Abstract
In this paper, the Chung’s strong law of large numbers is generalized to the random variables which do not need the condition of independence, while the sequence of Borel functions verifies some conditions weaker than that in Chung’s theorem. Some convergence theorems for martingale difference sequence such as L p martingale difference sequence are the particular cases of results achieved in this paper. Finally, the convergence theorem for A-summability of sequence of random variables is proved, where A is a suitable real infinite matrix.
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Project supported by the National Natural Science Foundation of China (No. 10571159) and the Specialized Research Fund for the Doctoral Program of Higher Education (No. 2002335090), China
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Lin, Zy., Shen, Xm. A note on strong law of large numbers of random variables. J. Zhejiang Univ. - Sci. A 7, 1088–1091 (2006). https://doi.org/10.1631/jzus.2006.A1088
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DOI: https://doi.org/10.1631/jzus.2006.A1088