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)

 
 

 

Factorization of measures and perfection


Author: Wolfgang Adamski
Journal: Proc. Amer. Math. Soc. 97 (1986), 30-32
MSC: Primary 28A50; Secondary 28A12, 60A10
DOI: https://doi.org/10.1090/S0002-9939-1986-0831381-5
MathSciNet review: 831381
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: It is proved that a probability measure $ P$ defined on a countably generated measurable space $ \left( {Y,\mathcal{C}} \right)$ is perfect iff every probability measure on $ {\mathbf{R}} \times Y$ having $ P$ as marginal can be factored. This result leads to a generalization of a theorem due to Blackwell and Maitra.


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

  • [1] D. Blackwell and A. Maitra, Factorization of probability measures and absolutely measurable sets, Proc. Amer. Math. Soc. 92 (1984), 251-254. MR 754713 (85j:28005)
  • [2] P. Gänssler and W. Stute, Wahrscheinlichkeitstheorie, Springer-Verlag, Berlin, Heidelberg and New York, 1977. MR 0501219 (58:18632)
  • [3] E. Marczewski and C. Ryll-Nardzewski, Remarks on the compactness and non-direct products of measures, Fund. Math. 40 (1953), 165-170. MR 0059996 (15:610c)
  • [4] J. K. Pachl, Disintegration and compact measures, Math. Scand. 43 (1978), 157-168. MR 523833 (80d:28020)
  • [5] V. V. Sazonov, On perfect measures, Amer. Math. Soc. Transl. (2) 48 (1965), 229-254.
  • [6] L. Schwartz, Radon measures on arbitrary topological spaces and cylindrical measures, Oxford Univ. Press, London, 1973. MR 0426084 (54:14030)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 28A50, 28A12, 60A10

Retrieve articles in all journals with MSC: 28A50, 28A12, 60A10


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1986-0831381-5
Article copyright: © Copyright 1986 American Mathematical Society

American Mathematical Society