Different necessary and sufficient conditions for the existence of regular conditional probabilities are found for the cases of countably generated, countably separated, and complete probability spaces. Perfection is $n.$ and $s.$ for countably generated spaces, "almost pre-standardness" for the countably generated and countably separated cases, and discreteness for complete spaces. Several different forms of the regular conditional probability property must be distinguished.
Publié le : 1985-02-14
Classification:
Conditional probability,
discrete measures,
disintegrations,
perfect measures,
regular conditional probability,
standard measures,
60A10,
60A28
@article{1176993081,
author = {Faden, Arnold M.},
title = {The Existence of Regular Conditional Probabilities: Necessary and Sufficient Conditions},
journal = {Ann. Probab.},
volume = {13},
number = {4},
year = {1985},
pages = { 288-298},
language = {en},
url = {http://dml.mathdoc.fr/item/1176993081}
}
Faden, Arnold M. The Existence of Regular Conditional Probabilities: Necessary and Sufficient Conditions. Ann. Probab., Tome 13 (1985) no. 4, pp. 288-298. http://gdmltest.u-ga.fr/item/1176993081/