4 problems

Let $A,B\subseteq\mathbb{R}^n$ be bounded measurable sets, and let $\Gamma$ be a set of isometries of $\mathbb{R}^n$. The sets $A$ and $B$ are $\Gamma$-equidecomposable if they adm…

Nonadjacent maximum-degree measurable edge-coloring conjecture. For every probability measure $\mu$ on $V$,

Unbalanced bipartite measurable edge-coloring conjecture. For every probability measure $\mu$ on $V$,

Let $P=(V,\preceq)$ be a measurable poset, meaning an ordered probability space with probabilistic measure $\mu$. Let $G_P$ be its incomparability graph, and let $\chi_{\mu}(G_P)$…