  In this paper, by establishing a link between a sequence of independent
random variables under the sub-linear expectation and a sequence of independent
random variables under a probability, we give the sufficient and necessary
conditions of the strong law of large numbers for independent and identically
distributed random variables under the sub-liner expectation, and the
sufficient and necessary conditions for the convergence of an infinite series
of independent random variables, without any assumption on the continuity of
the capacities. A purely probabilistic proof of a weak law of large numbers is
also given.
