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Exponential integrability in Gauss space

Exponential integrability in Gauss space

Talagrand showed that finiteness of ‫ޅ‬ e |∇ f (X )| 2 /2 implies finiteness of ‫ޅ‬ e f (X ‫ޅ-)‬ f (X ) , where X is the standard Gaussian vector in ‫ޒ‬ n and f is a smooth function.However, in this paper we show that finiteness of ‫ޅ‬ …