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The symmetric property ( τ ) for the Gaussian measure

Joseph Lehec — 2008

Annales de la faculté des sciences de Toulouse Mathématiques

We give a proof, based on the Poincaré inequality, of the symmetric property ( τ ) for the Gaussian measure. If f : d is continuous, bounded from below and even, we define H f ( x ) = inf y f ( x + y ) + 1 2 | y | 2 and we have e - f d γ d e H f d γ d 1 . This property is equivalent to a certain functional form of the Blaschke-Santaló inequality, as explained in a paper by Artstein, Klartag and Milman.

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