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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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Regular and purely irregular bounded charges: a decomposition theorem
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by Bruno Girotto and Silvano Holzer PDF
Proc. Amer. Math. Soc. 116 (1992), 683-693 Request permission

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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Additional Information
  • © Copyright 1992 American Mathematical Society
  • 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