An Anscombe-type theorem
  Let (X_n) be a sequence of random variables (with values in a separable metric space) and (N_n) a sequence of random indices. Conditions for X_{N_n} to converge stably (in particular, in distribution) are provided. Some examples, where such conditions work but those already existing fail, are given as well.   Key words and phrases: Anscombe theorem, Exchangeability, Random indices, Random sums, Stable convergence 
Patrizia Berti, Irene Crimaldi, Luca Pratelli, Pietro Rigo
math.PR math.ST stat.TH