2007/09/12 by Carl Graham, Graham, Carl
Mathematics · #60B10 #60G09 #60K35 (Primary) #62B05 (Secondary) #FOS: Mathematics #Probability (math.PR) #math.PR #msc:60B10 #msc:60G09 #msc:60K35 #msc:62B05
paper · pdf · doi:10.48550/arxiv.0709.1918
Third revision, v4. The paper is similar to the second revision v3, with several improvements
arxiv created 2008/10/16 · arxiv updated 2009/12/01
Classical results for exchangeable systems of random variables are extended to multi-class systems satisfying a natural partial exchangeability assumption. It is proved that the conditional law of a finite multi-class system, given the value of the vector of the empirical measures of its classes, corresponds to independent uniform orderings of the samples within each class, and that a family of such systems converges in law if and only if the corresponding empirical measure vectors converge in law. As a corollary, convergence within each class to an infinite i.i.d. system implies asymptotic independence between different classes. A result implying the Hewitt-Savage 0-1 Law is also extended.