  For non-decreasing real functions $f$ and $g$, we consider the functional $
T(f,g ; I,J)=\int_{I} f(x)\di g(x) + \int_J g(x)\di f(x)$, where $I$ and $J$
are intervals with $J\subseteq I$. In particular case with $I=[a,t]$,
$J=[a,s]$, $s\leq t$ and $g(x)=x$, this reduces to the expression in classical
Young's inequality. We survey some properties of Lebesgue-Stieltjes interals
and present a new simple proof for change of variables. Further, we formulate a
version of Young's inequality with respect to arbitrary positive finite measure
on real line including a purely discrete case, and discuss an application
related to medians of probability distributions and a summation formula that
involves values of a function and its inverse at integers.
