Before revision:  In particular, using results from Beiglb\"ock, Jourdain, Margheriti, and Pammer [ 4 ], we show that the set of martingale measures with fixed marginals is continuous, i.e., lower- and upper hemicontinuous, w.r.t. its marginals.
After revision:  In particular, using results from Beiglb\"ock, Jourdain, Margheriti, and Pammer [ 5 ], we show that the set of martingale measures with fixed marginals is continuous, i.e., lower- and upper hemicontinuous, w.r.t. its marginals.