Decomposition of group-valued measures on orthoalgebras
Fundamenta Mathematicae, Tome 158 (1998) no. 2, pp. 109-124
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
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.
@article{10_4064_fm_158_2_109_124,
author = {Paolo De Lucia and Pedro Morales},
title = {Decomposition of group-valued measures on orthoalgebras},
journal = {Fundamenta Mathematicae},
pages = {109--124},
publisher = {mathdoc},
volume = {158},
number = {2},
year = {1998},
doi = {10.4064/fm-158-2-109-124},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/fm-158-2-109-124/}
}
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Paolo De Lucia; Pedro Morales. Decomposition of group-valued measures on orthoalgebras. Fundamenta Mathematicae, Tome 158 (1998) no. 2, pp. 109-124. doi: 10.4064/fm-158-2-109-124
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