Geodesic
Two extension theorems. Modular functions on complemented lattices
Czechoslovak Mathematical Journal, Tome 52 (2002) no. 1, pp. 55-74 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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 
@article{CMJ_2002_52_1_a6,
     author = {Weber, Hans},
     title = {Two extension theorems. {Modular} functions on complemented lattices},
     journal = {Czechoslovak Mathematical Journal},
     pages = {55--74},
     year = {2002},
     volume = {52},
     number = {1},
     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/