  We consider the differential entropy of probability measures absolutely
continuous with respect to a given $\sigma$-finite reference measure on an
arbitrary measurable space. We state the asymptotic equipartition property in
this general case; the result is part of the folklore but our presentation is
to some extent novel. Then we study a general framework under which such
entropies satisfy a chain rule: disintegrations of measures. We give an
asymptotic interpretation for conditional entropies in this case. Finally, we
apply our result to Haar measures in canonical relation.
