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We consider open sets of maps in a manifold $M$ exhibiting non-uniformexpanding behaviour in some domain $S\subset M$. Assuming that there is aforward invariant region containing $S$ where each map has a unique SRBmeasure, we prove that under general uniformity conditions, the SRB measurevaries continuously in the $L^1$-norm with the map. As a main application weshow that the open class of maps introduced in [V] fits to this situation, thusproving that the SRB measures constructed in [A] vary continuously with themap.

Statistical stability for robust classes of maps with non-uniform expansion