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Date: 20-2-2021
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Let be a sequence of events occurring with a certain probability distribution, and let be the event consisting of the occurrence of a finite number of events for , 2, .... Then the probability of an infinite number of the occurring is zero if
Equivalently, in the extreme case of for all , the probability that none of them occurs is 1 and, in particular, the probability of that a finite number occur is also 1.
REFERENCES:
Hazewinkel, M. (Managing Ed.). Encyclopaedia of Mathematics: An Updated and Annotated Translation of the Soviet "Mathematical Encyclopaedia." Dordrecht, Netherlands: Reidel, pp. 435-436, 1988.
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