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Journal of Zhejiang University SCIENCE A 2006 Vol.7 No.6 P.1088-1091


A note on strong law of large numbers of random variables

Author(s):  LIN Zheng-yan, SHEN Xin-mei

Affiliation(s):  Department of Mathematics, Zhejiang University, Hangzhou 310027, China

Corresponding email(s):   zlin@zju.edu.cn, loveriver@zju.edu.cn

Key Words:  Strong law of large numbers (SLLN), Martingale difference sequence, A-summable sequence

LIN Zheng-yan, SHEN Xin-mei. A note on strong law of large numbers of random variables[J]. Journal of Zhejiang University Science A, 2006, 7(6): 1088-1091.

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DOI - 10.1631/jzus.2006.A1088

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 Lp 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.

Darkslateblue:Affiliate; Royal Blue:Author; Turquoise:Article


[1] Butković, D., Sarapa, N., 1981. On the summability of sequence of independent random variables. Glasnik Mat., 16:157-166.

[2] Chow, Y.S., Teicher, H., 1988. Probability Theory, 2nd Ed. Springer, New York, p.245-255.

[3] Chung, K.L., 1974. A Course in Probability Theory, 2nd Ed. Academic Press, New York, p.109-130.

[4] Jardas, C., Pečarić, J., Sarapa, N., 1998. A note on Chung’s strong law of large numbers. J. Math. Ana. Appl., 217(1):328-334.

[5] Petrov, V.V., 1975. Sums of Independent Random Variables. Springer, New York, p.263-268.

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