Copyright © 2010 Qing-pei Zang. This is an open access article distributed under the
Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Let be a sequence of independent and identically distributed (i.i.d.) random
variables, and is in the domain of the normal law and . In this paper, we obtain a general law of
complete moment convergence for self-normalized sums.