It is pointed out that an example due to J. Pachl shows the nonexistence of regular conditional probabilities in Doob's sense when the underlying space is a perfect probability space. This answers a question of Sazonov.
@article{1176994321,
author = {Ramachandran, D.},
title = {A Note on Regular Conditional Probabilities in Doob's Sense},
journal = {Ann. Probab.},
volume = {9},
number = {6},
year = {1981},
pages = { 907-908},
language = {en},
url = {http://dml.mathdoc.fr/item/1176994321}
}
Ramachandran, D. A Note on Regular Conditional Probabilities in Doob's Sense. Ann. Probab., Tome 9 (1981) no. 6, pp. 907-908. http://gdmltest.u-ga.fr/item/1176994321/