Continuity and linear extensions of quantum measures on Jordan operator algebras.

Let M be a W * -algebra on a JBW-algebra. A (finitely additive) quantum measure on M is a non-negative real valued function μ on the projections on M which satisfies the property μ(p 1 +...p n )=μ(p 1 )+...+μ(p n ), μ(1)=1 whenever p 1 ,...,p n are orthogonal projections of M