Continuous lattice effect algebras admitting order-continuous states
Lattice effect algebras give a common generalization of orthomodular lattices and MV-algebras. This paper gives a necessary and sufficient condition for the existence of a faithful order-continuous state on a complete modular atomic effect algebra. By generalizing \textit{I. Kaplansky}'s famous theorem [Ann. Math. (2) 61, 524-541 (1955; Zbl 0065.01801)] that every complete modular ortholattice is order-continuous, the author shows that every complete modular atomic effect algebra is order-continuous.
scientific article; zbMATH DE number 1917787