Let g be a smooth function on ℝn with values in [0, 1]. Using the isoperimetric property of the Gaussian measure, it is proved that φ(Φ-1(Eg)) - Eφ(Φ-1(g)) ≤ E \∇g\. Conversely, this inequality implies the isoperimetric property of the Gaussian measure.
Bibliographical noteFunding Information:
* Partially supported by the National Science Foundation and the Air Force Office of Scientific Research Grant 91-0030, the Army Research Office Grant DAAL03-92-G-0008, Grant 93-011-1454 of Russian Foundation for Scientific Research and Grant NXZ000 from the International Science Foundation.