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Independence and determination of probabilities


Authors: Zhiqiang Chen, Herman Rubin and Richard A. Vitale
Journal: Proc. Amer. Math. Soc. 125 (1997), 3721-3723
MSC (1991): Primary 60A99; Secondary 28A99
DOI: https://doi.org/10.1090/S0002-9939-97-03994-4
Addendum: Proc. Amer. Math. Soc. 129 (2001), 2817.
MathSciNet review: 1416079
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Abstract | References | Similar Articles | Additional Information

Abstract: A non-atomic probability measure is determined by its specification of independent events. We give two proofs and related results.


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

  • 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
Email: rvitale@uconnvm.uconn.edu

DOI: https://doi.org/10.1090/S0002-9939-97-03994-4
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
Article copyright: © Copyright 1997 American Mathematical Society

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