Examining the conditions of positively or negatively associated
sequences of random variables obeying the strong law of large numbers provided by
Alexander, the sequences of Gaussian random variables, nonnegative and uniformly bounded
sequences of random variables with general dependent structure were studied, and the
sufficient conditions for they obeying the strong law of large numbers were given. At
last, an example for Gaussian sequence satisfying the strong law of large numbers was
given.