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Statements

Subject Item: dbr:Hsu-Robbins-Erdos_theorem
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rdf:type: yago:Theorem106752293 yago:WikicatProbabilityTheorems yago:Proposition106750804 yago:Statement106722453 yago:Message106598915 yago:Abstraction100002137 yago:Communication100033020
rdfs:label: Hsu–Robbins–Erdős theorem
rdfs:comment: In the mathematical theory of probability, the Hsu–Robbins–Erdős theorem states that if is a sequence of i.i.d. random variables with zero mean and finite variance and then for every . The result was proved by Pao-Lu Hsu and Herbert Robbins in 1947. Since then, many authors extended this result in several directions.
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dbo:abstract: In the mathematical theory of probability, the Hsu–Robbins–Erdős theorem states that if is a sequence of i.i.d. random variables with zero mean and finite variance and then for every . The result was proved by Pao-Lu Hsu and Herbert Robbins in 1947. This is an interesting strengthening of the classical strong law of large numbers in the direction of the Borel–Cantelli lemma. The idea of such a result is probably due to Robbins, but the method of proof is vintage Hsu. Hsu and Robbins further conjectured in that the condition of finiteness of the variance of is also a necessary condition for to hold. Two years later, the famed mathematician Paul Erdős proved the conjecture. Since then, many authors extended this result in several directions.
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