  We consider classes of dynamical systems admitting Markov induced maps. Under
general assumptions, which in particular guarantee the existence of SRB
measures, we prove that the entropy of the SRB measure varies continuously with
the dynamics. We apply our result to a vast class of non-uniformly expanding
maps of a compact manifold and prove the continuity of the entropy of the SRB
measure. In particular, we show that the SRB entropy of Viana maps varies
continuously with the map.
