Convergence in Mallows distance is of particular interest when heavy-tailed distributions are considered. For 1≦α<2, it constitutes an alternative technique to derive central limit type theorems for non-Gaussian α-stable laws. In this note, we further explore the connection between Mallows distance and convergence in distribution. Conditions for their equivalence are presented.
 Barbosa, E. G., Dorea, C. C. Y.2009A note on the Lindeberg condition for convergence to stable laws in Mallows distanceBernoulli15922–924.