Marcinkiewicz's strong law of large numbers for non-additive expectation

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.