3 problems

Let $E$ and $D$ be Borel data structures, let $R$ denote the randomization Borel data structure with laws $\boldsymbol{\upsilon}$, and let $\operatorname{SYM}(E)$ denote the exchan…

Let $(X_1,X_2,\ldots)$ be an infinite exchangeable sequence, and let $K_n$ be the number of distinct values among its first $n$ terms. For $m\in\{1,2,\ldots,\infty\}$, let…

Converse characterisation conjecture. If the empirical distributions $(\eta_{n,m})$ form a reverse measure-valued martingale, then $X$ is separately exchangeable, meaning that for…