Bi-Convexity and Bi-Martingales
Robert J. Aumann and Sergiu Hart
A set in a product space
X x Y is bi-convex if all its x- and
y-sections are convex. A bi-martingale is a martingale with values
in X 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.
Israel Journal of Mathematics 54 (1986), 2, 159-180
Collected Papers of Robert J. Aumann, The MIT Press,
Vol. II (2000), 653-674