Construction d'une probabilité d'Edwards sur C(R_+,R).

We prove that the measures Q_T associated to the one-dimensional Edwards' model on the interval [0,T] converge to a limit measure Q when T goes to infinity, in the following sense : for every nonnegative time s and every event A depending on the canonical process only up to time s, Q_T(A) converges to Q(A). Moreover, we prove that, if P is the Wiener measure, there exists a martingale (D_s) indexed by s in R_+ such that Q(A) = E_P(1_A D_s) for every such event A, and we give an explicit expression for this martingale.