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Published in:
2017 | OriginalPaper | Chapter
1. Wasserstein Distance
Author : Szymon M. Walczak
Published in: Metric Diffusion Along Foliations
Publisher: Springer International Publishing
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Abstract
The Wasserstein distance of Borel probability measures will play the important role in metric diffusion along foliations. We here present the Kantorovich Duality Theorem for optimal transportation problem. We also recall the definition of the Wasserstein distance, together with the weak-∗ topology metrization theorem for the set \(\mathscr{P}(X)\) of Borel probability measures on a compact metric space X. The chapter is closed by some technical lemmas used in the later considerations.