Extensions of Some Univariate Bonferroni-Type Inequalities to Multivariate Setting

Several problems of probability theory lead to the need of estimating the distribution of the number m n = m n (A) of occurrences in a sequence A 1,A 2,…,A n of events. When the estimation of this distribution is in terms of linear combinations of the binomial moments of m n(A), we speak of Bonferroni-type inequalities. That is, let (1.1).