If $f$ is a positive function, the intuitive interpretation of the Riemann integral
$\int_a^b f(x) dx$
is the area under the curve $f$ between $a$ and $b$.
Suppose $f$ and $g$ are smooth positive functions. Is it correct to interpret the Riemann-Stieltjes integral
$\int_a^b f(x) d g(x)$ as the volume under a "ribbon", where the height of the ribbon at a point $u$ between $a$ and $b$ is determined by $f$ and the thickness is determined by $g'$?