no. 1
An almost sure central limit theorem for independent random variables
Annales de l'I.H.P. Probabilités et statistiques, Tome 30 (1994) no. 1, pp. 1-11. 
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     pages = {1--11},
     publisher = {Gauthier-Villars},
     volume = {30},
     number = {1},
     year = {1994},
     mrnumber = {1262890},
     zbl = {0793.60023},
     language = {en},
     url = {http://archive.numdam.org/item/AIHPB_1994__30_1_1_0/}
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Rodzik, Beata; Rychlik, Zdzislaw. An almost sure central limit theorem for independent random variables. Annales de l'I.H.P. Probabilités et statistiques, Tome 30 (1994) no. 1, pp. 1-11. http://archive.numdam.org/item/AIHPB_1994__30_1_1_0/

M. Atlagh and M. Weber, An Almost Sure Central Limit Theorem Relative to Subsequences, C. R. Acad. Sci. Paris, T. 315, Series I, 1992, pp. 203-206. | MR | Zbl

P. Billingsley, Convergence of Probability Measures, Wiley, New York, 1968. | MR | Zbl

G.A. Brosamler, An Almost Everywhere Central Limit Theorem, Math. Proc. Cambridge Philos. Soc., Vol. 104, 1988, pp. 561-574. | MR | Zbl

Y. Chow and Teicher H., Probability Theory, Springer-Verlag, New York, 1978. | MR | Zbl

D. Freedman, Brownian Motion and Diffusion, Holden-Day, 1971. | MR | Zbl

M.T. Lacey and W. Philipp, A Note on the Almost Sure Central Limit Theorem, Statist. Probab. Lett., Vol. 9, 1990, pp. 201-205. | MR | Zbl

P. Schatte, On Strong Versions of the Central Limit Theorem, Math. Nachr., Vol. 137, 1988, pp. 249-256. | MR | Zbl

V. Strassen, Almost Sure Behaviour of Sums of Independent Random Variables and Martingales, Proc. Fifth. Berkeley Symp. Math. Statist. Prob. 2, 1967, pp. 315-343, Univ. of California Press. | MR | Zbl