Factorization of measures and normal conditional distributions

Authors:
A. Maitra and S. Ramakrishnan

Journal:
Proc. Amer. Math. Soc. **103** (1988), 1259-1267

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 tail-like sub--field 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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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1988-0955019-3

Keywords:
Factorization,
disintegration,
conditional distribution,
normal conditional distribution,
perfect probability space,
tail-like -field,
measure-preserving transformation,
invariant -field,
symmetric -field

Article copyright:
© Copyright 1988
American Mathematical Society