The product integral of Riemann-Stieltjes and its application to the mean value functions of truncated distributions. (Spanish. English summary) Zbl 0589.47050
Summary: One gives a definition, in the manner of Riemann-Stieltjes, of the product integral that is adequate to solve the following problem.
If F is a distribution function of a probability one defines \(m=\omega (F)\) by \[ m(x)=\int_{(-\infty,x]}t dF(t)/F(x). \] In this case m is called the mean value function of the truncated distribution of F. It is intended to find the inverse transformation \(\omega^{-1}\) such that \(\omega^{-1}(\omega (F))=F\) and this can be done by means of the product integral defined above.
If F is a distribution function of a probability one defines \(m=\omega (F)\) by \[ m(x)=\int_{(-\infty,x]}t dF(t)/F(x). \] In this case m is called the mean value function of the truncated distribution of F. It is intended to find the inverse transformation \(\omega^{-1}\) such that \(\omega^{-1}(\omega (F))=F\) and this can be done by means of the product integral defined above.
