  Let $\Omega\subset \mathbb{R}^N$, $N=1,2,3$, be an open bounded and connected
set with continuous piecewise $\mathrm{C}^{\infty}$ boundary. Here we deal with
almost periodic distributions of the form $u(t,x)=\sum_{n=0}^{+\infty} c_n
S_n(x) \mathrm{e}^{i \lambda_n t}$ where $(c_n)_{n\in \mathbb{N}}\subset
\mathbb{C}$ belong to the space of slowing growing sequences $s^\prime$, and
$(\lambda_n^2)_{n\in\mathbb{N}}\subset \mathbb{R}$ and
$(S_n)_{n\in\mathbb{N}}\subset \mathrm{H}_0^{1}(\Omega)$ are respectively the
eigenvalues and eigenvectors of the Laplacian. Given $\omega\subset\Omega$, we
prove that there exists $T_{max}(\Omega,\omega)>0$ depending only on $\Omega$
and $\omega$ such that if $T>T_{max}(\Omega,\omega)$ and $u|_{\omega\times
]-T,T[}=0$, then $u\equiv 0$. Using this result we prove a unique continuation
property for the wave equation.
