On the reach of isometric embeddings into Wasserstein type spaces

Javier Casado, Manuel Cuerno, Jaime Santos-Rodríguez

We study the reach (in the sense of Federer) of the natural isometric embedding $X\hookrightarrow W_p(X)$ of $X$ inside its $p$-Wasserstein space, where $(X,\mathrm{dist})$ i…