  It is a classical result that every subharmonic function, defined and
${\mathcal{L}}^p$-integrable for some $p$, $0<p<+\infty$, on the unit disk
$\mathbb{D}$ of the complex plane ${\mathbb{C}}$ is for almost all $\theta$ of
the form $o((1-| z|)^{-1/p})$, uniformly as $z\to e^{i\theta}$ in any Stolz
domain. Recently Pavlovi\'c gave a related integral inequality for absolute
values of harmonic functions, also defined on the unit disk in the complex
plane. We generalize Pavlovi\'c's result to so called quasi-nearly subharmonic
functions defined on rather general domains in ${\mathbb {R}}^n$, $n\geq 2$.
