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)



On the independence of correspondences

Author: Xiaoai Lin
Journal: Proc. Amer. Math. Soc. 129 (2001), 1329-1334
MSC (2000): Primary 28B20, 60E05
Published electronically: October 10, 2000
MathSciNet review: 1709761
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: An almost independent set-valued process on a Loeb product space is shown to be representable as the closure of a sequence of its selections which are almost independent themselves. This provides a Castaing type representation in terms of independent correspondences. Different definitions of independence for correspondences in the literature are also unified in a general setting.

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

  • 1. Z. Artstein, On dense univalued representations of multivalued maps, Rend. Circ. Mat. Palermo 33 (1984), 340-350. MR 87d:28011
  • 2. Z. Artstein and S. Hart, Law of large numbers for random sets and allocation processes, Mathematics of Operations Research 6 (1981), 485-492. MR 84j:60042
  • 3. J. P. Aubin and H. Frankowska, Set Valued Analysis, Birkhäuser, Boston, 1990. MR 91d:49001
  • 4. P. Billingsley, Convergence of Probability Measures, Wiley, New York, 1968. MR 38:1718
  • 5. C. Castaing and M. Valadier, Convex analysis and measurable multifuctions, Lecture Notes in Mathematics 580 (1977). MR 57:7169
  • 6. A. E. Hurd and P. A. Loeb, An Introduction to Nonstandard Real Analysis, Academic Press, Orlando, Florida, 1985. MR 87d:03184
  • 7. M. A. Khan and Y. N. Sun, Non-cooperative games on hyperfinite Loeb spaces, J. Math. Econ. 31 (1999), 455-492. MR 2000b:91011
  • 8. P. A. Loeb, Conversion from nonstandard to standard measure spaces and applications in probability theory, Trans. Amer. Math. Soc. 211 (1975), 113-122. MR 52:10980
  • 9. M. Loève, Probability Theory I, 4th edition, Springer-Verlag, New York, 1977. MR 58:3132a
  • 10. G. Matheron, Random Sets and Integral Geometry, Wiley, London, 1975. MR 52:6828
  • 11. Y. N. Sun, A theory of hyperfinite processes: the complete removal of individual uncertainty via exact LLN, J. Math. Econ. 29 (1998), 419-503. MR 99j:28020
  • 12. Y. N. Sun, The almost equivalence of pairwise and mutual independence and the duality with exchangeability, Probability Theory and Related Fields 112 (1998), 425-456. CMP 99:05
  • 13. Y. N. Sun, The complete removal of individual uncertainty: multiple optimal choices and random exchange economies, Economic Theory 14 (1999), 507-544. CMP 2000:05
  • 14. D. H. Wagner, Survey of measurable selection theorems, SIAM J. Control and Optimization 15 (1977), 859-903. MR 58:6137

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 28B20, 60E05

Retrieve articles in all journals with MSC (2000): 28B20, 60E05

Additional Information

Xiaoai Lin
Affiliation: Department of Mathematics, National University of Singapore, Singapore 119260

Received by editor(s): May 13, 1999
Received by editor(s) in revised form: July 8, 1999
Published electronically: October 10, 2000
Additional Notes: The author is grateful to an anonymous referee and Yeneng Sun for many helpful suggestions on the exposition of the paper.
Communicated by: Carl G. Jockusch, Jr.
Article copyright: © Copyright 2000 American Mathematical Society

American Mathematical Society