A survey of decomposition and convergence theorems for \(l\)-group-valued measures. (English) Zbl 1121.28017
This paper is a survey on decompositions of \(\sigma\)-additive measures and convergence theorems for measures taking values in \(l\)-groups. The contribution of the authors lies mainly on new results relating the Stone extension of a measure to its Yosida-Hewitt decomposition. In order to obtain these results, the authors employ the \(\sigma\)-ideal principle and the Stone Isomorphism technique rather than the construction of the Rickart integral.
Reviewer: Marcia Federson (São Paulo)
MSC:
28B15 | Set functions, measures and integrals with values in ordered spaces |
28B10 | Group- or semigroup-valued set functions, measures and integrals |
46G10 | Vector-valued measures and integration |