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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.

References [Enhancements On Off] (What's this?)

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Keywords: Finitely additive measure, bounded charge, common extension problem
Article copyright: © Copyright 1994 American Mathematical Society