Decomposition of effect algebras and the Hammer-Sobczyk theorem
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.
scientific article; zbMATH DE number 5547243