  The glass transition temperature $T_g$ and the temperature $T_{\alpha}$
corresponding to the peak in the dielectric loss due to the $\alpha$-process
have been simultaneously determined as functions of film thickness $d$ through
dielectric measurements for thin films of polystyrene. A decrease of $T_g$ was
observed with decreasing film thickness, while $T_{\alpha}$ was found to remain
almost constant for $d > d_c$ and decrease drastically for $d < d_c$. Here,
$d_c$ is a critical thickness dependent on molecular weight. The thickness
dependence of $T_g$ is related to the distribution of relaxation times of the
$\alpha$-process, not to the relaxation time itself.
