3 problems

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 $\chi_{\mu}(G_P)$…

Let $P=(V,\preceq)$ be a Borel poset. Its height is the largest size of a chain in $P$, and an antichain is a set of pairwise incomparable elements. Borel dual Dilworth conjecture.…

Let $P=(V,\preceq)$ be a Borel poset, meaning that $V$ is a standard Borel space and the comparability relation is a Borel subset of $V\times V$. Its width is the maximum size of a…