A Generalization of a Theorem of Liao

Let X be a metrizable space and let .:. . X . X be a continuous flow on X. For any given {.t}.invariant Borel probability measure, this paper presents a {. t }.invariant Borel subset of X satisfying the requirements of the classical ergodic theorem for the continuous flow (X, {. t }). The set is more restrictive than the ones in the literature, but it might be more useful and convenient, particularly for non.uniformly hyperbolic systems and skew.product flows