Decomposition of group-valued measures on orthoalgebras
Tom 158 / 1998
Fundamenta Mathematicae 158 (1998), 109-124 DOI: 10.4064/fm-158-2-109-124
We present a general decomposition theorem for a positive inner regular finitely additive measure on an orthoalgebra $L$ with values in an ordered topological group $G$, not necessarily commutative. In the case where L is a Boolean algebra, we establish the uniqueness of such a decomposition. With mild extra hypotheses on $G$, we extend this Boolean decomposition, preserving the uniqueness, to the case where the measure is order bounded instead of being positive. This last result generalizes A. D. Aleksandrov's classical decomposition theorem.