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Quantified Cram\'er-Wold Continuity Theorem for the Kantorovich Transport Distance

Probability 2026-01-14 v3

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 Cram\'er-Wold continuity theorem for the weak convergence of probability measures.

Keywords

Cite

@article{arxiv.2412.10276,
  title  = {Quantified Cram\'er-Wold Continuity Theorem for the Kantorovich Transport Distance},
  author = {Sergey G. Bobkov and Friedrich Götze},
  journal= {arXiv preprint arXiv:2412.10276},
  year   = {2026}
}

Comments

Added more references and revised discussion of previous results