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A characterization of the strong law of large numbers for Bernoulli sequences

2020/08/01 by Luísa Borsato, Borsato, Luísa, Eduardo Horta +3
Decision Sciences · Economics, Econometrics and Finance · #60F15 #FOS: Mathematics #Financial Risk and Volatility Modeling #Probability (math.PR) #Probability and Risk Models #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2008.00318

openalex publication_date 2020/08/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The law of large numbers is one of the most fundamental results in Probability Theory. In the case of independent sequences, there are some known characterizations; for instance, in the independent and identically distributed setting it is known that the law of large numbers is equivalent to integrability. In the case of dependent sequences, there are no known general characterizations -- to the best of our knowledge. We provide such a characterization for identically distributed Bernoulli sequences in terms of a product disintegration.

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