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

Let be a 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 Multiminerals maxima and Girls Bucket Hats sums.If for some numerical sequences , we have for a nondegenerate distribution , and is a bounded Lipschitz 1 function, then almost surely, where stands for the standard normal distribution function, ,and ,.

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