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1996/1997 Bounded common extensions of vector measures
E. D’Aniello, A. Hirshberg, K. P. S. Bhaskara Rao, R. M. Shortt
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Real Anal. Exchange 22(2): 766-774 (1996/1997).


Let \(\mathcal{A}\) and \(\mathcal{B}\) be fields of subsets of a set \({\Omega}\), let \({\bf X}\) be a normed space with the Hahn-Banach extension property and let \({\mu: {\mathcal A}\rightarrow {\bf X}}\) and \({\nu: {\mathcal B} \rightarrow {\bf X}}\) be consistent, bounded, vector measures. We give necessary and sufficient conditions for \({\mu}\) and \({\nu}\) to have a bounded common extension to \({{\mathcal A} \vee {\mathcal B}}\), generalizing already known results for real valued charges.


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E. D’Aniello. A. Hirshberg. K. P. S. Bhaskara Rao. R. M. Shortt. "Bounded common extensions of vector measures." Real Anal. Exchange 22 (2) 766 - 774, 1996/1997.


Published: 1996/1997
First available in Project Euclid: 22 May 2012

zbMATH: 0941.28012
MathSciNet: MR1460987

Primary: 28B99
Secondary: 26B05

Keywords: bounded vector measure , common extension , Finitely additive vector measure

Rights: Copyright © 1996 Michigan State University Press

Vol.22 • No. 2 • 1996/1997
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