Decomposition of group-valued measures on orthoalgebras

Volume 158 / 1998

Paolo De Lucia, Pedro Morales 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.


  • Paolo De Lucia
  • Pedro Morales

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