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Some properties of spaces of measures. (English) Zbl 0696.46027
Atti del Seminario Matematico e Fisico dell’Universit√† di Modena, Vol. 35. Supplemento. Modena: Universit√† di Modena, Dipartimento di matematica Pura e Applicata “G. Vitali”. II, 286 p. (1989).
The main idea of this paper consists in a systematical use of the analogy between the theory of vector lattices and the theory of spaces of measures. To get theorems, which contain as special cases results for set functions as well as for maps defined on \(\ell\)-groups (in particular on vector lattices) the author studies maps on a structure inroduced by K. D. Schmidt [Compos. Math. 54, 51-62 (1985; Zbl 0561.06010)], for which Boolean rings and \(\ell\)-groups are special examples. In this abstract frame work the following properties are examined: the Nikodym- Darst property, the Nikodym-Brooks-Jewitt property, the Orlicz-Pettis property, the Grothendieck property, the Phillips property and the Vitali-Hahn-Saks property.
Reviewer: H.Weber

MSC:
46E27 Spaces of measures
46-02 Research exposition (monographs, survey articles) pertaining to functional analysis
28A33 Spaces of measures, convergence of measures
46A40 Ordered topological linear spaces, vector lattices
06F20 Ordered abelian groups, Riesz groups, ordered linear spaces