Exact conditions for countable inclusion-exclusion identity and extensions
arXiv:math/0602035
Abstract
We give simple necessary and sufficient conditions for the inclusion-exclusion identity to hold for an infinite countable number of sets. In terms of a random variable, whose range are nonnegative integers, this condition is equivalent to the convergence to zero of binomial moments. Some standard extensions of the countable inclusion-exclusion identity are also given.
4 pages