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Bounded vector measures on effect algebras

Published online by Cambridge University Press:  17 April 2009

Hong Taek Hwang ,
Longlu Li  and
Hunnam Kim
Hong Taek Hwang
Affiliation:
Department of Applied Mathematics, Kumoh National Institute of Technology, Gumi, Gyeongbuk 730 701, South Korea email: mathvision@hotmail.com
Longlu Li
Affiliation:
Department of Mathematics, Harbin Institute of Technology, China
Hunnam Kim
Affiliation:
Department of Applied Mathematics, Kumob National Institute of Technology, Gyeongbuk Foreign Language High School, South Korea
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Let (L, ⊥, ⊕,0,1) be an effect algebra and X a locally convex space with dual X′. A function μ: L → X is called a measure if μ(a ⊕ b) = μ(a) + μ(b) whenever a⊥b in L and it is bounded if 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.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 72 , Issue 2 , October 2005 , pp. 291 - 298
Copyright
Copyright © Australian Mathematical Society 2005

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