Czechoslovak Mathematical Journal, Vol. 59, No. 3, pp. 707-719, 2009

An extension theorem for modular measures on effect algebras

Giuseppina Barbieri

Giuseppina Barbieri, Dipartimento di Matematica e Informatica, Universita di Udine, Via delle Scienze 206, 33100 Udine, Italy, e-mail: giuseppina.barbieri@dimi.uniud.it

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, Nikodym theorems and range theorems to this setting.

Keywords: effect algebras, modular measures, extension, Vitali-Hahn-Saks theorem, Nikodym theorem, decomposition theorem, control theorems, range, Liapunoff theorem

Classification (MSC 2000): 06C15, 28E99


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