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)



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
Full-text PDF Free Access

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. J. Diestel and J. J. Uhl Jr., Vector measures, American Mathematical Society, Providence, R.I., 1977. With a foreword by B. J. Pettis; Mathematical Surveys, No. 15. MR 0453964
  • 2. Richard M. Dudley, Real analysis and probability, The Wadsworth & Brooks/Cole Mathematics Series, Wadsworth & Brooks/Cole Advanced Books & Software, Pacific Grove, CA, 1989. MR 982264
  • 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. Igor Kluvánek, Applications of vector measures, Proceedings of the Conference on Integration, Topology, and Geometry in Linear Spaces (Univ. North Carolina, Chapel Hill, N.C., 1979) Contemp. Math., vol. 2, Amer. Math. Soc., Providence, R.I., 1980, pp. 101–134. MR 621854
  • 5. E. L. Lehmann, Testing statistical hypotheses, John Wiley & Sons, Inc., New York; Chapman & Hall, Ltd., London, 1959. MR 0107933
  • 6. Michel Loève, Probability theory, Third edition, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto, Ont.-London, 1963. MR 0203748
  • 7. Lyapunov, A. (1940). Sur les fonctions-vecteurs completèment additives. Izvestia Akad. Nauk SSSR Ser. Mat. 4 (Russian, French summary) 465-478.

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 60A99, 28A99

Retrieve articles in all journals with MSC (1991): 60A99, 28A99

Additional Information

Zhiqiang Chen
Affiliation: Department of Mathematics, William Paterson College, Wayne, New Jersey 07470

Herman Rubin
Affiliation: Department of Statistics, Purdue University, West Lafayette, Indiana 47907

Richard A. Vitale

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