According to wiki: ” The name “Wasserstein distance” was coined by R. L. Dobrushin in 1970, after the Russian mathematician Leonid Vaseršteĭn who introduced the concept in 1969. “. And indeed, I found the paper written in Russian by Dobrushin, which mentioned in reference:” Л..Н. Васерштейн, Марковские процессы на счетном произведении прост­ранств, описывающие большие системы автоматов. Пробл. перед, информ. 5, 3 (1969), 64—73. “, and Leonid Vaseršteĭn is just english for Леонид Васерштейн.

Although I could not read Russian and I could not find the content of the original papr by Leonid Vaseršteĭn, the wiki still seems convincing.

However, it seems Fréchet distance is identical to 2-Wasserstein distance, and Fréchet distance was introduced in 1957, according to the original French paper “Sur la distance de deux lois de probabilité.”

Does it means Fréchet discovered it first and wiki is wrong about the origin? What’s more, should we call it Fréchet distance instead of Wasserstein distance?

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P.S.

If you search “Fréchet distance” on google, what comes out is not a distance for distribution but distance for path. I am confused by the relationship between “Fréchet distance of path” with “Fréchet distance of distribution”.