Decomposition of group-valued measures on orthoalgebras

• Autorzy: Paolo De Lucia , Pedro Morales
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 06F20: Ordered abelian groups, Riesz groups, ordered linear spaces
• 28B15: Set functions, measures and integrals with values in ordered spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 1998
• Tom: 158
• Numer: 2
• Strony: 109-124

Daty

wydano

1998

otrzymano

1997-01-20

poprawiono

1998-02-08

poprawiono

1998-04-27

Twórcy

autor

Paolo De Lucia

• Département de mathématiques et d'informatique, Université de Sherbrooke Sherbrooke, Québec J1K 2R1, Canada

autor

Pedro Morales

• Dipartimento di Matematica e Applicazioni, Università Federico II, Complesso Universitario Monte S. Angelo, I-80126 Napoli, Italy

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