    \begin{align}
        \sqrt{N_1} \hspace{2mm} \big\{\hat{\mu}_1 - \mu_1 \big\}(s,\omega) \overset{d}\to G_1(s, \omega), \label{Eq:CLT_Group_Mean_1} \\
        \sqrt{N_2} \hspace{2mm} \big\{\hat{\mu}_2 - \mu_2 \big\}(s,\omega) \overset{d}\to G_2(s, \omega), \label{Eq:CLT_Group_Mean_2}
    \end{align}
