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 and identically distributed (i.i.d.) random variables and denote ,.In this paper, miracle academy clothing we investigate the almost sure central limit theorem in the joint version for the maxima and sums.

If for some numerical sequences , we socialstudiesscholar.com have for a nondegenerate distribution , and is a bounded Lipschitz 1 function, then almost surely, where stands for the standard normal distribution function, ,and ,.