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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Weber, H. Two extension theorems. Modular functions on complemented lattices. Czechoslovak Mathematical Journal 52, 55–74 (2002). https://doi.org/10.1023/A:1021719320528
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DOI: https://doi.org/10.1023/A:1021719320528