An extension theorem for modular measures on effect algebras

Giuseppina Barbieri

Czechoslovak Mathematical Journal (2009)

  • Volume: 59, Issue: 3, page 707-719
  • ISSN: 0011-4642

Abstract

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We prove an extension theorem for modular measures on lattice ordered effect algebras. This is used to obtain a representation of these measures by the classical ones. With the aid of this theorem we transfer control theorems, Vitali-Hahn-Saks, Nikodým theorems and range theorems to this setting.

How to cite

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Barbieri, Giuseppina. "An extension theorem for modular measures on effect algebras." Czechoslovak Mathematical Journal 59.3 (2009): 707-719. <http://eudml.org/doc/37953>.

@article{Barbieri2009,
abstract = {We prove an extension theorem for modular measures on lattice ordered effect algebras. This is used to obtain a representation of these measures by the classical ones. With the aid of this theorem we transfer control theorems, Vitali-Hahn-Saks, Nikodým theorems and range theorems to this setting.},
author = {Barbieri, Giuseppina},
journal = {Czechoslovak Mathematical Journal},
keywords = {effect algebras; modular measures; extension; Vitali-Hahn-Saks theorem; Nikodým theorem; decomposition theorem; control theorems; range; Liapunoff theorem; effect algebra; modular measure; Vitali-Hahn-Saks theorem; Nikodým theorem; decomposition theorem; control theorem; Lyapunov theorem},
language = {eng},
number = {3},
pages = {707-719},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {An extension theorem for modular measures on effect algebras},
url = {http://eudml.org/doc/37953},
volume = {59},
year = {2009},
}

TY - JOUR
AU - Barbieri, Giuseppina
TI - An extension theorem for modular measures on effect algebras
JO - Czechoslovak Mathematical Journal
PY - 2009
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 59
IS - 3
SP - 707
EP - 719
AB - We prove an extension theorem for modular measures on lattice ordered effect algebras. This is used to obtain a representation of these measures by the classical ones. With the aid of this theorem we transfer control theorems, Vitali-Hahn-Saks, Nikodým theorems and range theorems to this setting.
LA - eng
KW - effect algebras; modular measures; extension; Vitali-Hahn-Saks theorem; Nikodým theorem; decomposition theorem; control theorems; range; Liapunoff theorem; effect algebra; modular measure; Vitali-Hahn-Saks theorem; Nikodým theorem; decomposition theorem; control theorem; Lyapunov theorem
UR - http://eudml.org/doc/37953
ER -

References

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