Abstract
We show that a finite orthomodular poset with a strong section Δ of states (probability measures) is distributive if and only if Δ has the unique Jordan-Hahn decomposition property(UJHDP). That this result does not extend to infinite orthomodular posets is shown by the projection lattices of von Neumann algebras without direct summand of typeI2, for which the set of completely additive states is strong and has theUJHDP. There also exist nondistributive σ-classes for which the set of countably additive states has theUJHDP.
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