Transportation cost spaces and their embeddings into $L_1$, a Survey

These notes present a basic survey on Transportation cost spaces (aka Lipschitzfree spaces, Wasserstein spaces) and their bi-Lipschitz and linear embeddings into $L_1$ spaces. To make these notes as self-contained as possible, we added the proofs of several relevant results from computational graph theory in the appendix.

这些笔记对运输成本空间（又名李普希茨自由空间、瓦瑟斯坦空间）及其到\(L_1\)空间的双李普希茨嵌入和线性嵌入进行了基本综述。为了使这些笔记尽可能自成一体，我们在附录中添加了来自计算图论的几个相关结果的证明。