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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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
Addendum: 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.


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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: http://dx.doi.org/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
Article copyright: © Copyright 1997 American Mathematical Society