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Hahn decomposition of modular measures and applications

Avallone A., Barbieri G., Vitolo P.

Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae

2003

[Z] 43(2)

149-168

We prove a Hahn decomposition theorem for [ro]-additive modular measures on [ro]-complete lattice ordered effect algebras. As a consequence, we establish an isomorphism between the space of all bounded real-valued modular measures on a such structure and the space of all completely additive measures on a suitable Boolean algebra. Another consequence is a Uhl type theorem concerning relative compactness and convexity of the range of nonatomic modular measures with values in Banach spaces.