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For a class of density functions $q$ we prove an inequality between the relative entropy $D(p||q)$ and a weighted sum of the conditional relative entropies $D(p_i(\\cdot|Y_1,..., Y_{i-1},Y_{i+1},..., Y_n) ||Q_i(\\cdot|Y_1,..., Y_{i-1},Y_{i+1},..., Y_n))$ that holds for any $p$. 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