In probability theory, Bobkov's inequality is a functional isoperimetric inequality for the canonical Gaussian measure. It generalizes the Gaussian isoperimetric inequality. The equation was proven in 1997 by the Russian mathematician Sergey Bobkov.
Bobkov's inequality Notation:
Let be the canonical Gaussian measure on with respect to the Lebesgue measure, be the one dimensional canonical Gaussian density the cumulative distribution function be a function that vanishes at the end points
Statement For every locally Lipschitz continuous (or smooth) function the following inequality holds
Generalizations There exists a generalization by Dominique Bakry and Michel Ledoux.
References