Real Analysis Exchange

Bounded common extensions of vector measures

E. D’Aniello, A. Hirshberg, K. P. S. Bhaskara Rao, and R. M. Shortt

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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.

Article information

Real Anal. Exchange, Volume 22, Number 2 (1996), 766-774.

First available in Project Euclid: 22 May 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 28B99: None of the above, but in this section
Secondary: 26B05: Continuity and differentiation questions

Finitely additive vector measure bounded vector measure common extension


D’Aniello, E.; Hirshberg, A.; Rao, K. P. S. Bhaskara; Shortt, R. M. Bounded common extensions of vector measures. Real Anal. Exchange 22 (1996), no. 2, 766--774.

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