When we consider maximum likelihood estimators for the drift coefficient 
of the Ornstein-Uhlenbeck process from both the continuous observations 
and the discrete ones, their asymptotic variances are 
related to each of Fisher informations. However, 
it is important to see that discrete observations are more applicable 
than continuous observations from the practical points of view. 
After delicate calculations, we show that the Fisher information 
from discrete observations is, of course, 
less than the one from continuous observations but almost equal to it, 
if the discretizing time-interval is sufficiently small.