  The goal of this short note is to relate the integrability property of the
exponential $e^{-2\phi}$ of a plurisubharmonic function $\phi$ with isolated or
compactly supported singularities, to a priori bounds for the Monge-Amp\`ere
mass of $(dd^c\phi)^n$. The inequality is valid locally or globally on an
arbitrary open subset $\Omega$ in $\bC^n$. We show that
$\int_\Omega(dd\phi)^n<n^n$ implies $\int_Ke^{-2\phi}<+\infty$ for every
compact subset $K$ in $\Omega$, while functions of the form
$\phi(z)=n\log|z-z_0|$, $z_0\in\Omega$, appear as limit cases. The result is
derived from an inequality of pure local algebra, which turns out a posteriori
to be equivalent to it, proved by A.Corti in dimension $n=2$, and later
extended by L.Ein, T.De Fernex and M.Musta\c{t}\v{a} to arbitrary dimensions.
