Kybernetika 40 no. 4, 459-468, 2004

Modular atomic effect algebras and the existence of subadditive states

Zdenka Riečanová


Lattice effect algebras generalize orthomodular lattices and MV-algebras. We describe all complete modular atomic effect algebras. This allows us to prove the existence of order-continuous subadditive states (probabilities) on them. For the separable noncomplete ones we show that the existence of a faithful probability is equivalent to the condition that their MacNeille completion is a complete modular effect algebra.