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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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