Abstract: In this paper, we generalize the concept
of sub-Gaussian random variable to that of "locally" sub-Gaussian
random variable. Some properties of locally sub-Gaussian random
variables are presented. It is shown that a "local" version of the
moment inequality used by Taylor and Hu in 1987 can be used to give an
equally simple proof of the strong law of large numbers for locally
sub-Gaussian random variables.