We present results concerning when the joint distribution of an exchangeable sequence is determined by the marginal distributions of its partial sums. The question of whether or not this determination occurs was posed by David Aldous. We then consider related uniqueness problems, including a continuous time analog to the Aldous problem and a randomized univariate moment problem.
"A negative answer to a problem of Aldous on determination of exchangeable sequences." Electron. J. Probab. 21 1 - 26, 2016. https://doi.org/10.1214/16-EJP4403