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Proceedings of the American Mathematical Society

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The Lebesgue decomposition theorem for partially ordered semigroup-valued measures

Author: Panaiotis K. Pavlakos
Journal: Proc. Amer. Math. Soc. 71 (1978), 207-211
MSC: Primary 46G10; Secondary 28A55
MathSciNet review: 0487449
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Abstract: The present paper is concerned with partially ordered semigroup-valued measures. Below are given generalizations of the classical Lebesgue Decomposition Theorem.

These results can be applied to Stone or $ {W^ \ast }$ algebra-valued positive measures (cf. [3], [12], [13], [14]).

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Keywords: Partially ordered semigroup, monotone complete partially ordered semigroup, partially ordered semigroup of the countable type, o-measure, absolutely continuous and singular o-measure, partially ordered topological semigroup, $ \sigma $-compatible topology with the partial ordering, $ {\tau _X}$-measure
Article copyright: © Copyright 1978 American Mathematical Society