1. Two extension theorems. Modular functions on complemented lattices
- Creator:
- Weber, Hans
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- complemented lattices, orthomodular lattices, exhaustive modular functions, measures, extension, Vitali-Hahn-Saks theorem, Nikodým theorems, and Liapunoff theorem
- Language:
- English
- Description:
- 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.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public