  In an optimal control framework, we consider the value $V_T(x)$ of the
problem starting from state $x$ with finite horizon $T$, as well as the value
$V_\lambda(x)$ of the $\lambda$-discounted problem starting from $x$. We prove
that uniform convergence (on the set of states) of the values $V_T(\cdot)$ as
$T$ tends to infinity is equivalent to uniform convergence of the values
$V_\lambda(\cdot)$ as $\lambda$ tends to 0, and that the limits are identical.
An example is also provided to show that the result does not hold for pointwise
convergence. This work is an extension, using similar techniques, of a related
result in a discrete-time framework \cite{LehSys}.
