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1998 | 158 | 2 | 109-124
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Decomposition of group-valued measures on orthoalgebras

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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.
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  • Département de mathématiques et d'informatique, Université de Sherbrooke Sherbrooke, Québec J1K 2R1, Canada
  • Dipartimento di Matematica e Applicazioni, Università Federico II, Complesso Universitario Monte S. Angelo, I-80126 Napoli, Italy
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