Exact Conditions for Countable Inclusion-Exclusion Identity and Extensions

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Shmuel Friedland
Elliot Krop
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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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