In this preliminary chapter, we introduce the problem of optimal transport, which is the main concept behind Wasserstein spaces. General references on this topic are the books by Rachev and Rüschendorf [107], Villani [124, 125], Ambrosio et al. [12], Ambrosio and Gigli [10], and Santambrogio [119]. This chapter includes only few proofs, when they are simple, informative, or are not easily found in one of the cited references.
CITATION STYLE
Panaretos, V. M., & Zemel, Y. (2020). Optimal Transport. In SpringerBriefs in Probability and Mathematical Statistics (pp. 1–35). Springer Nature. https://doi.org/10.1007/978-3-030-38438-8_1
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