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
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Abstract | References | Similar Articles | Additional Information
Abstract: It is proved that a probability measure defined on a countably generated measurable space
is perfect iff every probability measure on
having
as marginal can be factored. This result leads to a generalization of a theorem due to Blackwell and Maitra.
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- [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)
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Additional Information
DOI:
https://doi.org/10.1090/S0002-9939-1986-0831381-5
Article copyright:
© Copyright 1986
American Mathematical Society