We present a simplified proof of the Antonov-Lebovitz theorem, asserting that any spherical barotropic star having a mass density decreasing monotonically outwards and vanishing at its surface is stable to all non-radial perturbations. We also develop a simple argument showing in a straightforward way a related but somewhat weaker result, according to which any such star is stable if and only if it is stable to radial perturbations. Extension of these results to a star with non-decreasing specific entropy distribution is also briefly discussed.