  We study the invariant measure or the stationary density of a coupled
discrete dynamical system as a function of the coupling parameter \epsilon (0 <
\epsilon < 1/4). The dynamical system considered is chaotic and unsynchronized
for this range of parameter values. We find that the stationary density,
restricted on the synchronization manifold, is a fractal function. We find the
lower bound on the fractal dimension of the graph of this function and show
that it changes continuously with the coupling parameter
