  Strassen established that there exists a two step martingale with marginal
distributions $\mu$, $\nu$ if and only if $\mu$, $\nu$ are in convex order.
Recently Chon\'e-Gozlan-Kramarz obtained a transport characterization of the
stochastic order defined by convex positively 1-homogeneous functions, in the
spirit of Strassen's theorem under certain technical assumptions. In this note
we prove the Chon\'e-Gozlan-Kramarz result in full generality. We also observe
that the restriction of the result to the case where $\mu, \nu$ are supported
on a half space is equivalent to Strassen's classical theorem.
