Geodesic
On the coincidence of the canonical embeddings of a~metric space into a~Banach space
Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamics systems, combinatorial methods. Part XVI, Tome 360 (2008), pp. 153-161

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Recall the two classical canonical isometric embeddings of a finite metric space $X$ into a Banach space. That is, the Hausdorff–Kuratowsky embedding $x\to\rho(x,\cdot)$ into the space of continuous functions on $X$ with the max-norm, and the Kantorovich–Rubinshtein embedding $x\to\delta_x$ (where $\delta_x$ is the $\delta$-measure concentrated at $x$) with the transportation norm. We prove that these embeddings are not equivalent if $|X|>4$. Bibl. – 2 titles. 
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     author = {P. B. Zatitskii},
     title = {On the coincidence of the canonical embeddings of a~metric space into {a~Banach} space},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {153--161},
     publisher = {mathdoc},
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     url = {http://geodesic.mathdoc.fr/item/ZNSL_2008_360_a6/}
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P. B. Zatitskii. On the coincidence of the canonical embeddings of a~metric space into a~Banach space. Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamics systems, combinatorial methods. Part XVI, Tome 360 (2008), pp. 153-161. http://geodesic.mathdoc.fr/item/ZNSL_2008_360_a6/