  In this paper, we prove the equivalent conditions of complete moment
convergence of the maximum for partial weighted sums of independent,
identically distributed random variables under sublinear expectations space. As
applications, the Baum-Katz type results for the maximum for partial weighted
sums of independent, identically distributed random variables are established
under sublinear expectations space. The results obtained in the article are the
extensions of the equivalent conditions of complete moment convergence of the
maximum under classical linear expectation space.
