Sequences of Stieltjes integrals

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...

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.

Cauchy-stieltjes and Riemann-stielt Jes Integrals

On powers of Stieltjes moment sequences, I

For a Bernstein function f the sequence sn = f(1)·. . .·f(n) is a Stieltjes moment sequence with the property that all powers sn, c > 0 are again Stieltjes moment sequences. We prove that sn is Stieltjes determinate for c ≤ 2, but it can be indeterminate for c > 2 as is shown by the moment sequence (n!)c, corresponding to the Bernstein function f(s) = s. Nevertheless there always exists a uniqu...