, x2' ... , be iid U(O, e) where eE8 = (0, In this example the

If the true distribution P0 has a density then with P0 probability I, the It's are all equal to I and the conditional density of() given X1, X2, ... , X11 becomes

Mixtures are no longer tail-free and in general one has inconsistency. Ferguson et a!. ( 1996) has a nice example illustrating this phenomenon. Consistency issues in the case of mixtures of Dirichlet is studied in detail in Freedman and Diaconis (1983), where the following result is available.