Two extension theorems. Modular functions on complemented lattices |
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Authors: | Hans Weber |
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Institution: | (1) Dipartimento di Matematica e Informatica, Università degli Studi di Udine, via delle Scienze, 206, I-33100 Udine |
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Abstract: | We prove an extension theorem for modular functions on arbitrary lattices and an extension theorem for measures on orthomodular lattices. The first is used to obtain a representation of modular vector-valued functions defined on complemented lattices by measures on Boolean algebras. With the aid of this representation theorem we transfer control measure theorems, Vitali-Hahn-Saks and Nikodým theorems and the Liapunoff theorem about the range of measures to the setting of modular functions on complemented lattices. |
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Keywords: | complemented lattices orthomodular lattices exhaustive modular functions measures extension Vitali-Hahn-Saks theorem Nikodý m theorems Liapunoff theorem |
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