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The problem of statistical learning deals with the estimation of the Bayes: $$g^*=\\arg\\min_{g\\in\\GG}\\E_P \\ell(g(X),Y). $$ In this paper, we study this problem when we deal with a contaminated sample $(Z_1,Y_1),..., (Z_n,Y_n)$ of i.i.d. indirect observations. 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