Let be a sequence of independent and identically distributed (i.i.d.) random variables and fr5945 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 sherri hill dress 53129 have for a nondegenerate distribution , and is a bounded Lipschitz 1 function, then almost surely, where stands for the standard normal distribution function, ,and ,.