Stieltjes-type integrals

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...

Majorisation inequalities for Stieltjes integrals

Inequalities of the majorisation type for convex functions and Stieltjes integrals are given. Applications for some particular convex functions of interest are also pointed out.

Oregon State College Sequences of Stieltjes Integrals

there is no projection on (m) to (C), it may be shown that at least either there is no projection on (w) to F, or else there is no projection on (m) to the complementary subspace of F in (C). (An illustration of the case where there is no projection on (m) to the complementary subspace in (C) is provided by the case of a finite dimensional YC(Q.) In a paper in preparation on the extension of li...

Cauchy-stieltjes and Riemann-stielt Jes Integrals

On Ostrowski type inequalities for Stieltjes integrals with absolutely continuous integrands and integrators of bounded variation

Some Ostrowski type inequalities are given for the Stieltjes integral where the integrand is absolutely continuous while the integrator is of bounded variation. The case when |f ′| is convex is explored. Applications for the midpoint rule and a generalised trapezoid type rule are also presented.