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In this paper, the weak convergence of weighted empirical U-statistic with respect to the Skorohod topology is obtained when the random variables are absolutely regular. It is a generalization of the results of Puri and Harel (1994) for dependent random variables and Ruymgaart and van Zuijlen (1992) for i.i.d. random variables. Applications are given in section 5.

Convergence faible de la {$U$}-statistique empirique corrigée en condition de mélange