A Note on Almost Sure Central Limit Theorem in the Joint Version for the Maxima and Sums

A Note on Almost Sure Central Limit Theorem in the Joint Version for the Maxima and Sums

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Let be a mug washer sequence of independent and identically distributed (i.i.d.

) random variables and denote ,.In this paper, we investigate the almost sure central limit theorem in the joint version for the maxima and sums.If for some numerical sequences , we have for a nondegenerate distribution , and is equi jec 7 a bounded Lipschitz 1 function, then almost surely, where stands for the standard normal distribution function, ,and ,.