On the modulus of measures with values in topological Riesz spaces.
Measures from an algebra into a topological Riesz space are studied with particular concern for the existence of the modulus for a given measure. The authors demonstrate, for example, a countably additive measure to the Banach lattice \textit{c} with no modulus, in fact, no absolute majorant. An extensive analysis of properties of the measure versus properties of the majorant is presented. These include extensions of known results; for example, conditions ensuring that the modulus of a countably additive measure is also countably additive. Interesting constructions are provided for spaces with a measure which is a countably additive with the property that the modulus exists but is not countably additive. Consequences for operators and the modulus of an operator are considered utilizing a condition related to weakly compact. To cite one example, it is established that for a Banach lattice \(E\) with appropriate properties, if an order bounded weakly compact operator from the space of bounded measurable functions to \(E\) has a modulus (exists properly), then \(| T| \) is also weakly compact.
scientific article; zbMATH DE number 1908110