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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Hypercompletions of Riesz spaces


Author: Wolfgang Filter
Journal: Proc. Amer. Math. Soc. 109 (1990), 775-780
MSC: Primary 46A40; Secondary 46E27
MathSciNet review: 1021210
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Abstract: It is shown that each Riesz space with separating order continuous dual can be embedded in a unique " $ e$-hypercompletion," where $ e$ is a fixed weak unit of the extended order continuous dual.


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  • [1] W. D. L. Appling, Concerning a class of linear transformations, J. London Math. Soc. 44 (1969), 385-396. MR 0237734 (38:6015)
  • [2] -, An isomorphism and isometry theorem for a class of linear functional, Trans. Amer. Math. Soc. 199 (1974), 131-140. MR 0352385 (50:4872)
  • [3] W. C. Bell, A decomposition of additive set functions, Pacific J. Math. 72 (1977), 305-311. MR 0453952 (56:12205)
  • [4] -, Approximate Hahn decompositions, uniform absolute continuity and uniform integrability, J. Math. Anal. Appl. 80 (1981), 393-405. MR 614839 (82g:28003)
  • [5] W. C. Bell and M. Keisler, A characterization of the representable Lebesgue decomposition properties, Pacific J. Math. 83 (1979), 185-186. MR 555046 (81g:46036)
  • [6] C. Constantinescu, Duality in measure theory, Lecture Notes in Math., vol. 796, Springer-Verlag, Berlin, Heidelberg, and New York, 1980. MR 574273 (81i:28001)
  • [7] W. Filter, Atomical and atomfree elements of a Riesz space, Arch. Math. 52 (1989), 580-587. MR 1007633 (90g:46012)
  • [8] -, Hypercomplete Riesz spaces, Atti Sem. Mat. Fis. Univ. Modena (to appear). MR 1122681 (92g:46006)
  • [9] M. Keisler, Integral representation for elements of the dual of $ ba(S,\Sigma )$, Pacific J. Math. 83 (1979), 177-183. MR 555045 (81g:46035)
  • [10] W. A. J. Luxemburg and J. J. Masterson, An extension of the concept of the order dual of a Riesz space, Canad. J. Math. 19 (1967), 488-498. MR 0212540 (35:3411)
  • [11] J. S. MacNerney, Finitely additive set functions, Houston J. Math. 6 (1980). MR 621386 (83c:46001)
  • [12] R. D. Mauldin, A representation theorem for the second dual of $ C[0,1]$, Studia Math. 46 (1973), 197-200. MR 0346506 (49:11231)
  • [13] -, The continuum hypothesis, integration and duals of measure spaces, Illinois J. Math. 19 (1975), 33-40. MR 0377008 (51:13183)
  • [14] -, Some effects of set-theoretical assumptions in measure theory, Adv. in Math. 27 (1978), 45-62. MR 480385 (80i:28021)
  • [15] Y. A. Abramovich, A special class of vector lattices and its application to hypercomplete spaces, preprint.

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1990-1021210-2
PII: S 0002-9939(1990)1021210-2
Article copyright: © Copyright 1990 American Mathematical Society