In this paper, we extend the notion of Lyndon word to transfinite words. We
prove two main results. We first show that, given a transfinite word, there
exists a unique factorization in Lyndon words that are densely non-increasing,
a relaxation of the condition used in the case of finite words.
In the annex, we prove that the factorization of a rational word has a
special form and that it can be computed from a rational expression describing
the word.