We prove a Hahn decomposition theorem for σ-additive modular measures on σ-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 non-atomic modular measures with values in Banach spaces
Hahn decomposition of modular measures and applications
AVALLONE, Anna;VITOLO, Paolo
2003-01-01
Abstract
We prove a Hahn decomposition theorem for σ-additive modular measures on σ-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 non-atomic modular measures with values in Banach spacesFile in questo prodotto:
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