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Let X, X1, X2,... be a sequence of independent and identically distributed random variables in the domain of attraction of a normal distribution. A universal result in almost sure limit theorem for the self-normalized partial sums Sn/Vnis established, where Sn=∑i=1nXi,Vn2=∑i=1nXi2.Mathematical Scientific Classification: 60F15.

A note on the almost sure limit theorem for self-normalized partial sums of random variables in the domain of attraction of the normal law