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Keywords:
effect algebras; modular measures; extension; Vitali-Hahn-Saks theorem; Nikodým theorem; decomposition theorem; control theorems; range; Liapunoff theorem
effect algebras; modular measures; extension; Vitali-Hahn-Saks theorem; Nikodým theorem; decomposition theorem; control theorems; range; Liapunoff theorem
Summary:
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.
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