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The approximate Jordan-Hahn decomposition. (English) Zbl 0699.28001
On an orthoalgebra L (a generalization of Boolean algebra and other structures), a convex set $$\Delta$$ of probability charges has the approximate Jordan-Hahn property provided that for every element $$\mu$$ of the linear span of $$\Delta$$, there exist elements $$\nu$$, $$\lambda$$ in $$\Delta$$ and non-negative scalars s, t such that $$\mu =s\nu -t\lambda,$$ and for all $$\epsilon >0$$, there exists $$a\in L$$ with $$(s\nu)(a)+(t\lambda)(a')<\epsilon.$$
Two necessary and sufficient conditions for a convex set of probability charges to have the approximate Jordan-Hahn property are developed and applied in various settings. The existence of an approximate Jordan-Hahn decomposition for a single charge on a Boolean algebra is presented as a corollary.
Reviewer: J.W.Hagood

##### MSC:
 28A12 Contents, measures, outer measures, capacities 28A33 Spaces of measures, convergence of measures 06F99 Ordered structures
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