This section is devoted to studying the Gaussian Isoperimetric Inequality. This inequality is a special case of the Borell Isoperimetric Inequality (and hence also a special case of the General-Volume Majority Is Stablest Theorem); in particular, it’s the special case arising from the limit $\rho \to 1^{-}$.

Restating Borell’s theorem using rotation sensitivity [...]

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Ryan O'Donnell: Yes, thanks!Dmitry Sokolov: Exercise 28. Maybe $A \in \{-1, 1\}$ istead of $A \in \mathb...Ryan O'Donnell: Fixed, thanks!Ryan O'Donnell: It's the Holder conjugate of $q$ (i.e., the number satisfyin...Gautam Kamath: Is $q'$ defined here?Gautam Kamath: On this page, Hölder is displaying for me as H{ö}lder - is t...Ryan O'Donnell: Yes, you're right. This is not a well-written proof by the ...