7 problems

Let $\mu$ and $\nu$ be probability measures on $\mathds{R}^{d}$. The pair $(\mu,\nu)$ is irreducible if for all measurable sets $A,B\subseteq\mathds{R}^{d}$ with $\mu(A)>0$ and…

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…

Finitely additive stability conjecture. Some of the stability results that fail in the standard framework when $\Omega_i=\mathbb{R}^d$ should nevertheless be valid in a finitely ad…

Finitely additive no-gap conjecture. Replacing the standard class $\Gamma$ of countably additive probabilities by $M$ should make the absence of a duality gap in the martingale pro…

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

Minimality conjecture for closures of convex components. The closures $4\overline{C_x}4$ are the smallest possible closed convex sets on which all martingale transports are confine…

Let $[\b5]$ be a right-continuous peacock, and let $\mathrm{LimCurt}([\b5])$ denote the set of limit curtain processes associated with it. Uniqueness conjecture. There is exactly o…