  We prove an inequality of the Lo\'{e}ve-Young type for the Riemann-Stieltjes
integrals driven by irregular signals attaining their values in Banach spaces
and, as a result, we derive a new theorem on the existence of the
Riemann-Stieltjes integrals driven by such signals. Also, for any $p\ge1$ we
introduce the space of regulated signals $f:[a,b] \rightarrow W$ ($a<b$ are
real numbers and $W$ is a Banach space), which may be uniformly approximated
with accuracy $\delta>0$ by signals whose total variation is of order
$\delta^{1-p}$ as $\delta\rightarrow 0+$ and prove that they satisfy the
assumptions of the theorem. Finally, we derive more exact, rate-independent
characterisations of the irregularity of the integrals driven by such signals.
