Ergodic properties of smooth dynamical systems are considered. A point is called regular for an ergodic measure μ \mu if it is generic for μ \mu and the Lyapunov exponents at it coincide with those of μ \mu . We show that an ergodic measure with no zero Lyapunov exponent is absolutely continuous with respect to unstable foliation [ L ] [\text {L}] if and only if the set of all points which are regular for it has positive Lebesgue measure.