×

Representations of Riesz spaces as spaces of measures. II. (English) Zbl 0803.46009

The paper is a continuation of the preceding paper [cf. review above].The author studies discrete representation spaces and gives simple descriptions of the dual spaces of Riesz subspaces of some spaces. Also \(\sigma\)-hypercomplete Riesz spaces are introduced and investigated.

MSC:

46A40 Ordered topological linear spaces, vector lattices
46E27 Spaces of measures

Citations:

Zbl 0803.46008
PDF BibTeX XML Cite
Full Text: EuDML

References:

[1] Y. A. Abramovich: Remarkable points and \(X_{(N)}\)-spaces. Positive operators, Riesz spaces and economics, Proceedings of a conference at Caltech, April 16-20, 1990, to appear.
[2] C. D. Aliprantis and O. Burkinshaw: Locally solid Riesz spaces. Academic Press, New York-San Francisco-London, 1978. · Zbl 0402.46005
[3] C. Constantinescu: Duality in measure theory. LN in mathematics 796, Springer-Verlag, Berlin-Heidelberg-New York, 1980. · Zbl 0429.28009
[4] W. Filter: A note on Archimedean Riesz spaces and their extended order duals. Libertas Math. 6 (1986), 101-106. · Zbl 0612.46007
[5] W. Filter: Hypercomplete Riesz spaces. Atti Sem. Mat. Fis. Univ. Modena 38 (1990), 227-240. · Zbl 0716.46008
[6] W. Filter: Hypercompletions of Riesz spaces. Proc. Amer. Math. Soc. 109 (1990), 775-780. · Zbl 0716.46009
[7] W. Filter: Representations of Riesz spaces as spaces of measures I. Czechoslovak Math. J. 42(117) (1992), 415-432. · Zbl 0803.46008
[8] D. H. Fremlin: Topological Riesz spaces and measure theory. Cambridge Univ. Press, London-New York, 1974. · Zbl 0273.46035
[9] H. Hahn and A. Rosenthal: Set functions. The University of New Mexico Press, Albuquerque, 1948.
[10] A. C. Zaanen: Riesz spaces II. North-Holland Publ. Comp., Amsterdam-New York-London, . · Zbl 0519.46001
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.