Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

Journals Home Search My Subscriptions Subscribe
Previous issue | This issue | Most recent issue | All issues (1950–Present) | Next issue | Previous article | Articles in press | Recently published articles | Next article
Request Permissions
 
 

 

On the extensions of vector-valued Loeb measures


Authors: Horst Osswald and Yeneng Sun
Journal: Proc. Amer. Math. Soc. 111 (1991), 663-675
MSC: Primary 28E05; Secondary 03H05, 28B05, 46G10, 46S20
DOI: https://doi.org/10.1090/S0002-9939-1991-1047007-6
MathSciNet review: 1047007
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Two ways of constructing countably additive vector measures from internal vector measures are given. The connection of the extendability of vector-valued Loeb measures and the existence of the internal control measures is shown.

References [Enhancements On Off] (What's this?)

  • [1] J. Diestel and J. J. Uhl, Vector measures, Mathematical Surveys Number 15, Amer. Math. Soc., Providence, RI, 1977. MR 0453964 (56:12216)
  • [2] A. Grothendieck, Sur les applications linearies faiblement compactes d'espaces du type $ C(K)$, Canad. J. Math. 5 (1953), 129-173. MR 0058866 (15:438b)
  • [3] C. W. Henson and L. C. Moore, Nonstandard analysis and theory of Banach spaces, Nonstandard analysis recent developments (A. E. Hurd, ed.), Lecture Notes in Math., vol. 983, Springer-Verlag, Berlin, 1983. MR 698954 (85f:46033)
  • [4] A. E. Hurd and P. A. Loeb, An introduction to nonstandard real analysis, Academic Press, Orlando, Florida, 1985. MR 806135 (87d:03184)
  • [5] P. A. Loeb, Conversion from nonstandard to standard measure spaces and applications in probability theory, Trans. Amer. Math. Soc. 211 (1975), 113-122. MR 0390154 (52:10980)
  • [6] -, A functional approach to nonstandard measure theory, Contemp. Math. 26 (1984), 251-261. MR 737406 (86b:28026)
  • [7] P. A. Loeb and H. Osswald, Nonstandard integration theory in solid Riesz space (to appear).
  • [8] Y. Sun, On the theory of vector valued Loeb measures and integration (to appear). MR 1153991 (93a:46146)
  • [9] -, A nonstandard proof of the Riesz representation theorem for weakly compact operators on $ C(\Omega )$, Math. Proc. Comb. Phil. Soc. 105 (1989), 141-145. MR 966150 (89i:47059)
  • [10] -, A Banach space in which a ball is contained in the range of some countably additive measure is superreflexive, Canad. Math. Bull. 33 (1990), 45-49. MR 1036854 (91a:46018)
  • [11] -, Nonstandard theory of vector measures, Ph.D. dissertation, University of Illinois, Urbana, Illinois, 1989.
  • [12] R. T. Zivaljevic, Loeb completion of internal vector valued measures, Math. Scand. 56 (1985), 276-286. MR 813641 (87k:28021)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 28E05, 03H05, 28B05, 46G10, 46S20

Retrieve articles in all journals with MSC: 28E05, 03H05, 28B05, 46G10, 46S20

Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1991-1047007-6
Article copyright: © Copyright 1991 American Mathematical Society

American Mathematical Society