  In this paper, we establish an improved decay estimate for the Dirichlet
energy of Dir-stationary $Q$-valued functions. As a direct application of this
estimate, we derive a Liouville-type theorem for bounded Dir-stationary
$Q$-valued functions defined on $\mathbb{R}^m$. Additionally, in an attempt to
establish the continuity of Dir-stationary $Q$-valued functions, we confirm
that such functions exhibit the Lebesgue property at every point within their
domain. Finally, we observe that the improved decay estimate implicates that
Dir-stationary $Q$-valued functions reside within a generalized
Campanato-Morrey space.
