Decomposition of group-valued measures on orthoalgebras

Paolo De Lucia; Pedro Morales

Fundamenta Mathematicae (1998)

  • Volume: 158, Issue: 2, page 109-124
  • ISSN: 0016-2736

Abstract

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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.

How to cite

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De Lucia, Paolo, and Morales, Pedro. "Decomposition of group-valued measures on orthoalgebras." Fundamenta Mathematicae 158.2 (1998): 109-124. <http://eudml.org/doc/212306>.

@article{DeLucia1998,
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.},
author = {De Lucia, Paolo, Morales, Pedro},
journal = {Fundamenta Mathematicae},
keywords = {group-valued measures; orthoalgebra; orthomodular posets; decomposition},
language = {eng},
number = {2},
pages = {109-124},
title = {Decomposition of group-valued measures on orthoalgebras},
url = {http://eudml.org/doc/212306},
volume = {158},
year = {1998},
}

TY - JOUR
AU - De Lucia, Paolo
AU - Morales, Pedro
TI - Decomposition of group-valued measures on orthoalgebras
JO - Fundamenta Mathematicae
PY - 1998
VL - 158
IS - 2
SP - 109
EP - 124
AB - 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.
LA - eng
KW - group-valued measures; orthoalgebra; orthomodular posets; decomposition
UR - http://eudml.org/doc/212306
ER -

References

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