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

Bounded common extensions of charges


Authors: A. Basile, K. P. S. Bhaskara Rao and R. M. Shortt
Journal: Proc. Amer. Math. Soc. 121 (1994), 137-143
MSC: Primary 28A12
MathSciNet review: 1176064
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Abstract: Let $ \mathcal{A}$ and $ \mathcal{B}$ be fields of subsets of a set X and let $ \mu :\mathcal{A} \to {\mathbf{R}}$ and $ \nu :\mathcal{B} \to {\mathbf{R}}$ be consistent, bounded, finitely additive measures (i.e., charges). We give necessary and sufficient conditions for $ \mu $ and $ \nu $ to have a bounded common extension to $ \mathcal{A} \vee \mathcal{B}$. Conditions on $ \mathcal{A}$ and $ \mathcal{B}$ are given under which any bounded consistent charges $ \mu $ and $ \nu $ have a bounded common extension.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1994-1176064-4
PII: S 0002-9939(1994)1176064-4
Keywords: Finitely additive measure, bounded charge, common extension problem
Article copyright: © Copyright 1994 American Mathematical Society