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Exact conditions for countable inclusion-exclusion identity and extensions

Shmuel Friedland·Elliot Krop
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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.

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Shmuel Friedland, Elliot Krop. 2006-02-02. Exact conditions for countable inclusion-exclusion identity and extensions. https://arxiv.org/abs/math/0602035

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