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On the independence of correspondences
Author(s):
Xiaoai
Lin
Journal:
Proc. Amer. Math. Soc.
129
(2001),
1329-1334.
MSC (2000):
Primary 28B20, 60E05
Posted:
October 10, 2000
MathSciNet review:
1709761
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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:
-
- 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
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Additional Information:
Xiaoai
Lin
Affiliation:
Department of Mathematics, National University of Singapore, Singapore 119260
Email:
scip8206@nus.edu.sg
DOI:
10.1090/S0002-9939-00-05652-5
PII:
S 0002-9939(00)05652-5
Received by editor(s):
May 13, 1999
Received by editor(s) in revised form:
July 8, 1999
Posted:
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.
Copyright of article:
Copyright
2000,
American Mathematical Society
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