Geodesic
Two extension theorems. Modular functions on complemented lattices
Czechoslovak Mathematical Journal, Tome 52 (2002) no. 1, pp. 55-74.

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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.
Classification : 06B30, 06C15, 28E99
Keywords: complemented lattices; orthomodular lattices; exhaustive modular functions; measures; extension; Vitali-Hahn-Saks theorem; Nikodým theorems; Liapunoff theorem 
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     author = {Weber, Hans},
     title = {Two extension theorems. {Modular} functions on complemented lattices},
     journal = {Czechoslovak Mathematical Journal},
     pages = {55--74},
     publisher = {mathdoc},
     volume = {52},
     number = {1},
     year = {2002},
     mrnumber = {1885457},
     zbl = {0998.06006},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2002__52_1_a6/}
}
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Weber, Hans. Two extension theorems. Modular functions on complemented lattices. Czechoslovak Mathematical Journal, Tome 52 (2002) no. 1, pp. 55-74. http://geodesic.mathdoc.fr/item/CMJ_2002__52_1_a6/