  Let $B_{1}(\Omega, \mathbb R)$ be the first Baire class of real functions in
the pluri-fine topology on an open set $\Omega \subseteq \mathbb C^{n}$ and let
$H_{1}^{*}(\Omega, \mathbb R)$ be the first functional Lebesgue class of real
functions in the same topology. We prove the equality $B_{1}(\Omega, \mathbb
R)=H_{1}^{*}(\Omega, \mathbb R)$ and show that for every $f\in B_{1}(\Omega,
\mathbb R)$ there is a separately continuous function $g: \Omega^{2} \to\mathbb
R$ in the pluri-fine topology on $\Omega^2$ such that $f$ is the diagonal of
$g.$
