This is an announcement for the paper “Riemann-Stieltjes integrals driven by irregular signals in Banach spaces and rate-independent characteristics of their irregularity” by R. M. Lochowski.

Abstract: Using truncated variation techniques we derive a new theorem on the existence of the Riemann-Stieltjes integral driven by irregular signals in Banach spaces. Next, for any $p\geq 1$ we introduce the space of regulated functions $f: [a, b]\rightarrow W$ ($a<b$ are real numbers and $W$ is a Banach space), which may be uniformly approximated with accuracy $\delta>0$ by functions whose total variation is of order $\delta_{1-p}$ as $\delta\rightarrow 0+$. As an application of these results we derive more exact, rate-independent characterisations of the irregularity of the integrals driven by irregular signals.

The paper may be downloaded from the archive by web browser from URL http://arxiv.org/abs/1602.02269