First Baire class functions in the pluri-fine topology

Let $B_1(\mathrm{\Omega },\mathbb{R})$ be the first Baire class of real functions in the pluri-fine topology on an open set $\mathrm{\Omega }\subseteq {\mathbb{C}}^n$ and let $H_1^{\ast }(\mathrm{\Omega },\mathbb{R})$ be the first functional Lebesgue class of real functions in the same topology. We prove the equality $B_{1}(\Omega, \mathbb R)=H_{1}^{*}(\Omega, \mathbb R)$andshowthatforevery$f\in B_{1}(\Omega, \mathbb R)$thereisaseparatelycontinuousfunction$g: \Omega^{2} \to\mathbb R$inthepluri-finetopologyon$\Omega^2$suchthat$f$isthediagonalof$g.$