Inequalities for the Gaussian measure of convex sets

TL;DR

This paper introduces new inequalities related to the Gaussian measure of convex sets, extending the Gaussian correlation inequality in multiple directions to deepen understanding of measure properties.

Contribution

It presents novel inequalities for Gaussian measures of convex sets, broadening the scope of the Gaussian correlation inequality.

Findings

Extended the Gaussian correlation inequality to new classes of convex sets

Established bounds for Gaussian measures of convex sets

Provided theoretical insights into measure inequalities

Abstract

This note presents families of inequalities for the Gaussian measure of convex sets which extend the recently proven Gaussian correlation inequality in various directions.