This paper deals with empirical processes of the type Cn(B) = n^(1/2) {µn(B) - P(Xn+1 in B | X1, . . . ,Xn)} , where (Xn) is a sequence of random variables and µn = (1/n)SUM(i=1,..,n) d(Xi) the empirical measure. Conditions for supB|Cn(B)| to converge stably (in particular, in distribution)...

Let (µn : n = 0) be Borel probabilities on a metric space S such that µn - µ0 weakly. Say that Skorohod representation holds if, on some probability space, there are S-valued random variables Xn satisfying Xn - µn for all n and Xn - X0 in probability. By Skorohod s theorem, Skorohod...

Let (omega,F,P) be a probability space. For each G in F, define G as the s-field generated by G and those sets f in F satisfying P(f) in {0, 1}. Conditions for P to be atomic on the intersection of the complements of Ai for i=1,..,k, with A1, . . . ,Ak in F sub-s-fields, are given. Conditions...

Let (omega, beta) be a measurable space, An in B a sub-sigma-field and µn a random probability measure, n = 1. In various frameworks, one looks for a probability P on B such that µn is a regular conditional distribution for P given An for all n. Conditions for such a P to exist are given. The...