Factorization of measures and normal conditional distributions
Authors:
A. Maitra and S. Ramakrishnan
Journal:
Proc. Amer. Math. Soc. 103 (1988), 12591267
MSC:
Primary 60A10; Secondary 28D05
MathSciNet review:
955019
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Abstract: Let be a probability space. If every probability measure on with marginal on admits a factorization, where is the Borel field on the real line, must be perfect. Conversely if is perfect and is generated, then (a) for any measure on with marginal , where is any field of subsets of a set , there is a factorization; (b) for every taillike subfield of , there is a normal conditional distribution given . In special cases of interest, normal conditional distributions, satisfying additional desirable properties, are shown to exist.
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 R. A. Purves and W. D. Sudderth, Some finitely additive probability, Ann. Probab. 4 (1976), 259276. MR 0402888 (53:6702)
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 C. RyllNardzewski, On quasicompact measures, Fund. Math. 40 (1953), 125130. MR 0059997 (15:610d)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029939198809550193
PII:
S 00029939(1988)09550193
Keywords:
Factorization,
disintegration,
conditional distribution,
normal conditional distribution,
perfect probability space,
taillike field,
measurepreserving transformation,
invariant field,
symmetric field
Article copyright:
© Copyright 1988
American Mathematical Society
