  Given a measurable space (X, M) there is a (Galois) connection between
sub-sigma-algebras of M and equivalence relations on X. On the other hand
equivalence relations on X are closely related to congruences on stochastic
relations. In recent work, Doberkat has examined lattice properties of posets
of congruences on a stochastic relation and motivated a domain-theoretic
investigation of these ordered sets. Here we show that the posets of
sub-sigma-algebras of a measurable space do not enjoy desired domain-theoretic
properties and that our counterexamples can be applied to the set of smooth
equivalence relations on an analytic space, thus giving a rather unsatisfactory
answer to Doberkat's question.
