## Does a non-exchangeable empirical reverse-martingale exist?

Consider a possible finite sequence ξ1,ξ2,… of random variables and consider the measure-valued empirical process ηn=∑ni=1δξin,n=1,2,… Assume ηn is a reverse martingale, in the sense that (∫fdηn) is a reverse-martingale for every f≥0. Does it automatically hold that (ηn) is exchangeable? I.e., does it hold that for any f1,…,fn and permutation p of {1,…,n} E(∫f1η1⋯∫fnηn)=E(∫f1ηp(1)⋯∫fnηp(n))? … Read more