SRB measures for partially hyperbolic systems with one-dimensional center subbundles

For a partially hyperbolic attractor with a center bundle splitting in a dominatedway into one-dimensional subbundles we show that for Lebesgue almost every point there is anempirical measure from $x$ with a SRB component. Moreover if the center exponents are nonzero, then $x$ lies in the basin of an ergodic hyperbolic SRB measure and there are only finitely many such measures. This gives another proof of the existence of SRB measures in this context, which was established firstly in [11] by using random perturbations. Moreover this generalizes results of [15,18] which deal with a single one-dimensional center subbundle.