Bull. Austral. Math. Soc. 72(2) pp.291--298, 2005.

Bounded vector measures on effect algebras

Hong Taek Hwang

Longlu Li

Hunnam Kim

Received: 4th May, 2005

This paper was supported by Kumoh National Institute of Technology.


Let (L,$ \bot $, $ \oplus $ , 0, 1) be an effect algebra and X a locally convex space with dual X$\scriptstyle \prime $. A function $ \mu $ : L $ \rightarrow $ X is called a measure if $ \mu $(a $ \oplus $ b) = $ \mu $(a) + $ \mu $(b) whenever a$ \bot $b in L and it is bounded if $ \bigl \{$$ \mu $(an)$ \bigr \}_{{n=1}}^{{\infty }}$ is bounded for each orthogonal sequence {an} in L. We establish five useful conditions that are equivalent to boundedness for vector measures on effect algebras.

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(Metadata: XML, RSS, BibTeX) MathSciNet: MR2183410 Z'blatt-MATH: 02246391


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