Two properties of sequence of vector measures on effect algebras |
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Authors: | Qing-shui Lin Rong-lu Li |
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Institution: | Department of Mathematics, Harbin Institute of Technology, Harbin 150006, China |
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Abstract: | Let (L,⊕, 0, 1) be an effect algebra and let X be a Banach space. A function μ: L → X is called a vector measure if μ(a⊕b) = μ(a)+μ(b) whenever a?b in L. The function μ is said to be s-bounded if lim $
\mathop {\lim }\limits_{n \to \infty } \mu (a_n )
$
\mathop {\lim }\limits_{n \to \infty } \mu (a_n )
= 0 in X for any orthogonal sequence (a
n
)
n∈? in L. In this paper, we introduce two properties of sequence of s-bounded vector measures and give some results on these properties. |
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Keywords: | Effect algebra s-bounded vector measure |
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