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 sequence of independent Hoodies/Fleece 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 , Bump Mask and is a bounded Lipschitz 1 function, then almost surely, where stands for the standard normal distribution function, ,and ,.