Necessary and Sufficient Conditions for Complete Convergence in the Law of Large Numbers
نویسندگان
چکیده
منابع مشابه
Necessary and Sufficient Conditions for the Uniform Law of Large Numbers in the Stationary Case
Necessary and sufficient conditions for the uniform law of large numbers for stationary ergodic sequences of random variables are given. Three different types of conditions are investigated and established. Firstly it is shown that eventually total boundedness in mean is necessary and sufficient. This fact enables one to deduce the equivalence among almost sure convergence, convergence in mean,...
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ژورنال
عنوان ژورنال: The Annals of Probability
سال: 1980
ISSN: 0091-1798
DOI: 10.1214/aop/1176994835