, We build f and show (17) on [b k , b j ] only. The interval [b i , b k ] can be treated with a symmetric proof

, Then consider the most recent ? g(u) ? h m + ?(g, ?)

, Now that we have shown that f is continuous

, Under (A), we have g = f ? ?, and furthermore

, To show g(t) = f (?(t)) it is enough to see that (18) {k : t ?

, Now to show that ? is a (d g , d f ) isometry, we need only show that for x < y, min [x,y] g = min

, Then for every i, x ? [a i , c i ] implies y ? [a i , c i

, = f (?(x)) = g(x) = min

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, Mathématiques Pures et Appliquées E-mail address: mickael.maazoun@ens-lyon.fr