  The sub-linear expectation space is a nonlinear expectation space having
advantages of modelling the uncertainty of probability and distribution. In the
sub-linear expectation space, we use capacity and sub-linear expectation to
replace probability and expectation of classical probability theory. In this
paper, the method of selecting subsequence is used to prove Marcinkiewicz type
strong law of large numbers under sub-linear expectation space. This result is
a natural extension of the classical Marcinkiewicz's strong law of large
numbers to the case where the expectation is nonadditive. In addition, this
paper also gives a theorem about convergence of a random series.
