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Let (Xn, n&#x2265;1) be a standardized nonstationary Gaussian sequence. Let Mn= max{Xk,1&#x2264;k&#x2264;n} denote the partial maximum and Sn=&#x2211;k&#x2212;1nXk for the partial sum with &#x03C3;n= (Var Sn)1/2. In this paper, the almost sure convergence of (Mn, Sn/&#x03C3;n) is derived under some mild conditions

Almost Sure Convergence for the Maximum and the Sum of Nonstationary Guassian Sequences