Two extension theorems. Modular functions on complemented lattices

Title:

Two extension theorems. Modular functions on complemented lattices

Creator:

Weber, Hans

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:30ef65a9-af18-4ad5-bb1d-d56aef0b78a7
uuid:30ef65a9-af18-4ad5-bb1d-d56aef0b78a7

Subject:

complemented lattices, orthomodular lattices, exhaustive modular functions, measures, extension, Vitali-Hahn-Saks theorem, Nikodým theorems, and Liapunoff theorem

Type:

model:article and TEXT

Format:

bez média and svazek

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.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

55-74

Source:

Czechoslovak Mathematical Journal | 2002 Volume:52 | Number:1

Harvested from:

CDK

Metadata only:

false