Teddy Seidenfeld, Mark J. Schervish and Joseph B. Kadane
Improper regular conditional distributions (rcd's) given a -field
have the following anomalous property. For sets , is not always equal to the indicator of A. Such a property
makes the conditional probability puzzling as a representation of
uncertainty. When rcd's exist and the -field is countably
generated, then almost surely the rcd is proper. We give sufficient
conditions for an rcd to be improper in a maximal sense, and show that
these conditions apply to the tail -field and the -field of symmetric events.