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Since a few years, the Schr\"odinger problem captures the attention of agrowing community of mathematicians interested in optimal transport problems.The first result of existence of a solution to this problem dates back to 1940,when Fortet published an article on the subject. In these notes, Fortet'soriginal proof of existence and uniqueness of a solution to the Schr\"odingersystem is revisited.

Revisiting Fortet's proof of existence of a solution to the Schr\"odinger system