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We give complete details on an alternative formulation of the Polya-Szegoprinciple that was mentioned in Remark 1 of our paper "Isoperimetry andSymmetrization for Logarithmic Sobolev inequalities". We also provide analternative proof to a result in the same paper.

Addendum to Isoperimetry and Symmetrization for Logarithmic Sobolev inequalities