By applying the Skorohod martingale embedding method, a strong approximation theorem for partial sums of asymptotically negatively
dependent (AND) Gaussian sequences, under polynomial decay rates, is established. As applications, the law of the iterated
logarithm, the Chung-type law of the iterated logarithm and the almost sure central limit theorem for AND Gaussian sequences
LetSn be the partial sums of ?-mixing stationary random variables and letf(x) be a real function. In this note we give sufficient conditions under which the logarithmic average off(Sn/sn) converges almost surely to ?-88f(x)dF(x). We also obtain strong approximation forH(n)=?k=1nk-1f(Sk/sk)=logn ?-88f(x)dF(x) which will imply the asymptotic normality ofH(n)/log1/2n. But for partial sums of i.i.d. random variables our results will be proved under weaker moment condition than assumed for ?-mixing random variables.