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Filter, Wolfgang

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

Czech. Math. J. 42, No. 4, 635-648 (1992).
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.
Reviewer: B.Riečan (Bratislava)

Cited in 1 Review
Cited in 1 Document

MSC:

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

Keywords:

discrete representation spaces; dual spaces of Riesz subspaces of some spaces; \(\sigma\)-hypercomplete Riesz spaces

Citations:

Zbl 0803.46008
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\textit{W. Filter}, Czech. Math. J. 42, No. 4, 635--648 (1992; Zbl 0803.46009)
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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 · doi:10.2307/2048219
[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
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