Bi-convexity and bi-martingales

A set in a product space X×Y is bi-convex if all its x- and y-sections are convex. A bi-martingale is a martingale with values in X×Y whose x- and y-coordinates change only one at a time. This paper investigates the limiting behavior of bimartingales in terms of the bi-convex hull of a set - the smallest bi-convex set containing it - and of several related concepts generalizing the concept of separation to the bi-convex case.