We prove that every closed exhaustive vector-valued modular measure on a lattice ordered effect algebra L can be decomposed into the sum of a Lyapunov exhaustive modular measure (i.e. its restriction to every interval of L has convex range) and an ”anti-Lyapunov” exhaustive modular measure. This result extends a Kluvanek-Knowles decomposition theorem for measures on Boolean algebras
Lyapunov decomposition of measures on effect algebras
AVALLONE, Anna;VITOLO, Paolo
2009-01-01
Abstract
We prove that every closed exhaustive vector-valued modular measure on a lattice ordered effect algebra L can be decomposed into the sum of a Lyapunov exhaustive modular measure (i.e. its restriction to every interval of L has convex range) and an ”anti-Lyapunov” exhaustive modular measure. This result extends a Kluvanek-Knowles decomposition theorem for measures on Boolean algebrasFile in questo prodotto:
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