In the framework of a strictly local regular Dirichlet space ${\bf X}$ we introduce the subspaces $PW_{\omega},\>\>\omega>0,$ of Paley-Wiener functions of bandwidth $\omega$. It is shown that every function in
$PW_{\omega},\>\>\omega>0,$ is uniquely determined by its average values over a family of balls $B(x_{j}, \rho),\>x_{j}\in {\bf X},$ which form an admissible cover of ${\bf X}$ and whose radii are comparable to $\omega^{-1/2}$. The entire development heavily depends on some Poincar\'e-type inequalities.