4 problems

Let $\Gamma_{\mathcal{F}}(\mu,\nu)$ be the set of $\mathcal{F}$-transports between $\mu$ and $\nu$, with an associated measure $\theta$ on an index space $I$ and conditional measu…

Let $\Omega$ be the underlying space, let $\mu$ and $\nu$ be the source and target measures, and let $\Gamma_{\mathcal{F}}(\mu,\nu)$ denote the set of $\mathcal{F}$-transports betw…

Let $\mu$ and $\nu$ be measures in convex order, and let the irreducible convex paving be the finest partitioning that constrains all martingale transports between them. A Borel se…

Martingale-polar equivalence conjecture. In the setting of the main convex-component theorem, for every $4N\subseteq\operatorname{gr}(C)4$,