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arXiv · 2412.10276

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

Sergey G. Bobkov·Friedrich Götze
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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.

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Sergey G. Bobkov, Friedrich Götze. 2024-12-13. Quantified Cram\'er-Wold Continuity Theorem for the Kantorovich Transport Distance. https://arxiv.org/abs/2412.10276

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