Probability bounds given by multitrees

Upper bounds are presented for the probability of the union of finite number of events. The bounds are based on few terms of probabilities of intersections of at most m + 1 events. The bounds are computed by means of special hypergraphs called m-multitrees. The main theorem is a generalization of the results of D. Hunter, K.J. Worsley and a former result of A. Prékopa and the author. The efficiency of the new bounds are shown by tests for estimation of the values of multivariate normal distribution functions.