irregular bounded charges: a decomposition theorem


Authors: Bruno Girotto and Silvano Holzer
Journal: Proc. Amer. Math. Soc. 116 (1992), 683-693
MSC: Primary 28C15; Secondary 60B05
DOI: https://doi.org/10.1090/S0002-9939-1992-1099340-0
MathSciNet review: 1099340
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Abstract: We introduce the notions of regular and purely irregular charges with respect to a pair of pavings and study their structural properties. Moreover, we link regularity and $ \sigma $-additivity, obtaining some generalizations of well-known theorems. Finally, when the pavings satisfy some reasonable weak conditions, we can decompose any bounded charge into regular and purely irregular decomposants; this decomposition becomes the Hewitt-Yosida one, whenever the charges are defined on the Baire $ \sigma $-field of a countably compact space.


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DOI: https://doi.org/10.1090/S0002-9939-1992-1099340-0
Keywords: Normal subspace decomposition, normal decomposition of a bounded charge, paving, regular and purely irregular charges, $ \sigma $-compact set system, Baire and Borel sets
Article copyright: © Copyright 1992 American Mathematical Society