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Independence and determination of probabilities
Author(s):
Zhiqiang
Chen;
Herman
Rubin;
Richard
A.
Vitale
Journal:
Proc. Amer. Math. Soc.
125
(1997),
3721-3723.
MSC (1991):
Primary 60A99;
Secondary 28A99
Addenda:
Proc. Amer. Math. Soc. 129 (2001), 2817.
MathSciNet review:
1416079
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Abstract:
A non-atomic probability measure is determined by its specification of independent events. We give two proofs and related results.
References:
- 1.
- Diestel, J. and Uhl, Jr., J.J. (1977). Vector Measures. Amer. Math. Soc. Surveys 13. MR 56:12216
- 2.
- Dudley, R.M. (1989). Real Analysis and Probability. Wadsworth and Brooks/Cole, Pacific Grove. MR 91g:60001
- 3.
- Dvoretzky, A., Wald, A., and Wolfowitz, J. (1951). Relations among certain ranges of vector measures. Pac. J. Math. 1, 59-74. MR 13:331f
- 4.
- Kluvánek, I. (1980). Applications of vector measures. In Integration, Topology, and Geometry of Linear Spaces. Contemporary Mathematics 2, Amer. Math. Soc. (W.H. Graves, R.L. Davis, F.B. Wright, eds.). MR 82m:28019
- 5.
- Lehmann, E.L. (1959). Testing Statistical Hypotheses. Wiley, New York. MR 21:6654
- 6.
- Loève, M. (1963). Probability Theory, I (third edition). Van Nostrand, New York. MR 34:3596
- 7.
- Lyapunov, A. (1940). Sur les fonctions-vecteurs completèment additives. Izvestia Akad. Nauk SSSR Ser. Mat. 4 (Russian, French summary) 465-478.
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Additional Information:
Zhiqiang
Chen
Affiliation:
Department of Mathematics, William Paterson College, Wayne, New Jersey 07470
Email:
z_chen@smtplink.wilpaterson.edu
Herman
Rubin
Affiliation:
Department of Statistics, Purdue University, West Lafayette, Indiana 47907
Email:
hrubin@stat.purdue.edu
Richard
A.
Vitale
Affiliation:
Department of Statistics, University of Connecticut, Storrs, Connecticut 06269
Email:
rvitale@uconnvm.uconn.edu
DOI:
10.1090/S0002-9939-97-03994-4
PII:
S 0002-9939(97)03994-4
Keywords:
Determining conditions,
independence,
Lyapunov Convexity Theorem,
non--atomic measure,
stochastic independence
Received by editor(s):
March 12, 1996
Received by editor(s) in revised form:
July 1, 1996
Additional Notes:
The first author was supported in part by a grant from the Center for Research, School of Science and Health, William Paterson College.
The third author was supported in part by ONR Grant N00014-90-J-1641.
Communicated by:
Stanley Sawyer
Copyright of article:
Copyright
1997,
American Mathematical Society
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