Quantified Cramér-Wold Continuity Theorem for the Kantorovich Transport Distance
arXiv:2412.10276
Abstract
An upper bound for the Kantorovich transport distance between probability measures on multidimensional Euclidean spaces is given in terms of transport distances between one dimensional projections. This quantifies the Cramér-Wold continuity theorem for the weak convergence of probability measures.
Added more references and revised discussion of previous results