Two extension theorems. Modular functions on complemented lattices

Hans Weber

Czechoslovak Mathematical Journal (2002)

  • Volume: 52, Issue: 1, page 55-74
  • ISSN: 0011-4642

Abstract

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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.

How to cite

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Weber, Hans. "Two extension theorems. Modular functions on complemented lattices." Czechoslovak Mathematical Journal 52.1 (2002): 55-74. <http://eudml.org/doc/30685>.

@article{Weber2002,
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.},
author = {Weber, Hans},
journal = {Czechoslovak Mathematical Journal},
keywords = {complemented lattices; orthomodular lattices; exhaustive modular functions; measures; extension; Vitali-Hahn-Saks theorem; Nikodým theorems; Liapunoff theorem; complemented lattices; orthomodular lattices; exhaustive modular functions; measures; extension; Vitali-Hahn-Saks theorem; Nikodým theorems; Lyapunov theorem},
language = {eng},
number = {1},
pages = {55-74},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Two extension theorems. Modular functions on complemented lattices},
url = {http://eudml.org/doc/30685},
volume = {52},
year = {2002},
}

TY - JOUR
AU - Weber, Hans
TI - Two extension theorems. Modular functions on complemented lattices
JO - Czechoslovak Mathematical Journal
PY - 2002
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 52
IS - 1
SP - 55
EP - 74
AB - 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.
LA - eng
KW - complemented lattices; orthomodular lattices; exhaustive modular functions; measures; extension; Vitali-Hahn-Saks theorem; Nikodým theorems; Liapunoff theorem; complemented lattices; orthomodular lattices; exhaustive modular functions; measures; extension; Vitali-Hahn-Saks theorem; Nikodým theorems; Lyapunov theorem
UR - http://eudml.org/doc/30685
ER -

References

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