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Proceedings of the American Mathematical Society

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Factorization of probability measures and absolutely measurable sets


Authors: David Blackwell and Ashok Maitra
Journal: Proc. Amer. Math. Soc. 92 (1984), 251-254
MSC: Primary 28A50; Secondary 60A10
DOI: https://doi.org/10.1090/S0002-9939-1984-0754713-3
MathSciNet review: 754713
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Abstract: We find necessary and sufficient conditions for a separable metric space $ Y$ to possess the property that for any measurable space $ \left( {X,\mathcal{A}} \right)$ and probability measure $ P$ on $ X \times Y$, $ P$ can be factored.


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

  • [1] M. Jirina, Conditional probabilities on $ \sigma $-algebras with countable basis, Czechoslovak. Math. J. 4 (1954), 372-380; English transl., Selected Transl. Math. Statist. Prob., Vol. 2, Amer. Math. Soc., Providence, R.I., 1962, pp. 79-86. MR 0069416 (16:1034j)
  • [2] K. Kuratowski, Topology, Vol. 1, 5th ed., PWN, Warsaw; Academic Press, New York; "Mir", Moscow, 1966. MR 0259836 (41:4468)
  • [3] E. Marczewski, On compact measures, Fund. Math. 40 (1953), 113-124. MR 0059994 (15:610a)
  • [4] Jan K. Pachl, Disintegration and compact measures, Math. Scand. 43 (1978), 157-168. MR 523833 (80d:28020)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1984-0754713-3
Keywords: Probability measure, product space, transition function, factorization, absolutely measurable set, prior distribution, posterior distribution
Article copyright: © Copyright 1984 American Mathematical Society

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