  We study the projective logarithmic potential $\mathbb{G}_{\mu}$ of a
Probability measure $\mu$ on the complex projective space $\mathbb{P}^{n}$. We
prove that the Range of the operator $\mu\longrightarrow \mathbb{G}_{\mu}$ is
contained in the (local) domain of definition of the complex Monge-Amp\`ere
operator acting on the class of quasi-plurisubharmonic functions on
$\mathbb{P}^n$ with respect to the Fubini-Study metric. Moreover, when the
measure $\mu $ has no atom, we show that the complex Monge-Amp\`ere measure of
its Logarithmic potential is an absolutely continuous measure with respect to
the Fubini-Study volume form on $\mathbb{P}^{n}$
