On the positivity of Riemann-Stieltjes integrals

TL;DR

This paper investigates conditions under which the Riemann-Stieltjes integral of a positive continuous function with respect to a non-negative bounded variation function remains positive.

Contribution

It provides new insights into the positivity criteria of Riemann-Stieltjes integrals involving non-negative functions of bounded variation.

Findings

Identifies conditions ensuring positivity of the integral.

Establishes relationships between the integrand and integrator.

Provides theoretical results on integral positivity.

Abstract

We study the question, whether a Riemann-Stieltjes integral of a positive continuous function with respect to a non-negative function of bounded variation is positive.