An inequality for correlated measurable functions

TL;DR

This paper generalizes a classical inequality from monotone functions to a broader class of measurable functions and characterizes when equality holds, with applications in probability theory.

Contribution

It extends a classical inequality to a larger class of functions and provides a complete characterization of equality cases.

Findings

Generalized the inequality to non-monotone measurable functions

Characterized all families of functions where equality holds

Applied the results to a probability theory problem

Abstract

A classical inequality, which is known for families of monotone functions, is generalized to a larger class of families of measurable functions. Moreover we characterize all the families of functions for which the equality holds. We apply this result to a problem arising from probability theory.