We consider the non autonomous dynamical system {τn}, where τn is a continuous map X→X,
Nearby in the stack
and
X
is a compact metric space. We assume that
{τn}
converges uniformly to
τ.
The inheritance of chaotic properties as well as topological entropy by
τ
from the sequence
{τn}
has been studied in Can1, Can2, Li,Ste,Zhu. In You the generalization of SRB\ measures to non-autonomous systems has been considered. In this paper we study absolutely continuous invariant measures (acim) for non autonomous systems. After generalizing the Krylov-Bogoliubov Theorem KB and Straube's Theorem Str to the non autonomous setting, we prove that under certain conditions the limit map