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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

Lattice-valued Borel measures. II

Author: Surjit Singh Khurana
Journal: Trans. Amer. Math. Soc. 235 (1978), 205-211
MSC: Primary 28A55
MathSciNet review: 0460590
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Abstract: Let T be a completely regular Hausdorff space, $ {C_b}(T)$ the set of all bounded real-valued continuous functions on T, E a boundedly monotone complete ordered vector space, and $ \varphi :{C_b}(T) \to E$ a positive linear map. It is proved that under certain conditions there exist $ \sigma $-additive, $ \tau $-smooth or tight E-valued measures on T which represent $ \varphi $.

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PII: S 0002-9947(1978)0460590-2
Keywords: $ \tau $-smooth measures, tight measures, weakly $ \sigma $-distributive lattices, monotone order $ \sigma $-continuous, order $ \sigma $-continuous, monotone order $ \sigma $-closed, order $ \sigma $-closed
Article copyright: © Copyright 1978 American Mathematical Society