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Decomposition of effect algebras and the Hammer-Sobczyk theorem. (English) Zbl 1171.28004

The Hammer-Sobczyk theorem states that every \([0,\infty[\)-valued finitely additive measure \(\mu\) on a Boolean algebra can be expressed as the (at most countable) sum \(\mu=\mu_0+\Sigma\mu_i\) of measures such that \(\mu_0\) is continuous and \(\mu_i\) are two-valued. In the paper the theorem is proved for exhaustive modular measures on D-lattices.

MSC:

28B10 Group- or semigroup-valued set functions, measures and integrals
28A60 Measures on Boolean rings, measure algebras
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