Under mild regularity assumptions, the transport problem is stable in following sense: if a sequence of optimal plans π1,π2,… converges weakly to plan π, then π also (between its marginals). Alfonsi, Corbetta and Jourdain (Ann. Inst. Henri Poincaré Probab. Stat. 56 (2020) 1706–1729) asked whether same property true for martingale problem. This question seems particularly pressing since motivate...