  We study the limiting behavior of the Dirichlet and Neumann eigenvalue
counting function of generalized second order differential operators
$\frac{d}{d \mu} \frac{d}{d x}$, where $\mu$ is a finite atomless Borel measure
on some compact interval $[a,b]$. Therefore, we firstly recall the results of
the spectral asymptotics for these operators received so far. Afterwards, we
make a proposition about the convergence behavior for so called random
$V$-variable Cantor measures.
