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

Abstract

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.

Authors

  • Paolo De Lucia
  • Pedro Morales

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