Consider the generalized Anderson Model
$H^\omega=\Delta+\sum_{n\in\mathcal{N}}\omega_n P_n$, where $\mathcal{N}$ is a countable set, $\{\omega_n\}_{n\in\mathcal{N}}$ are iid randomvariables and $P_n$ are rank $N<\infty$ projections. For these models one can prove theorems analogous to that of Jak\v{s}i\'{c}-Last on the
equivalence of measures.

We show that if the projection $Q_m^\omega P_n$ (where $Q^\omega_m$ is
cannonical projection on the subspace generated by $H^\omega$ and range of
$P_m$) has same rank as $P_n$, then the trace measure
$\sigma_i(\cdot)=tr(P_iE_{H^\omega}(\cdot)P_i)$ and absolute continuous
part of the measure $P_iE_{H^\omega}(\cdot)P_i$ are equivalent for $i=n,m$.