We consider batch reinforcement learning problems in continuous space,expected total discounted-reward Markovian Decision Problems when the training data is composed of the trajectory of some fixed behaviour policy. The algorithm studied is policy iteration where in successive iterations the action-value functions of the intermediate policies are obtained by means of approximate value iteration. PAC-style polynomial bounds are derived on the number of samples needed to guarantee near-optimal performance. The bounds depend on the mixing rate of the trajectory, the smoothness properties of the underlying Markovian Decision Problem, the approximation power and capacity of the function set used. One of the main novelties of the paper is that new smoothness constraints are introduced thereby significantly extending the scope of previous results.