Φ V[h] and Riemann-Stieltjes integration

Riemann-Stieltjes integrals

This short note gives an introduction to the Riemann-Stieltjes integral on R and Rn. Some natural and important applications in probability theory are discussed. The reason for discussing the Riemann-Stieltjes integral instead of the more general Lebesgue and LebesgueStieltjes integrals are that most applications in elementary probability theory are satisfactorily covered by the Riemann-Stieltj...

Necessary and Sufficient Conditions for Riemann and Riemann-stieltjes Integrability

RIEMANN AND RIEMANN-STIELTJES INTEGRABILITY Looking back over the notes already posted on this and related subjects, I felt that their organization did not emphasize the things that are important on the subject of the caption. Hence these notes, which will initially reprise things that are already treated in the others, but with different emphasis. The material on almost-everywhere continuity a...

Cauchy-stieltjes and Riemann-stielt Jes Integrals

The Riemann-stieltjes Integral on Time Scales

We study the process of integration on time scales in the sense of Riemann-Stieltjes. Analogues of the classical properties are proved for a generic time scale, and examples are given.

On Approximation of the Riemann–stieltjes Integral and Applications

Several inequalities of Grüss type for the Stieltjes integral with various type of integrand and integrator are introduced. Some improvements inequalities are proved. Applications to the approximation problem of the Riemann–Stieltjes integral are also pointed out.